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Implementaon of an autonomous taxi service in a
mul-modal trac simulaon using MATSim
Master thesis in Complex Adapve Systems
Sebasan Hörl
Göteborg, 2016
Department of Energy and Environment
Implementaon of an autonomous taxi service in a
mul-modal trac scenario using MATSim
SEBASTIAN HÖRL
Claes Andersson, Associate Professor (Docent)
Chalmers, Examiner
Dr. Alexander Erath
ETHZ, Supervisor
Pieter J. Fourie
ETHZ, Supervisor
Department of Energy and Environment
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden 2016
Implementaon of an autonomous taxi service in a mul-modal trac scenario using
MATSim
SEBASTIAN HÖRL
© SEBASTIAN HÖRL, 2016
Report No. 2016:05
Department of Energy and Environment
Chalmers University of Technology
SE-41296 Göteborg
Sweden
Telephone +42 (0)31-772 1000
Cover:
Snapshot of a trac simulaon using MATSim. Graphic created using SENOZON VIA.
Abstract
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Keywords
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Contents
1 Introduction 1
2 Simulation Framework 5
2.1 Agent-based transport simulation ....................... 5
2.2 Utility-based scoring .............................. 7
2.3 Evolutionary replanning ............................ 8
2.4 Queue-based simulation ............................ 10
3 The Sioux Falls Scenario 15
3.1 Network generation and adjustment ...................... 17
3.2 Public Transport Adaptation .......................... 19
3.3 Scenario Calibration .............................. 21
4 Dynamic Agents in MATSim 27
4.1 DVRP Extension ................................ 27
4.2 The AgentLock framework ........................... 30
4.3 AgentFSM .................................... 32
4.4 Comparison ................................... 32
5 Autonomous Taxi Fleet Model 35
5.1 Agent behavior ................................. 35
5.2 Distribution Algorithm ............................. 36
5.3 Dispatcher Algorithm .............................. 38
5.4 Routing Algorithm ............................... 42
5.4.1 Online Speed Calculation ....................... 44
5.4.2 Stochastic Variation Model ....................... 45
5.4.3 Performance Measures ......................... 46
5.4.4 Static Trip Replacement ........................ 51
i
6 Simulation Results 53
6.1 Baseline Scenario ................................ 53
6.1.1 Trip Statistics .............................. 54
6.1.2 Mode Choice .............................. 56
6.1.3 AV Operation and decreased supply .................. 57
6.2 Supply Analysis ................................. 61
6.3 Cost Dependencies ............................... 62
6.4 Economic Analysis ............................... 67
7 Conclusion 71
8 Outlook 72
8.1 Infrastructure Extensions ............................ 73
8.2 Usage and interaction with the AV service .................. 74
9 References 77
ii
1 Introduction
Autonomous vehicles are expected to have a great impact on how the traffic situation
in our cities will look like in the not so far future. During the last years, autonomous
vehicle technology took great leaps forward, examples being Google’s self-driving cars
(Google,2016) or Tesla’s latest software updates on autonomous parking functionality
(Tesla,2016). Furthermore, renowned car manufacturers such as Audi recently joined the
competition. Ambitious tests in real-world conditions are fostered all over the world, ex-
amples being Volvo’s DriveMe project with 100 autonomously driving cars on the highways
of Gothenburg (City of Gothenburg,2016), the LUTZ pathfinder project, establishing the
use of three autonomous transport pods in the city center of Milton Keynes (Transport
Systems Catapult,2016) and a case study of autonomous taxis in Singapore (LTA,2015).
Especially big cities like Singapore could gain a lot from autonomous car technology, be
it from privately owned cars to publicly owned services. A floating fleet of autonomous
vehicles (AVs) could have a drastic impact on land usage, reducing the area of parking
space needed in the urban environment. At the same time, it has the potential improve
road safety, access to transportation, congestion, and emissions (Tan and Tham,2014). In
fact, it is predicted that an AV fleet size of one-third the size of the number of private cars
could serve the associated demand that is generated today (Spieser et al.,2014). From
a user perspective, shared autonomous taxis could solve the classic “last mile problem”
where AVs could bridge the transport gap from the closest public transport facility to the
homes of the people (Litman,2015). As soon as a particular supply of AVs is reached,
prices are predicted to become highly competitive to if not even cheaper than private car
ownership (Chen and Kockelman,2016).
On the other side, with the adaptation of autonomous transport, fundamental moral
problems (Hevelke and Nida-Rümelin,2015) need to be discussed, and related questions in
liability and ownership need to be answered (Anderson et al.,2016). In general, predicting
how and when autonomous vehicles will be on the roads is a highly complex problem, and
most of the proclaimed benefits can easily be defeated due to a lack of reliable data.
To give an example, one of these benefits is having less congestion (International Transport
Forum,2014). However, it is claimed that to make a passenger comfortable in a self-
driving car, significantly smaller accelerations and decelerations are allowed, and thus the
overall movements on the roads will be slowed down (Le Vine et al.,2015). Therefore,
having only assumptions on how people would experience shared AV services, replacing a
1
huge percentage of contemporary cars with autonomous ones could in fact increase overall
congestion.
Another example is the overall travel demand, which might increase with the introduction
of autonomous vehicles as a consequence of people seeing it as more convenient and cost-
efficient to other modes. This, in turn, could lead to the aversive effect of increased
congestion (Litman,2015).
In consequence, while the technological development in autonomous driving already came
a long way, there is still much demand for research on an upper level, looking at the
overall economic and societal picture (Silberg et al.,2013;Schoettle and Sivak,2014).
A valuable tool for doing this is the use of traffic simulation (Fagnant and Kockelman,
2014;International Transport Forum,2014;Zachariah,2013). Numerous efforts have been
made in predicting the usefulness of AVs for a city regarding AV supply, i.e. answering
the question how many shared AVs would be needed to serve an existing demand fraction
(Boesch et al.,2016;Fagnant et al.,2015). On the contrary, fewer results are available on
how the new travel mode would interact with existing travel options and how customer
preferences influence the mode choice.
The agent- and activity-based traffic simulation framework MATSim (Horni et al.,2015)
allows for such research (Boesch and Ciari,2015) by taking into account assumed customer
preferences and letting people interact with a newly added means of transportation. The
framework has been successfully used in a range of studies from autonomous taxi services
in Berlin and Barcelona (Bischoff and Maciejewski,2016) up to the simulation of the
whole transport network of Singapore (Erath et al.,2012). While the framework allows
for a quite precise prediction of traffic flows for scenarios involving car traffic and public
transport, it yet does not allow the simulation of dynamically acting autonomous vehicles
embedded in the overall traffic situation.
Therefore, the purpose of this thesis will be to implement means of simulating autonomous
taxis within the MATSim framework. Subsequently, measurements on how people would
switch to the new transport mode given certain supply levels, acceptance levels, and
pricing schemes will be made. A major challenge will be to account for an acceptable
simulation speed while keeping the dynamic detail, which is needed in order to simulate
intelligently acting AV taxi fleets. At the same time the functionality should be kept as
versatile and extendable as possible in order to make it possible to gain research results
on a multitude of factors, which influence the adaptation of autonomous vehicles. Based
on these criteria, a new framework for simulating dynamic agents has been developed
(section 4).
2
In the scope of this thesis, a basic model of autonomous vehicles, which are transporting
one passenger, is developed. Many interesting aspects such as shared AVs, AVs for the
purpose of feeding public transport facilities or simulating a refuel/recharging infrastruc-
ture can be subject of future research. Since the model relies on how likely people are
to use autonomous technology, the model at the moment will be mainly pointed towards
finding qualitative results on the interplay between factors that define the traffic situa-
tion. However, customer preferences, actual experiences of AV technology and pricing
information will become available over the next years.
Given those data sets, the simulation developed in the thesis has the potential to act as
a valuable tool in transport planning and urban development. It will be useful in plan-
ning for the implementation of the needed infrastructure, the development of pinpointed
transport solutions and a restructuring of the present traffic network to account for the
adaptation of autonomous vehicles.
The thesis at hand is structured in four main parts: Section 2will introduce how traffic
simulation is performed in the MATSim framework and highlight the aspects that are
important to know for the implementation of autonomous vehicles. Section 3, as another
prerequisite for setting up a meaningful simulation, covers the adaptation of the readily
available MATSim scenario of the city of Sioux Falls. In sections 4and 5, the technical
implementation of the AV simulation will be explained in detail on two abstraction layers,
first introducing a new framework for simulating dynamically acting agents in MATSim
and then creating a model of autonomous taxis based on that. Then, in section 6the
model will be tested with a variety of parameter configurations, giving insights on the
general working of the model and predictions of AV usage in the artificial Sioux Falls
test scenario. Finally, section 7provides an overview about the qualitative results, while
section 8will give an outlook on a multitude of possible extensions of the model and
further research questions that can be answered using the model at hand.
3
4
2 Simulation Framework
The investigations of autonomous vehicles in this thesis will be based on the agent-based
transport simulation MATSim (Horni et al.,2015). The following sections will outline how
the framework works and where it can be extended to shape it towards an autonomous
taxi simulation. An overview will be given on which components need to be modified and
how the final transport situation will result from all the different parts that make up the
simulation.
2.1 Agent-based transport simulation
The approach that is used in MATSim is to simulate a virtual population of a city on a
per-agent timestep-based level. At the beginning of a simulation run, each person in the
synthetic population has an initial plan of what it is supposed to do during the simulated
day. Those plans consist of two elements:
Activities have a start and an end time, as well as, depending on the respective sce-
nario, certain constraints on when the earliest start or latest end time could be, i.e.
how much the current values could be altered to still give a realistic time frame.
Furthermore, minimum durations can be defined for which an agent has to stay at a
certain activity location. Those locations are given as facilities, which have specific
coordinates on the scenario map. Usual activities are “home” (which usually is the
first plan element of a day) and “work”. More elaborate simulations can additionally
use an arbitrary number of secondary activities.
Legs are the second type of plan elements. These describe connections between two
activity locations and contain information like which mode of transport the agent
will use (e.g. “car”, “public transport”, or “walk”) and, depending on the selected
mode, further data like the route that should be taken through the street network.
A typical day plan of a MATSim agent can be seen in figure 1. The agent starts at home,
then walks to his job, stays there for a certain time and then goes back home. Each agent
in a popuation (which can range from several hundred to hundeds of thousands) has its
individual plan that is executed when one day is simulated.
The network, on which the simulation is taking place, is described through nodes and
connecting links. These are defined by a specific flow capacity which tells the simulation
5
Figure 1: A typical agent plan in MATSim
how many vehicles are able to pass the link within a certain time frame while the length
and an average link speed determine how fast vehicles will travel to the next node.
The whole MATSim simulation is performed time-step by time-step. In a single simulation
step (usually 1 second) the agents that are currently in an activity do not need to be taken
into account unless their scheduled activity end is reached. The other agents, which are
currently on a leg, are simulated in a dedicated traffic network simulation. This simulation
moves the agents according to the capacity and current congestion from the start node
to the end node of the respective links. Traffic is not simulated on a micro-level (i.e. the
vehicles do not have distinct positions along the link) to increase the simulation speed.
Consequently, congestion on the traffic network is emerging from the travel plans of all
the agents. If there are too many agents who try to use one route at the same time, the
overall congestion will increase.
The actual routes that are being taken by the agents are generated based on the gen-
eralized least cost path through the network for a certain leg, with a certain amount
stochasticity added into the pathfinding process in order to avoid artificially created bot-
tlenecks. This approach allows the optimization of the plans to be separated from the
actual simulation of the plans, but is not suitable for the simulation of an AV taxi ser-
vice, where routes through the network must be generated dynamically, based on the
current demand. Therefore, to simulate dynamic agents for AVs, which are not statically
residing in a fixed-timed activity or a predefined leg route, significant changes need to be
made, and some of the computational advantages of the simulation approach need to be
partly circumvented. This, however, mainly addresses implementational details and will
be discussed later in the thesis in section 4.
All steps described above, i.e. the simulation of activities and legs during a whole sim-
ulation day, are summarized as the “Mobility Simulation” or, in short, Mobsim of the
MATSim framework.
6
2.2 Utility-based scoring
As pointed out in the previous section, individual travel decisions might lead to waiting
times on the network, which then can also lead to late arrivals at the designated activity
locations, which usually would be disadvantageous in the real world. Therefore, it might
be beneficial for an agent to reconsider the time and route choices that had been made
for the current day, just as a real person would do.
In order to “know” whether a plan worked out well or was disadvantageous, the single
elements need to be weighed and quantified. This is done using the Charypar-Nagel
scoring function (Horni et al.,2015, pp. 27):
Splan =
N−1
X
q=0
Sact,q +
N−1
X
q=0
Strav,mode(q)(1)
It combines the marginal utilities of all activities (Sact,q) ranging over the Nactivities in
a plan and the marginal utilities for all the legs in between.
The marginal utility for the activities, among other factors, depends on how long the
activity has been performed, whether the agent needed to wait to start it (due to an early
arrival) or whether it was forced to leave early. For more details the complete computation
is shown in Horni et al. (2015).
For the scope of this thesis the travel utility is more interesting. A basic version for a
single leg qcan look as follows:
Strav,mode(q)=Cmode(q)+βtrav,mode(q)·ttrav,q +γd,mode(q)·βm·dtrav,q (2)
Mode Choice The first term, Cmode(q), describes a constant (dis)utility for the choosing
a certain mode for the leg. It can be interpreted as how “favorable” going on a trip
in the specific mode is and is negative. An classic use of the parameter is to model
constant costs per trip in a mode.
Travel Time The parameter βtrav,mode(q)is the marginal utility of traveling, which is
multiplied by the time spent on the leg ttrav,q. It signifies how favorable it is to spend
time on such a leg, i.e. the longer one needs to stay in a car or public transport, the
larger the disutility gets (and therefore the parameter is usually negative). Values
which are smaller, therefore, stand for travel modes where time is spent less useful
or comfortably. The unit is “utility per time”.
7
Travel Cost The third element involves the (positive) marginal utility of money βm,
which is a universal simulation parameter and describes how the utility of money
can be weighed against e.g. time., the unit being “utility per monetary unit”, e.g.
EUR. It is multiplied by the (negative) monetary distance rate γd,mode(q), which
states, to how much disutility per spanned distance the leg will lead. For the given
example it would be stated as “EUR per meter”. The parameter is useful for imposing
distance-based fares in a transport mode and thus making it monetarily attractive
or unattractive compared to other ways of traveling.
Beyond these parameters, which are usually used for all travel modes, there are a number
of additions, e.g. for public transport, or yet unused options, such as a direct marginal
utility of distance traveled.
For the purpose of simulation autonomous taxi services, one addition is made:
Sav =C+βtrav,av ·ttrav +γd,av ·βm·dtr av +βwait,av ·twait (3)
Here, βwait is the marginal utility of waiting time, quantifying how disadvantageous it is
to wait for an AV to arrive.
The utility computations presented here are used in the “scoring phase”, which is taking
place in MATSim after one simulation day1has been performed. Then all experienced
legs and activities are scored, and each agent is assigned a final score, depending on which
further replanning is done, as described in the next part.
2.3 Evolutionary replanning
The last step is to make all the agents replan their day in order to “learn” more optimal
plans which ensure that they arrive on time at the activity locations and avoid congestion.
This is done using an evolutionary algorithm that works as follows:
Usually, an agent will start out with one quite random plan, go through it during one
whole day and then get a score for it. Afterward, if the agent is selected in a random draw,
it’s plan is copied and modified slightly. Those modifications can happen with respect to
start and end times of activities, mode choices for certain legs, etc. So after one iteration
the agent might already have two plans to select.
1A simulated day in MATSim can be defined to be longer than 24 hours to ensure that all agents
departing late at night are given enough time to arrive at their destinations, and thus not be penalized
for having infinite travel time.
8
Before the next day starts, one of the available plans is selected according to a certain
strategy. The standard approach is to do a multinomial selection with respect to the
previously obtained plan scores. So one after another plans, will be created, scored,
modified, rescored and so on. Because of the selection process, which favors high scores,
better and better choices will be made.
However, this is done for each and every agent, so while improving the performance of
one agent’s plans, this might effect the performance of other agents negatively, which
is especially true if one thinks about the example of highly congested roads due to too
many agents choosing the same route. Finally, though, the algorithm reaches a quasi-
equilibrium, which in MATSim is usually referred to as the “relaxed state”, in which the
average score of the used plans stabilizes within a reasonable variance.
Each “day” that is simulated in this manner is usually called an “iteration” of the sim-
ulation. It is common to divide these iterations into two parts. The first one is the
“innovation phase”, where plans have a certain probability to be modified while innova-
tion is turned off in the second phase. This means that the agent will only choose among
the present plans in his repertoire (usually around 5) and rescore them again and again,
until the most favorable is selected.
All of the above is known as the “replanning” in MATSim. Putting everything together,
a whole cycle in a MATSim simulation can be seen in figure 2. Since the final traffic
situation evolves from the evolutionary choice in the replanning and selection, as well as
from the emergent congestion in the Mobsim, this whole cycle is usually referred to as a
“co-evolutionary” algorithm.
Figure 3shows a typical progression of the population-wide score in a MATSim simula-
tion. What one can see there is an average of the worst and best plans of each agent.
Additionally the mean of the per-agent average scores in their list of plans is displayed.
Finally, one can see the average of all the plans that have been executed by the agents in
a particular iteration.
The first phase until iteration 100 is the innovation phase, where time and mode choices
can be made, following which it is turned off at iteration 100. At this point, all agents
select from their existing stock of plans, stochastically favoring higher scores. What was
a high-scoring plan during the innovation phase might now perform substantially worse,
while another plan in each agent’s choice set might produce better scores under these newly
imposed conditions. This change is reflected in the lowering of the average maximum plan
9
Figure 2: The basic co-evolutionary algorithm of MATSim, showing the three main stages:
Mobsim, Scoring and Replanning/Selection
score and increase of average executed score after 100 iterations in figure 3. Finally, a
quite stable population-wide relaxed state is reached.
2.4 Queue-based simulation
The heart of the simulation in MATSim is the queue simulation (QSim), which is a specific
implementation of the beforementioned Mobsim. This part of the framework is iterating
through all the agents that need to take action in the current simulation step.
Itself, the QSim is split into the handling of agents which are currently performing an
activity (i.e. are in an idle state in terms of the traffic simulation) and another part, the
Netsim, which is simulating the traffic network.
When running the Netsim, the agents are moved on the network according to their current
route and dependent on congestion. After moving an agent, the Netsim checks whether
the agent should end its trip at the current link to which he has been moved. If this is
the case, the agent is removed from the Netsim and the next agent state is computed.
The result of this computation is either that the agent wants to start a leg, in which case
he is reinserted into the Netsim, or that he wants to start an activity, which will add the
agent to the activity queue.
This activity queue is the other main component of the QSim. In fact, it is a priority
queue, where all agents are sorted according to the time at which they want to end the
next activity. So when adding an agent to the activity queue, it first checks when the
activity should be ended and then the agent is inserted at the corresponding position in
the queue.
The processing of this queue in the QSim for each simulation step then works as follows:
The first element of the queue is checked, whether the agent should already end the
activity. If this is not the case, the simulation step is already finished. On the other hand,
if the activity should be ended now (or previously if the time resolution of the simulation
is quite high), the agent is removed from the top of the queue and the next state is
10
0 20 40 60 80 100 120 140
Iteration
−2
0
2
4
6
8
10
Average Score
Executed
Worst
Average
Best
Figure 3: Typical progression of the agent scores throughout a MATSim simulation.
“Worst” means that the plans with the worst scores from all the agents are taken and
averaged, the same applies for the other graphs.
11
computed as described above. Then the new top element of the queue is examined. The
whole QSim simulation is schematically rendered in figure 4.
The big advantage of this simulation architecture is as follows: When an agent is in an
activity, no computation needs to be performed. So instead of polling all the agents in
every simulation step to check if they want to end an activity, the computational demand
is much lower when using the queue, since many agents can be skipped. The sequential
processing of the priority queue is very fast in terms of computational complexity (O(1)
for checking the top element and O(log n)for fetching it) (Java API,2016).
Furthermore, the same concept is used within the Netsim to speed up the computation of
the traffic situation. In both cases, for the QSim and Netsim, those savings in computation
time naturally decrease the versatility of the simulation environment.
One major drawback is that if an agent, which is already queued, should abort its current
activity, it needs to be removed from the queue and added at a new position. Both
operations are quite costly for the priority queue (Java API,2016), so if more and more
reschedulings are needed, the computational overhead can become quite large.
However, for truly dynamic agents, like autonomous vehicles, it is necessary to adopt
their plans frequently and thus some thought needs to be put into how to achieve this
freedom while still keeping as many advantages from the existing simulation architecture.
Section 4will explain how this problem has been overcome in this thesis.
12
Figure 4: Simplified structure of the QSim in MATSim.
13
14
3 The Sioux Falls Scenario
The City of Sioux Falls in South Dakota (figure 5) has been a classic test case in transport
research for more than four decades, being first mentioned in this context in Morlok et al.
(1973). While none of the numerous implementations of the network are intended to
be accurate and realistic with respect to the actual City of Sioux Falls, they are merely
aiming towards providing downscaled, computationally tractable test cases for transport
planning and simulation problems.
In Chakirov and Fourie (2014), the scenario (“Sioux-14”, figure 6) has been adapted to the
MATSim framework. A sparse street network, which is computationally easy to handle
by the simulation, was introduced. It consists of 27 nodes and 76 links, representing the
main arterial roads of the city, split further down into 282 nodes and 334 links in order to
arrive at partial link sizes of less than 500m. This is necessary because MATSim agents
start their travels at the start node of a link and thus a high resolution is needed to avoid
unrealistic clustering.
On the supply side, there is furthermore a public transport network, which consists of 5
lines with bus stops along the arterial roads at intervals of 600m. The stops are placed
at a distance of 5mperpendicular to the road and departures from the lines’ respective
start links take place every 5 minutes.
Much of effort has been put into the modeling of the demand side, covering the realistic
generation of home locations, workplaces, secondary activity locations, as well as the
distribution of socio-economic factors such as age, car ownership and gender across a
synthetic population, as it is needed for the agent-based simulation.
In this regard, the scenario provides a lightweight example of a complete MATSim sim-
ulation, where it is easy to test different parameters and extensions to the framework
on a near-realistic baseline scenario. However, while working with the original Sioux-14
network during the course of this thesis, it became evident that the simplified structure
of the underlying traffic network does not provide enough resolution for the simulation of
autonomous vehicles.
The main reason is that agents, who choose to take a car in the Sioux-14 network, prob-
ably living in the middle of the rectangular regions of the network would be teleported
to the nearest link to start their travels. This would also be true for autonomous ve-
hicles, which is not a realistic assumption in both cases, especially when comparing it
with public transport, where agents in MATSim are explicitly penalized for covering the
distance between home and bus stop by foot. Furthermore, the effect of people being
15
Figure 5: Map of Sioux Falls. The bounding box encapsulates the processed region with
longitude from −96.8105◦to −96.6653◦and latitude from 43.4729◦to 43.6286◦.
16
1km 2km 3km 4km 5km 6km 7km
1km
2km
3km
4km
5km
6km
7km
8km
9km
10km
11km
Figure 6: Sioux-14 road and public transport network
more inclined to opt for an autonomous taxi when living far from public transport can
only be convincingly simulated on a finer network.
The following sections will describe how, starting from the initial Sioux-14 scenario, a
new more fine-grained versatile test scenario for MATSim has been developed, which in
turn has been used as the basis of the following investigations in this thesis.
The new Sioux-16 network, which has been developed in this thesis, is based on the
demand model of Sioux-14, which means that all locations for homes, workplaces and
secondary activities are kept equal, while it differs on the supply side, aiming to resemble
the original scenario as closely as possible. The following sections will describe, how
the Sioux Falls network from OpenStreetMap (with the state as of 18 Apr 2016) has
been converted and adjusted to be compatible with MATSim and closely match the prior
version of the test scenario. Furthermore, it will be explained, how the public transport
network has been adapted to the fine-grained Sioux-16 scenario.
3.1 Network generation and adjustment
For the creation of the new scenario, an area covering Sioux Falls has been captured from
OpenStreetMap, which can be seen in figure 5. Using the MATSim exporter in the JOSM
tool 2, a simplified, MATSim-compatible network of the selected region has been created.
2https://josm.openstreetmap.de/
17
2km 4km 6km 8km 10km 12km 14km
2km
4km
6km
8km
10km
12km
14km
16km
18km
Figure 7: Automatic network modifications: Red links have been removed while blue links
have been shrunk to the closest border points of a bounding box enclosing the facilities
of the scenario. Green lines have been removed either for being detached from the main
network being sinks/sources.
In this process, all primary, secondary and tertiary streets have been selected, while road
types further down the hierarchy (for instance residential streets) have been omitted.
However, some adjustment was needed for the network to play nicely with the given
facilities from the Sioux-14 scenario. Most importantly, the network from OSM was
defined in the EPSG:3857 coordinate system, while Sioux-14 uses EPSG:26914. Therefore,
in a first step, the coordinates of all the generated nodes needed to be converted to the
old system.
In a second step, the positions of all facilities in Sioux-14 have been obtained and a
bounding box with a margin of 500maround them has been computed. Subsequently,
all links, which were located out of the bounding box, were removed from the network,
while those who were crossing the borders have been cut to fit into the area. The initial
network with all removed (red) and cut (blue) roads can be seen in figure 7. In total 352
outside links have been removed, and 83 links have been adjusted.
After that, a cleanup up the network needed to be done, partly because of artifacts due
to the filtering of road types, partly because of the removal of the external sections. This
removal was done in a couple of steps:
18
1. The lengths of all the links have been updated to the L2distance of their respective
start and end nodes in the new coordinate system.
2. The network has been searched for sources (nodes that only have outgoing links)
and sinks (nodes that only have incoming links). Those have been removed, because
they make no practical sense. This procedure led to 53 removed links in total.
3. One seed node has been defined, which definitely belongs to to the street network and
then by traversing the all paths from that node, it was determined which streets
belong to the main network. All remaining nodes and links, which have become
detached from this main network have been removed (11 nodes and 14 links).
4. Finally, the network has been searched for duplicate links with the exact same start
and end node. Only the first of those links have been kept, which led to the removal
of 3 duplicates.
5. In Sioux-14, the links have been split such that there are no connections longer than
500m. This procedure has also been applied to the network at hand, leading to 389
split links, which have been cut into a number of equal parts with less than 500m
length depending on their overall length.
Regarding nodes, these procedures in total lead to an increase of nodes from 1392 to 1806
and in an increase of links from 2957 to 3335. The links that have been removed during
the cleanup are colored in green in figure 7.
3.2 Public Transport Adaptation
The adaptation of the public transport network to the new (“Sioux-16”) scenario posed
some challenges that needed to be solved:
•The links of the original network did not exist anymore, obviously the routes for
the different public transport needed to be mapped to the new network.
•The stops from the original network could not be mapped easily to the new roads,
partly because some streets in Sioux-14 were “invented”, only approximating con-
nections in the finer network on a very coarse level, but also because roads that
consisted of two overimposed links for both directions were now split up into two
spatially distinct lanes (as can be seen in the upper left part of figure 8).
19
In order to get a rough routing for the bus lines, the main nodes of the Sioux-14 network
have manually been mapped by hand to nodes in the Sioux-16 network. This made it
possible to obtain new public transport roads in terms of those guide points: For each of
the lines it has been defined, which guide points should be traversed and in which order.
Then, the Dijkstra algorithm (Dijkstra,1959) with travel time as the objective has been
used to find the shortest path from waypoint to waypoint. After fitting those partial
paths together, the whole routes in terms of the links of the Sioux-16 network have been
obtained. As can be seen in the colored routes in figure 8this made it easy to obtain
routes that take into account the specific map structure (for instance the highway on the
upper left or the one-way streets, which are traversed by the blue line in the center of the
map).
The generation of bus stop facilities was a more challenging problem. Given the location
from Sioux-14, one could roughly match the stops to links along the new routes, which
worked in principle. However, using this approach, bus stops were cluttered all along the
lines. With the intention of having a rather realistic network some conditions needed to
be taken into account:
•The bus stops of one line should be on opposite sides of a street and not have a
large longitudial distance. While satisfiying results could obtained, for instance in
the center with the blue line, the same approaches did not work well for the highway
connectors on the left for the green line, and vice versa.
•The bus stops of parallel lines should be at the same locations, i.e. in the center
where the green line uses the same roads as the red one, the same locations should
be chosen. This constraint usually interfered with the approaches that took into
account the first constraint (especially in the center for the blue line).
•Finally, some of the Sioux-14 locations where completely off the network in Sioux-16,
for instance for the red line, where one can see a bend in the diagonal connection,
which was modelled as a straight line in Sioux-14.
Given all those constraints the best approach seemed to put in manual work with some
automated help. The final approach made use of a small program, written to manually
choose the stop locations along all roads and then subsequently choose which stop loca-
tions should belong to which line. In this step one did not take into account the cases of
two lanes, as just the general positions needed to be known (e.g. for the blue line in the
center an approximate position between the two lines would be chosen).
20
In another step, the locations that had been assigned to each line have been assigned to
the respective links along the line. So for the blue line, the average points in between
would have been assigned to a link underneath for one direction, and another stop would
be created for the link above. This resulted in a final set of stop locations.
Furthermore, some stop locations were located on one single link. This can happen if
there is a link of roughly 500mand the stops are for instance located at 1mand 499m
along the link. In those cases, the network needed to be broken up at those positions. In
the current scenario, this leads to the splitting of only four links.
Finally, according to the setup of Sioux-14 the stop locations have been moved to a
position normal to the link direction, with a distance of 5m. Additionally a schedule with
buses departing in 5min intervals has been created.
The final public transport network can be seen in figure 8. It features 150 stops with an
average distance of 520mand a median of 566m. This is a result of not being able to
put the stops as accurately in intervals of 600mas it is possible in Sioux-14. Moreover,
the L2distance between two stops along the routes have been used instead of a measure
along the actual path. The minimum and maximum distance between stops are 218m
and 847m, respectively.
All steps that have been described above have been implemented in a reusable and
parametrized way. For instance, one could choose to allow a maximum link length of
5km and would still obtain a valid network at the end, probably just with a larger num-
ber of split links during the processing of the public transport.
3.3 Scenario Calibration
The Sioux-14 network features artificially chosen link capacities, which are based on a
minimum of two and a maximum of three lanes per link, where three have only be chosen
for a fraction of highway links (Chakirov and Fourie,2014). While the added minor streets
in Sioux-16 should not make too much of an impact on overall capacity, the highways
and main arterials of the real network usually feature greater capacity (for instance by
providing four lanes on the western highway).
Looking at figure 9, it can be seen that the travel time (of cars) in the new network is
lower (red), compared to Sioux-16 (black). This effect can partly be explained by the
increased capacity, but also by the multitude of new options to choose the most effective
route for a trip through the fine-grained network. In fact, the route choice might be the
21
1km 2km 3km 4km 5km 6km 7km 8km 9km
1km
2km
3km
4km
5km
6km
7km
8km
9km
10km
11km
12km
13km
14km
15km
Figure 8: Sioux-16 network with five public transport lines and respective stop facilities
22
major influence when comparing with the data from figure 10. There the decrease in
link speeds (relative to the freespeed) can be seen, which is quite similar, indicating a
comparable amount of congestion in the network.
Depending on how important the comparability to Sioux-14 in a specific scenario is and
what time of the day should be compared, it might be beneficial to adjust the flow capacity
of the network3: In terms of travel times a scaling of 50% would resemble the afternoon
peak way better than the 100% version, while the morning peak would best be recovered
by a value in between (figure 9). A similar situation arises for the link speeds in figure 10,
where a value of 50% is better suited for comparing the morning peak while the 100%
scaling creates more comparable results in the evening.
Furthermore, in terms of link speeds, it can be seen that the Sioux-16 scenario features
less congestion during the off-peak hours due to the possibility of distributing trips all
over the network.
In any case it has to be kept in mind that comparing the speed decreases is only a
rough measure of network congestion. Most importantly, the values displayed are average
values, which means that they biased towards outliers, i.e. capturing the changes in main
arterials. That is a good comparison to Sioux-14, but on the other hand, the average is
also taken over an increased number of links, of which some might rarely be used and
therefore dragging the average down.
A comparison of the scenarios in terms of average travel times, distances and more shares
can be found in table 1. What can be seen is that averaged over the whole day, values
stay roughly the same, with the biggest differences being present in car traffic. There,
especially the decrease in travel distance is noticeable but expected, since more direct
routes can be taken. For public transport, the result of Sioux-16 is similar to Sioux-14,
which is an indicator that the network is strongly resembling the former version.
Looking at the travel time and distance for the transit walk to and from public transport
facilities, one can see that changes are quite small, which allows the conclusion that the
fine-grained network does not incline agents to switch to the car mode on the new network.
This is verified by a comparison of the mode shares, which stay roughly constant for the
scenarios. A major difference can be seen in the mode shares of walking and public
transport legs, where roughly two to three percent of the agents in the network switch
from the walking mode to public transport.
3In MATSim, this can be easily done in the Mobsim configuration, e.g. qsim.flowCapacityFactor
for QSim
23
06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00
0
5
10
15
20
25
30
Average Car Trip Duration [min]
Sioux-14
50% Flow Capacity
100% Flow Capacity
Figure 9: Comparison of the average duration of car trips by day time in Sioux-14 and
Sioux-16 with 50% and 100% flow capacity.
The test simulations with the Sioux-14 network yielded an average computation time of
9.37son a test machine, while for Sioux-14 it is increased to 12.31s. Of course on other
machines, different computation times will be achieved, but one can state that with the
same simulation parametres (number of threads etc.), the increase in computation time
is around 30%.
24
06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00
0%
2%
4%
6%
8%
10%
12%
14%
Average decrease in link speed
Sioux-14
50% Flow Capacity
100% Flow Capacity
Figure 10: Comparison of the decrease of link speeds by day time in Sioux-14 and Sioux-16
with 50% and 100% flow capacity.
Table 1: Comparison of Sioux-14 and Sioux-16 in terms of travel measures. The respective
distances and travel times of the walking legs to and from public transport facilities are
included in the measures for public transport
Scenario Sioux-14 Sioux-16 Sioux-16 Sioux-16
Flow Capacity 50% 70% 100%
Travel Distances [km]
Car 5.30 3.79 3.74 3.70
Walking 1.31 1.29 1.27 1.26
Public Transport 3.73 3.82 3.86 3.89
(Transit Walk) 1.31 0.53 1.28 1.28
Travel Times [mm:ss]
Car 11:56 08:39 06:59 05:08
Walking 26:16 25:48 25:19 25:08
Public Transport 32:37 29:05 28:32 28:14
(Transit Walk) 24:05 21:50 21:55 21:59
Mode Shares
Car 63.57% 63.23% 64.84% 65.71%
Walking 9.29% 7.50% 6.80% 6.56%
Public Transport 27.14% 29.27% 28.36% 27.72%
25
26
4 Dynamic Agents in MATSim
The behavior of ordinary agents in MATSim can be described as static in the way that
they now before one day is simulated how their plans look like. The actual departure
times and routes through the network can be computed in advance and the only element
that brings variation are delays in the traffic network due to congestion.
Certain participants in the traffic network though need to be simulated in a dynamic
way, where it is not clear in advance when they should arrive at which locations and
where those are. Several approaches have been proposed to allow for dynamic behavior
in MATSim. The decision on which option is best depends mainly on what a level of
complexity in the behavior is needed.
A simple version of dynamic behavior is implemented in the public transport (PT) ex-
tension, where passenger agents are saved in a list as soon as they reach the link in the
network, where they should be picked up by a public transport agent. As soon as the PT
agent (e.g. a bus) arrives at that link, persons from the link are deregistered from the list
and “teleported” to the destination stop as soon as the vehicle arrives there. This setup
fits very well into the queue based structure of MATSim.
An even more dynamic approach is used in the DVRP (Dynamic Vehicle Routing Problem)
framework, which will be discussed in the first part of this section. At the time of this
thesis and for the specific use case of autonomous vehicles, some drawbacks will be shown
and finally a new abstraction layer for dynamically acting agents will be presented, which
has been part of the thesis work.
4.1 DVRP Extension
The DVRP extension (Maciejewski and Nagel,2012;Horni et al.,2015) is designed to
provide a level of abstraction to the simulation of dynamic transport services, such as
taxis. Its general structure is quite flexible so that it is easy to implement for instance
electric vehicles (Bischoff and Maciejewski,2014) (which need to recharge at some point
during the simulation) or taxis, which are roaming randomly through the city and serving
requests when they are made by passengers (Maciejewski and Bischoff,2015).
However, this flexibility comes at a cost: The architecture of DVRP circumvents the
efficient queue simulation of MATSim for activities. While “normal” agents are simulated
as described before, dynamic agents (DynAgents) have two modifications:
27
Legs are sent to the conventional Netsim component of the QSim. However, agents have
the ability to change their paths dynamically, i.e. one can modify the route of the
agent during the simulation steps and the next time the Netsim wants to move the
agent or checks whether the agent should arrive at the current link, its response is
calculated from the updated path.
Activities are simulated separately from the non-dynamic agents. As soon as a DynA-
gent starts an activity it is added to a list of active agents. In each simulation step
a specific callback for each of those agents is called and then it is checked whether
the agent wants to end this activity or not. This polling approach, as depicted in
figure 11, makes sure that it is not necessary to know when an activity (for instance
a taxi waiting for any requests) should end or how long it should take. On the
other hand, this approach is much more computationally expensive than the effi-
cient queue simulation. Given that the simulation is done on a second-by-second
basis, an activity that would take one hour, would cost only one insert and one
lookup on the acitivty queue. In the polling approach it costs 3600 calls to the
simulation step callback (even if it does not actually compute anything, this adds a
computational overhead) and 3600 checks whether the activity should be ended.
Using DVRP, Bischoff and Maciejewski (2016) ran a study on autonomous vehicles, where
the demand in Berlin has been obtained using an ordinary MATSim simulation. Then the
link speeds of the underlying network have been modified, to resemble the traffic situation
in a congested situation and then only autonomous vehicles have been simulated. This
means that the simulation could be run once, and the results were obtained because only
the QSim was used and not the evolutionary learning of MATSim.
However, in the project of this thesis, autonomous vehicles should be tested in an existing
multi-modal scenario, where the evolutionary learning is necessary for the agents to arrive
at their quasi-optimal mode choices. So when Bischoff and Maciejewski (2016) mentions
computational times of 20h for a large number of agents, it is a measure for one iteration
of the evolutionary algorithm. For the scenarios that will be tested here, with only
one hundred iterations a satisfactory equilibrium cannot be reached, although having a
theoretical computation time of 2000h already.
Measurements have been made to determine, how much the simulation of an idle agent,
which always stays in one activity, would cost regarding execution time on a test machine4.
4Intel(R) Core(TM) i7-3612QM CPU @ 2.10GHz
28
Figure 11: Polling approach of the DVRP framework
The final results gave an average time of 25ns. So simulating for instance 8000 agents for
a common simulation time of 30h, would lead to an execution time of:
T30h= 25
|{z}
Nomial
·3600 ·30
| {z }
One day in seconds
·8000
|{z}
Agents
= 21.6s(4)
For the whole MATSim simulation, this needs to be multiplied by at least 100 iterations,
so that the overhead of a simulation of 8000 agents doing nothing would already reach a
(highly optimistic) computational overhead of
Tsim = 21.6s·100 = 36min (5)
Therefore one can say, independent of the machine, that the constant polling in DVRP
causes a non-negligible computational overhead.
Furthermore, while working with DVRP, it has been found that one needs to put in-
creased efforts into making the framework compatible with parallelized computation in
the Netsim, presenting a substantial barrier to a clear avenue for improving simulation
performance.
In summary, one can say, that DVRP allows for great freedom in simulating dynamic
behavior and its structure and signaling flows are very straight-forward and easy to work
with. However, for large numbers of iterations, it would be beneficial to find more efficient
ways for the simulation.
29
4.2 The AgentLock framework
As an alternative to the simulation of dynamic agents using DVRP, the AgentLock frame-
work has been developed as part of this thesis. It tries to combine the advantages of a
queue simulation while providing as much flexibility as possible to create rich and dynamic
agent behaviors in MATSim.
The basic idea is as follows: Usually agents in MATSim do not need much processing
power, i.e. the per-agent simulation step of DVRP is hardly ever used and can usually
replaced by some callbacks and event handlers outside of the actual agent simulation.
Furthermore, this means that an activity just means that an agent is residing at a certain
position in the network and not taking part of the network. So an activity for an agent
is just keeping the agent back from joining the traffic network again after a certain time
or event.
With this idea in mind, three different types of ways to “lock” an agent into an activity
have been proposed:
Blocking activities will just let the agent reside in this activity until it is released through
a call from outside.
Time-based activites are the ones from the basic MATSim simulation: They have a
certain duration and therefore a fixed end time.
Event-based activities let the agent reside in the activity until a certain event happens.
The heart of the AgentLock extension is the LockEngine. Whenever it encounters an agent
that wants to start a blocking or event-based activity, it is removed from the simulation
and only added back using a specific function call or as soon as the event occurs. Then it
either is passed to the ordinary Netsim or the next activity is started, just as requested
by the agent logic.
For time-based activities, a similar approach to the activity queue for ordinary agents is
taken. The first idea that would come to one’s mind is to order the agents by the end
time of their activity and as soon as there is a change in plans, remove the element from
the priority queue and add it back at a certain position.
Compared to DVRP, where a change of plans would cost nothing, here this would lead to
an overhead of O(log n)and O(n)for these operations (Java API,2016). So it is necessary
to weigh the overhead of the polling in DVRP against the overhead of the rescheduling,
30
Figure 12: Per-Iteration procedure of the LockEngine in the AgentLock framework
which mainly depends on how often such reschedulings appear. In the concrete example
of autonomous taxis, this itself depends directly on the travel demand.
If one sacrifices a slightly increased memory consumption for the sake of having a faster
computation time, this setup can be improved further, as done for the AgentLock frame-
work. Here, every time a time-based activity is started, a handle to the corresponding
agent is saved into the priority queue, ordered by the end time of that activity. Further-
more, an indicator is saved, whether the handle is still valid. So if in the meantime the
plan is changed (i.e. before the end of the activity has been processed), this handle will
be invalidated, and it will simply be ignored when processing the priority queue.
The whole process (figure 12) works as follows: In every simulation step, the top element
of the priority queue is checked. If the top lock handle is scheduled for the current or
a past time step, the associated agent is saved for further processing. If the handle
already had been invalidated, the processing continues with the updated top element of
the priority queue until a handle is found that has an expiry time which lies in the future.
Subsequently, the new state (activity or leg) is computed for each saved agent, and a new
lock handle is added to the handle queue if it is time-based.
The main advantage of this setup is that elements are only removed at the top of the
queue, which is significantly less expensive than removing elements at arbitrary positions
within the queue.
31
Furthermore, the AgentLock framework provides methods for dynamically ending legs,
and it has been made sure that all the functionality has a high degree of compatibility
with the existing parts of MATSim, such as the multi-threaded Netsim.
4.3 AgentFSM
While the AgentLock extension mainly provides an abstraction layer for the dynamic
rescheduling of activities and legs, another layer has been developed, which is loosely
resembling a finite state machine (Choi and Kang,2013, pp. 256), tailored towards
agents in MATSim.
In this framework all the activities and legs are predefined states in a finite state machine
and the transitions from one step to another can either be triggered through a specific
function call (which is the blocking lock from above), by time (time-base lock) or by an
event (event-based lock).
The main task of the AgentFSM framework is to encapsulate common programming steps
when designing dynamic behavior in MATSim. This means that one usually just has to
define which states the behavior is built of and how the transition from one to another
works. All of this functionality is provided with a simple programming interface.
In more detail, each state is either a LegState or an ActivityState. For each state, an
enter callback exists, which the programmer can use to execute arbitrary code. It needs
to either return how this state is locked from the three options above or issue a direct
switch to another state.
As soon as the state is ended due to the above conditions, the leave callback of a state is
called, which must return to which next state the simulation should switch.
The concrete implementation for the autonomous vehicles will be discussed in section 5.
4.4 Comparison
An implementation of autonomous vehicles in DVRP has been compared to an imple-
mentation using the AgentLock framework. A specific number nof autonomous vehicles
are created and put into a list. As soon as an agent wants to start a leg using an AV, the
top element of the list will drive to that position, pick up the passenger, bring him to the
final destination and drop him off. Then the AV will be added back to the end of that
list. This dispatching algorithm is quite inefficient but sufficient to do investigations in
32
terms of computation time for the two implementations since the behavior is equal and
easily understandable.
Simulations with n= 2000,4000,8000 AVs have been done on the Sioux-14 scenario.
What can be seen in figure 13 is the number AV legs in the simulation and the associated
computation time. For a large range, the implementation using AgentLock/AgentFSM
(solid) is much faster than the corresponding DVRP implementation (dashed). In fact,
for n= 8000 only at a (quite unrealistically big) AV share of around 60%, DVRP starts
to be more efficient.
Important to notice is that the performance of DVRP stays roughly the same over the
whole range of shares. This is because all 8000 AVs are simulated in every single time-step,
no matter if they are active or not. In the AgentLock implementation, however, agents
are only simulated if they are really in use. At 110klegs, though, when the reschedulings
of used AVs are getting too frequent, the repeated queue operations get more expensive
than the polling and therefore DVRP becomes more efficient.
As a result, one can say that the AgentLock implementation is usually more efficient than
the DVRP version if there is a limited number of reschedulings. If they get too frequent,
i.e. the behavior is characterized by many alterations of some initial plan, the polling
structure of DVRP gets more efficient. For the purpose of simulating autonomous taxis
in this thesis, the number of such reschedulings should be minimal, as it will be described
in section 5. Therefore, the development of the AgentLock framework indeed bears a
computational advantage for this thesis.
Regarding a multithreaded Mobsim, only tests with the new AgentLock implementation
could be done, as shown in figure 14. Obviously, though the improvement is small, the
simulation with two threads performed best. This shows that it is an advantage to be able
to use the multithreaded Mobsim. Similar results have been found for other scenarios.
For instance, the optimal number of threads for the Singapore scenario has been found
to be four (Erath et al.,2012). More generally, Dobler (2010) shows that dependent on
the scenario characteristics significant improvements can be made using the multi-core
simulation.
In conclusion, while the AgentLock framework is suited for the investigations in this thesis,
a hybrid framework, offering both approaches, would be highly beneficial. Even more, it
would be interesting to investigate adaptive algorithms, which could switch intelligently
between the processing modes, dependent on the actual computation time and number of
reschedulings in a specific simulation.
33
20k 40k 60k 80k 100k 120k
Number of AV legs
0
10
20
30
40
50
60
70
Computation time [s]
Supply of 2000 AVs
Supply of 4000 AVs
Supply of 8000 AVs
Figure 13: Comparison of Mobsim runtimes between DVRP (dashed) and Agent-
Lock/AgentFSM (solid) implementation, dependent on the number of AV legs. The
scenario is Sioux-14 with a total number of legs of around 180k.
20k 40k 60k 80k 100k 120k
Number of AV legs
5
10
15
20
25
30
35
40
Computation time [s]
1 Thread
2 Threads
3 Threads
4 Threads
Figure 14: Comparison of different numbers of threads for the Mobsim with the AgentLock
implementation
34
5 Autonomous Taxi Fleet Model
Based on the previously presented layers for the simulation of dynamic agents in MATSim,
a model for the specific case of autonomous vehicle taxi agents is developed in the following
sections. First, the general behavior is defined, which an AV agent needs to follow to
serve a customer. Furthermore, the questions of how to distribute AVs at the beginning
of the simulation and how to assign AVs to pending requests in an efficient manner are
answered. Finally, algorithms for routing AVs through the street network are presented
and evaluated.
5.1 Agent behavior
The behavior of an autonomous taxi is not a lot different from an ordinary one, except that
there is no need of random roaming to find new customers. Therefore, the AV behavior
presented here is mainly inspired by the model in Maciejewski and Bischoff (2015), where
ordinary taxi services have been simulated.
The behavior of an autonomous taxi agent can be described in terms of a task life cycle.
When the agent is not on a task, he is in idle mode, basically (for the basic model)
meaning that he will just stay at the current position and wait for further instructions.
The following steps in the life cycle are depicted in figure 15.
1. Pickup Drive is the phase where the AV has got a task and is moving to the
requested pick up location. If the AV is already at the right location, this point can
be skipped. Otherwise, it represents a leg driving from the current position to the
pickup location.
2. Waiting is the phase in which the AV has arrived at the pickup location, but
the passenger is not there yet. This can only happen if passengers request cars in
advance, prior to the time when they want to be picked up. If the passenger is
already present at the time of the arrival at the pickup location, this state can be
skipped.
3. Pickup is the state in which the passenger is picked up. It is modeled as a fixed
time, e.g. one minute and starts as soon as both the AV and the passengers are
present at the pickup location.
4. Dropoff Drive represents the leg going from the pickup location to the dropoff
point.
35
5. Dropoff is the point where the passenger leaves the vehicle. Again, this is modeled
as a fixed time interaction.
6. Idle is the final (and initial) state of the AV life cycle. At this point, the AV will
just wait until it receives a new task to pick up another passenger.
The states described above fit very well to the distinction of Activities and Legs in MAT-
Sim as well as to the structure of the AgentFSM framework, which has been developed
for this purpose. Resulting from this behavioral model, a couple of parameters and im-
plementational questions arise, which must be configured accordingly:
The Idle behavior for the basic model just means that the AV will stay at its last
position. Future extensions could make use of parking facilities or do an intelligent
repositioning to improve the overall performance of the service.
Pickup and Dropoff duration need to be specified. In accordance with Bischoff and
Maciejewski (2016), tpickup = 120sand tdropof f = 60shave been chosen. The time
used for the pickup action will not be counted as waiting time (which, in turn, would
be penalized through the marginal utility of waiting as described in section 2.2).
5.2 Distribution Algorithm
At the beginning of a day simulation in MATSim, all the navailable AVs must be placed
somewhere in the network. Two simple distribution algorithms have been implemented
for the purpose of testing in this thesis.
The first one is Random Distribution. Here nlinks are chosen randomly from all
available network links. While this is an easy distribution strategy for testing, it creates
a quite unrealistic scenario. Obviously, in a real AV service, vehicles would be relocated
overnight, such that they can serve as many passengers as possible during the morning
peek.
Therefore, a more elaborate distribution strategy has been implemented, which should
lead to more realistic results. One can define a density over the network, such that every
link has a certain probability to get an AV assigned. Then, in nsteps, the navailable AVs
are added to a link dependent on the assignment probability. This probability density
can be based on many factors. The ones that are implemented for this thesis are:
36
Figure 15: State chart of an AV agent. Activity states are displayed in green while Leg
states are yellow.
37
Population Density The population density is measured in terms of how many people
are having their “home” activity on a certain link, since agents will start their first
simulated legs on a day from these locations. It should be roughly related to the
expected number of AV legs from that link.
AV Density For each link it is counted how many agents have chosen the AV mode for
their first leg (the one that is starting from home).
While the prior one is static, the latter on is dynamic in the sense that for every iteration
in the evolutionary learning, the density will change. So while the population-density
based distribution is a fixed constraint, the latter one captures the factor of availability.
For instance, if there are many agents using AVs in a certain area, the availability is very
high, and thus, more people might be inclined to use it. On the other hand, if availability
is low in an area, it might lead to longer waiting times and people are less likely to use
AVs.
While it might be interesting to observe different emerging patterns of availability, the
population density is better suited for the scope of this thesis. A detailed investigation
would need to be done if any results from the AV leg density come from the mode choice
of the agents or of feedback behavior within the algorithm itself.
5.3 Dispatcher Algorithm
The dynamic dispatching of taxi vehicles is a complex scheduling problem, which is hard
to solve or needs numerous assumptions to be feasible. In general, the problem will be
NP-hard, and heuristical solution strategies need to be applied if fast solutions are needed.
An overview, as well as a proposed heuristic algorithm, can be found in Maciejewski and
Bischoff (2015); Bischoff and Maciejewski (2016).
The algorithm there can be described in two different states:
Oversupply occurs when there are more available autonomous vehicles than requests.
This means that each request can be assigned without delay. In that case, as soon
as a request arrives at the dispatcher, the closest vehicle to this request is searched
and assigned to serve the customer.
Undersupply is the case when all autonomous vehicles are occupied. In that case re-
quests will stack up, which cannot be handled immediately. In this case the algo-
38
Figure 16: Schematic grid search algorithm for the dispatcher
rithm works the other way round: As soon as an autonomous vehicle gets available,
it is dispatched to the closest request.
According to the beforementioned papers this strategy gives a near-optimal solution with
fast computational times.
The implementation for this thesis is based on a spatial relaxation of the traffic network.
This means that a grid with a specific resolution in x and y is fitted over the links. One
of these grids saves the locations of all the available AVs while another grid saves the
locations of all open requests. Because the grids have a fixed structure, finding the closest
AV or request is quite simple, since each position in x and y belongs to one specific cell
of the grid. If no option is found in a certain cell, the search continues with all cells in its
Moore neighborhood (all eight surrounding cells). If this still gives no result, the radius is
increased and so forth. As soon as one or more candidates are found in a cell, a random
one is selected as the result of the search algorithm. This means that no further weighing
of the candidates is performed, which would lead to increased computation cost. The
procedure is depicted in figure 16.
This search algorithm imposes new parameters to the implementation, which are the cell
counts in horizontal and vertical direction. Depending on the topology of the network,
different parameters might be more efficient. If the grid is chosen to be too dense, many
iterations are needed in the algorithm, while a too sparse one in the extreme case can
lead to finding most of the items in only one single cell, effectively transforming the to a
simple random selection.
In fact, for some topologies, it might probably be more efficient to use different data
structures like a binary tree or quadtree to improve the search procedure. Also, more
elaborate network search algorithms could be used, which make direct use of the topology
(Chen,2014).
39
20k 40k 60k 80k 100k 120k
Number of AV legs
25
30
35
40
45
Average trip duration [min]
2
5
10
20
50 100
200
20k 40k 60k 80k 100k 120k
Number of AV legs
5
10
15
20
25
30
35
40
45
Computation time [s]
Figure 17: Performance of different grid sizes in the dispatching algorithm for Sioux Falls
For the Sioux-14 scenario, it has been tested which impact the choice of the grid size has
on the results. In figure 17 one can see, that very high-resolution grids (n= 200) lead to
an increase in computational time, due to the necessary “expansion” of unoccupied cells,
as described above. On the contrary, very low grid sizes lead to poor results in terms of
the overall average travel time of the agents, because selecting a random agent from one
of a few cells is just a random assignment. A good value for the Sioux Falls network has
been found to be n= 20, which is computed fast over the whole range of AV legs and
furthermore does a good job in decreasing the overall travel time.
Once one open AV request is assigned to one idle AV using these two grids, the trip is
computed, which mainly consists of finding a route for the AV to move to the pickup
40
location and finding a route from there to the dropoff point. The actual implementation
of this routing process will be described later (section 5.4).
While in the first version of the dispatcher the routing was performed sequentially after
all trips had been assigned, the dispatching process could be improved by parallelizing
the routing stage with the whole QSim cycle as shown in figure 18. At one point in the
dispatcher, the assignments between requests and AVs are made, just as before. Then,
though, the actual task of finding the routes is delegated to an arbitrary number of parallel
routers. Each of those routers has a queue which can be used to spread the routing tasks
over all routers (i.e. if there are two routers and six tasks, each one will process three
tasks, which are added to the respective queues). After all tasks have been sent to the
routers, the MATSim simulation continues as usual; the “work-in-progress” services are
saved temporarily in the dispatcher. After one whole QSim loop (i.e. simulating the
traffic network, static activities, ...) the dispatcher is called again. Then it waits for
all the routers to finally dispatch the requests that have been assigned in the previous
simulation step. Subsequently, the assignment step for the current simulation step is
performed.
Figure 19 shows the impact of adding this feature: Clearly, adding the parallel function-
ality accounts for a significant decrease in computation time. However, using more than
one parallel router does not further increase the performance. This is a strong indicator
for the assignment step (together with the QSim) for being the restricting time factor
here. The routing of all tasks takes less time than the other processes, even when only
one router is present, and thus no further gain in computation time can be made. Looking
at the end of the graph, one can see though that the offset in computation time that is
accounted to the routing is increasing faster than the computation time of the rest of
the simulation. Therefore, with a higher count of AV legs, there should appear the point
where two routers are more efficient than one.
In theory, the parallelization of the dispatcher could be pushed even further. However,
the assignment step, which is the other expensive component in the algorithm, would
probably be hard to parallelize because concurrent workers would need to access the same
grid structures. The overhead of managing which worker has access is likely to add more
overhead than improvement to the simulation quickly. One could, however, put the whole
assignment process as a serial procedure in parallel to the QSim, as done with the routers.
This could be a promising approach to decreasing the computation time even further.
41
Figure 18: Dispatcher implementation with routing parallel to the MATSim loop
42
20k 40k 60k 80k 100k 120k
Number of AV legs
5
10
15
20
25
30
35
40
Computation time [s]
1 Router
2 Routers
3 Routers
4 Routers
Serial
Figure 19: Computational performance of the dispatcher with sequential and parallel
routing
43
5.4 Routing Algorithm
The routers in the AV simulation have the task to find a route through the street network.
For each AV service, there are two of such routes: The pickup route from the AV’s current
position to the customer and the drop off route on which the customer is transported to the
predefined drop off location. To find the routes, the Dijkstra algorithm is used (Dijkstra,
1959), with travel time as the objective to be minimized. This travel time is computed
using the length of the selected links and the speeds on those links.
The most simple idea for those speeds, however, would be to use the predefined free-flow
speed values in the scenario network. While this approach works for small shares of AVs,
it leads to heavy overcongestion with high numbers of AVs on the streets. The reason
for this is that for similar trips, similar routes are chosen, leading AVs to make extensive
use of the main arterials, but also of specific low-capacity links, which are optimal for
topological reasons. By not taking into account any information on how congested the
links are, more and more vehicles attempt to enter them, creating huge traffic jams.
In the top-level MATSim loop, such congestion can mainly be avoided by introducing small
stochastic and congestion-based alterations to the car-using agents. This way, iteration by
iteration, such routes are eliminated from their plans because they lead to a bad scoring
of the respective plans. Furthermore, the traffic situation by daytime in the network is
measured and used as a basis for planning in subsequent iterations.
In the following sections, two more advanced approaches for defining the link speeds are
presented. First, continuous online tracking of link speeds during the day is discussed in
section 5.4.1, followed by an approach based on the introduction of stochasticity into the
process (section 5.4.2).
The problem of routing all vehicles in a network (which is in principal the case for very high
shares of the AV mode), is a complex problem in itself. In this perspective, the presented
routing algorithms are versions of a local optimization of the route for each agent and trip.
However, this does in no way guarantee that a global optimum is reached (depending on
what the objective is). In that regard global routing algorithms and heuristics might be
worth to study in the future.
5.4.1 Online Speed Calculation
One approach that has been tested for the routing is to base the link speeds on actual
online measurements in the network. The traffic situation on a link can be described by
44
the three interconnected measures flow, density and speed. Flow describes the throughput
of the link, i.e. at the start or the end of the link it is measured how many vehicles cross
that link in a certain time interval while the density describes how many vehicles are on
the link at a certain time.
Each link in MATSim has a certain flow capacity qcin veh
hdefined, stating the maximum
number of cars per hour, that are allowed to pass the link. Furthermore, for each link it
can be counted how many cars are on the street by counting the number of cars going
in nin and out nout, whenever either event happens. This allows one to computed the
density on the link:
d=∆n
l=nin −nout
l(6)
with lbeing the length [km]of the respective link. These values can be combined to
arrive at the current link speed by computing:
v=qc
d=qc·l
∆n(7)
The result is a velocity in km
h. It states the maximum possible speed when a certain
density dappears on a link with the maximum flow capacity of qc.
Of course, computing this value might lead to speeds, which exceed the predefined maxi-
mum free-flow speed of the link, so the final value is bounded from above. Also, for the
proper working of the Dijkstra algorithm, a minimum speed is defined to 1km
h:
v0=
1km
hif v < 1km
h
velse
vfif v > vf
(8)
In order to avoid the same computation whenever a link should be traversed, the network
is computed collectively after a fixed time span, e.g. every 30sin simulation time.
5.4.2 Stochastic Variation Model
The second idea is to add stochasticity to the Dijkstra process, thus creating slightly
perturbed routes. What needs to be answered for using this approach is, which magnitude
those perturbations should have. To solve this problem, the Sioux-16 baseline scenario
45
has been examined. The 30h day has been divided into N= 720 bins (2min each) and
for each the relative decrease in speed for all link passages starting has been computed:
ri,j =1
ni
ni
X
j=1
vi,j,free−f low −vi,j,simulation
vi,j,free−f low
(9)
Here niis the number of link passages (all agents and all links) that occurred in bin
number iand ri,j is the relative decrease of speed in each bin for each passage.
As can be seen in figure 20, the distribution of decreases in travel speeds of the network
links can roughly be approximated using a Gamma distribution. The outliers, which can
be seen on the right, are those cases where there is a much congestion during peak hours.
Because those are exactly the cases that one wants to avoid here, they are omitted in
the following steps. The assumption of a Gamma distribution is wholly motivated by
the shape of the histogram, performing an educated derivation of the distribution shape
would be an interesting investigation, which is out of the scope of this thesis.
A Gamma distribution is defined by a shape parameter kand a scale parameter θ. For
all bins in the baseline scenario, the respective parameters have been obtained using the
MLE estimator for θand a Newton approximation for kas described in Minka (2002).
Figure 21 shows the parameter values for each bin on top, after they have been smoothed
using a moving average filter of length 20. Also, for the times before roughly 5 am and
after 10 pm, average parameter values over the off-peak hours in the middle of the day
have been inserted due to a lack of sufficient data for fitting the speed decreases in these
outer areas.
Also shown in figure 21 (on the bottom) is the mean of the speed decrease at each time
of the day, framed by the 10% and 90% quantiles, now instead of simulation results
based on the statistical model. It can be seen that due to the Gamma model, the range
of probable decreases is high during peak hours, up to 70%, while the 10% stays quite
constant during the day. The graph of the mean suggests that the presented model is a
reasonable approximation, which qualitatively makes sense.
The final travel speed for the router can now be described as a random variable:
Vi,j,routing =vi,j,f ree−f low ·(1 −min{Ri,1})(10)
with Ri∼Γ(ki, θi)being Gamma-distributed for each bin.
46
0% 20% 40% 60% 80% 100%
2
4
6
8
10
12
14
Figure 20: Example distribution (pdf) of relative decreases in link speed
The overall effect of this model is then as follows: There is a certain increase in travel
time expected for each link, which depends on its free-flow speed and the time of the day.
However, especially during peak hours, when the bottlenecks would be a critical problem,
more variation is added to the expected increases in travel time and thus a better variation
in the routing is reached.
The expected increases are founded on the actual network characteristics of the Sioux-
16 network and might be different for other networks. Furthermore, it has not been
investigated whether different link types might show different statistical properties, which
is very likely. Establishing a comprehensive statistical model of the decreases in link
speeds, depending on a greater variety of variables, would be beneficial.
5.4.3 Performance Measures
Basic tests of the AV taxi fleet model without the evolutionary replanning have been
performed to test the performance of the routing algorithms. For that purpose, the
scenario has been simulated for one iteration, without any further refining of the agent
plans. First, the plans of 30% of the agents using a car in the population have been
changed to use AVs. Figure 22 shows how the average travel time in the network changes
with an increasing number of AVs. If only a few AVs are available, the waiting time
for an AV is very high, because there are not enough vehicles to cover the demand.
With an increasing number of available AVs the congestion in the network increases and
therefore the average travel time (of cars) in the network increases. Clearly, the online
speed tracking performs better in preventing congestion while the Gamma distribution
approach shows a similar performance to a simple routing based on the free-flow speed.
47
06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Distribution Parameters
Shape k
Scale θ
06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00
0%
10%
20%
30%
40%
50%
60%
70%
Relative decrease in speed
Figure 21: Statistic model for the relative decrease in link speed. Top: Parameters for the
Gamma distribution model by day time. Bottom: Mean value of the respective Gamma
distribution and the 10% and 90% quantiles.
48
Another case is presented in figure 23. There the number of available AVs has been fixed
to 2000, and different shares of AV trips in the population have been examined. In that
dimension that waiting time increases with a higher share of the population, since more
demand is generated, which the taxi service is less and less likely to cover the more agents
are using it. Interesting is the decrease in overall travel time, which occurs because at
some point the number of waiting people exceeds the number of people on the road, which
is freeing the network from congestion, while letting people wait for a much longer time.
Finally, while the former cases were “relaxed” in the way that although leading to high
waiting times, the demand could be covered in the 30h simulation day, figure 24 shows
the case were this is not the case anymore. In that figure, 70% of all car trips have been
replaced by AV trips. The solid lines show the average travel time of cars in the network
for cases in which all agents could finish their plans; the dotted lines indicate cases where
agents were not able to do so. In the beginning of the graph, for a very low number of
AVs, all algorithms break down in this regard. This is due to the disability to serve the
demand with that number of vehicles.
For the online calculation approach, one can see, that it is performing badly throughout
the whole range of values. One explanation for that is that AVs react to any slowdown in
the network, effectively trying to find alternative routes to prevent them. This leads the
AVs to find unnecessarily long trips, which take irrational routes through the network.
What is missing in this routing approach is a sense of expected congestion. In a network,
where the capacity of the roads is not able to allow for a free flow at all times, the routing
algorithm should be able to bargain between joining a traffic jam and expecting it to
dissolve soon or choosing a completely different route through low-capacity links. In this
approach, the latter will lead to even more severe congestion because those links are used
more frequently than would be necessary.
Comparing the free-flow speed router and the stochastic one, the performance is similar.
There is a gap in the middle of the graph, showing the area in which too much congestion
is produced by the AVs, such that agents get stuck. Before the gap, one has the regime
where AVs serve multiple requests since there are not enough AVs available to have one
AV for each request. Then, if the number of AVs gets bigger, it happens that because
more and more users get their “unique” AV, more cars go on the street, and too much
congestion occurs. Finally, if there are even more AVs, the situation relaxes again, because
now almost every request has it’s own car. There is no need to perform additional pickup
trips to the customers since there are enough AVs distributed over the network.
49
2k 4k 6k 8k 10k
Number of available AVs
5
6
7
Average Travel Time [min]
2k 4k 6k 8k 10k
Number of available AVs
0
20
40
60
80
100
120
140
Average Waiting Time [min]
Freespeed
Online
Gamma
Figure 22: Comparison of different routing algorithms in terms of average travel time and
average waiting time with a fixed share of 30% of car users in the population using AVs.
The gaps presented in this scenario are likely to be resolved when the evolutionary re-
planning is introduced into the model. Because people can reschedule their departures,
the situation can be relaxed. Also in the replanning, agents would choose other means of
transport if the use of AVs gets to disadvantageous. However, it has been found that also
with the replanning, for some scenarios it occurs that not all agents arrive at the end of
the day. As can be seen in figure 24, the stochastic approach can cover a larger range of
cases, and it also has been found that in combination with the replanning, this approach
yields the strongest reliability. Therefore, it is chosen in the following simulations of the
whole model.
50
0% 20% 40% 60% 80% 100%
Fraction of people using AVs
4
5
6
7
Average Travel Time [min]
0% 20% 40% 60% 80% 100%
Fraction of people using AVs
0
10
20
30
40
50
60
70
Average Waiting Time [min]
Freespeed
Online
Gamma
Figure 23: Comparison of different routing algorithms in terms of average travel time and
average waiting time with a fixed number of 2000 available AVs.
51
5k 10k 15k 20k
Number of available AVs
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Average Travel Time [min]
Freespeed
Online
Gamma
Figure 24: Comparison of different routing algorithms in terms of average travel time
with a fixed share of 70% of car users in the population using AVs. Dotted lines show
areas where agents were not able to finish their plans during the 30h simulation period.
5.4.4 Static Trip Replacement
From the data for the stochastic routing, it was possible to find a structured dependency of
the number of available AVs and the number of replaced cars in terms of the waiting time
for passengers without performing any additional measurements. The result is presented
in figure 25. There, the existing data points are depicted as crosses, while all combinations
with an average passenger waiting time of less than 10min have been highlighted. A
pareto front over the existing measurements has been constructed. So in the case of a
bare replacement of car trips by AV trips, one can see that in order to replace 40% of the
car fleet, 10,000 AVs are necessary to reach the desired waiting time, which is only 15%
of the cars in the baseline scenario. So in total one would be left with a total car and av
fleet size of 75%. In the case of a replacement of 70% of private cars with AVs, one would
need to convert 30% of vehicles to AVs, which would yield a total fleet size of 60%.
Furthermore it should be mentioned, that taking the average as a waiting time threshold
might yield misleading results, i.e. if the distribution is heavily biased towards low waiting
times. Experiments with using quantile functions instead of the average showed that in
fact the opposite case is observed here. The shown average coincides quite accurately
with the 80% quantile, thus yielding an answer to the more solid question: How many
AVs are needed to replace a certain percentage of the initial car fleet if 80% of the waiting
times should be less than 10 minutes.
52
0k
0% 5k
8% 10k
15% 15k
23% 20k
30%
Number of available AVs and percentage of total cars
10%
20%
30%
40%
50%
60%
70%
80%
Percentage of replaced car trips
Figure 25: Dependency of the number of available AVs and the number of replaced cars.
The crosses indicate distinct measurements; the highlighted ones yield an average passen-
ger waiting time of less than 10 minutes.
These results are a first indicator of the performance of the model, but of course lack the
flexibility of the evolutionary replanning. By letting agents alter their departure times
the demand situation should become more relaxed and therefore waiting times should
decrease. This, in turn would mean that the displayed front would decrease in slope. The
next section will cover the results gained from the combined simulation framework, where
all components are added together.
53
54
6 Simulation Results
Once the simulation model had been established, simulation runs with carefully defined
parameters have been performed. The following sections will give an overview about the
simulation results.
First, a baseline scenario will be defined with the corresponding utility parameters. The
resulting trip statistics and mode choices will be analyzed (section 6.1). In section 6.2
different levels of supply will be examined and their effects on the overall net mileage
and waiting times will be shown. Section 6.3 shows relevant traffic statistics, such as the
AV mode share, in dependency on the pricing scheme, while section 6.4 will introduce
an operator model and analyze the profitability of the AV mode from a service provider
perspective.
The simulations performed in this chapter have been computed over 500 iterations, with
the innovation of agents’ plans being turned off after 420 steps. Generally, this is a
generous setup, since relaxation is usually reached after around 200 iterations. In terms
of computation time, the increase was found to be linearly dependent on the number
of AV legs, with an increase of 80% per 100,000 legs compared to the baseline Sioux-16
scenario without AVs.
6.1 Baseline Scenario
The model with the implementation that has been described in the previous chapters has
been tested on the Sioux-16 network with a flow capacity scaling of 70% to allow for a
reasonable amount of congestion.
The travel disutility parameter has been chosen to be zero, as is the travel disutility
for taking a car in Sioux-16. The reason behind this is that there are numerous studies
indicating positive and negative effects of autonomous vehicles, so it is hard to decide
whether the perception of AVs will tend towards one side or the other compared to cars.
The constant disutility for cars in the Sioux-14 scenario has been computed by combining
the travel disutility for 10min walking (as to account for getting to and from a parking
lot) and the monetary disutility for paying $6 for parking. For the AVs in this simulation
it has been assumed that there is no such additional cost, but a monetary fee per AV
trip. This assumes that a fictitious operator already included the costs of parking into
the pricing scheme (which is reasonable taking the values from actual taxi services).
55
Table 2: Baseline Scenario Parameters
Parameter Computation Baseline Value
Constant Utility per Trip Cav =−βm·$3.60 −0.2232
Marginal Utility of Travel Time βtrav,av =βtrav,car 0.0
Monetary Distance Rate γav = 2.19$/km 0.00219
Marginal Utility of Wait Time βwait,av =βwait,pt −0.18
Since the values in Sioux-14 are based on measurements in Sydney, the current maximum
charges for taxi trips there have been used as a reference (Transport for NSW,2016).
According to this source, an initial charge of $3.60 has been set as the constant disutility
per trip, while the monetary distance factor for AVs has been set to $2.19 per km. This
pricing scheme has been chosen to allow for a comparison with a service that exists in
reality. As will be shown later on, this setup leads to a surprisingly high share of the AV
mode.
Finally, the disutility for waiting for an AV has been assumed to be the same as the waiting
disutility for public transport from Sioux-14, which itself is just a vague assumption
(Chakirov and Fourie,2014), but at least allows for a systematic comparison.
Using these parameters, which are summarized in table 2, the scenario has been simulated
until relaxation. The following paragraphs will show the respective results in terms of the
traffic situation. A sufficiently high number of available AVs (N= 8000) has been chosen
to show how agents make a choice for taking an AV based on their utility evaluation.
6.1.1 Trip Statistics
Table 3shows the basic trip statistics of the case where AVs have been introduced to
the baseline scenario. It can be seen that with the given utility parameters, the AVs
reach a share of around 25% averaged over the day, mainly decreasing the share of public
transport and walking while also attracting some of the former private car users. Given
the quite expensive price structure for the AV mode, this result is surprising and likely
a result of the calibration of the existing parameters from the Sioux-14 scenario, which
might only be consistent in themselves. Nevertheless, comparisons to this AV baseline
scenario allow for qualitative conclusions regarding the simulation outputs.
Interesting to see is that for public transport and walking agents the travel distances
decreases because relatively long trips in those modes will be replaced by AVs, thus
56
0246810
Distance in [km]
2k
4k
6k
8k
10k
12k
Number of Trips
Public Transport
Private Car
Autonomous Taxi
Walking
Figure 26: Number of trips for each node by traveled distance
drawing the average down to shorter trips, while it increases for cars. Here, mainly
the shorter car trips are replaced by AVs.
These results can also be in figure 26, where the distribution of travel distances by mode
is presented. Clearly, AVs act as a competitor towards public transport there, serving
mainly the same range of trips with the assumed utility parameters.
In terms of travel times, it can be seen that there is a slight increase for the car mode,
which stems from the same argument as before. The decrease in travel time for public
transport and walking agents is quite significant, though. For the walking agents, the
change is obvious as described before. The decrease for public transport can be explained
by the switch of agents, who needed to have long walking distances to the closest bus
stop, which is included in the calculation. By only keeping those agents at using public
transport, who live nearby a bus stop, the overall travel time decreases quite substantially.
The waiting times for AVs in the baseline scenario are on average around 04:40 min in the
morning peak and 02:55 min in the afternoon, while the daily average lies at 01:40 min.
A more detailed analysis of waiting times is given in section 6.2.
57
Table 3: Traffic measures for the relaxed AV baseline scenario
Baseline With AV
Travel Distances [km]
Car 3.73 4.04
Walking 1.25 0.82
Public Transport 3.88 3.25
Autonomous Taxi 2.94
Travel Times [mm:ss]
Car 07:20 08:07
Walking 25:01 16:29
Public Transport 28:48 20:41
Autonomous Taxi 10:41
Mode Shares
Car 65.04% 55.08%
Walking 6.79% 3.08%
Public Transport 28.17% 16.65%
Autonomous Taxi 25.19%
In terms of travel distances the total amount of kilometers driven increased from around
424,000 km in the baseline to 553,000 km in the AV scenario. The amount of kilometers
driven by AVs is 162,500 km from which around 37,800 are for the purpose of picking up
passengers, i.e. they are unoccupied while covering this distance, which is roughly 23%.
This is around half compared to ordinary taxis with 52% as stated in recent statistics for
Oslo (Geir Martin Pilskog,2015) or around 50% in Barcelona (Amat et al.,2014).
6.1.2 Mode Choice
Table 4shows how the mode choice that takes place after AVs have are introduced. The
rows show the original modes while the percentages indicate how many of the initial users
switch to the mode in the column after the introduction of AVs. What can be seen is that
44% of all initial public transport users and 56% of all walking people opted for taking an
AV while only 14% of car users switch modes. This again shows that with the baseline
parameters, AVs rather work as a competitor against public transport while additionally
drawing new adopters from the walking people. Therefore, this scenario represents the
rather unwanted case where AVs lead to a less optimal situation on the road, leading to
more congestion and less use of collective transportation.
A further impression on the choice behavior of the agents can be obtained through fig-
ure 27. In the upper plot one can see the public transport trips in the baseline without
58
Table 4: Migration matrix showing which agents switched from one mode to another:
The rows resemble the initial choices of the agents while the columns resemble the mode
choice after the introduction of AVs. The percentages denoted how many users of the
original mode switched to another option.
AV Car PT Walking
Car 13.69% 84.41% 1.68% 0.23%
Public Transport 44.29% 0.60% 54.91% 0.21%
Walking 56.21% 0.18% 1.38% 42.24%
AVs (blue), which have not changes during the introduction of the new mode while the
red dots show those combinations of trip duration and distance in the original scenario,
which have changed to AV. Comparing the blue and red areas it becomes evident that
users with rather long trips in terms of travel time switch to AVs. The green dots show
the combinations after the change has been taken place, i.e. the travel duration and dis-
tance in the converted AV trips. It can be seen that after the introduction of AVs the
travel durations get much less, so for the public transport users, the AV mode is mainly
attractive because it provides shorter net travel durations.
The lower plot in figure 27 shows the same arrangement for private car users. One can
see that the switching users (red) are clustered for short trips in distance and duration.
Their travel times, contrary to the public transport users, increase when using the AVs,
indicating that the monetary benefit of using the AV instead of going on a private car
trip (and paying for parking) is stronger than the desire to have a minimal travel time.
From the utility parameters, one can equate the resulting utility of a private car and an
AV trip with the same distance:
Ccar +βm·γcar ·d=Cav +βm·γav ·d(11)
Solving for the variable distance, one reaches at a critical distance, at which AV trips
should get unfavorable, which is:
dcrit = 3.05km (12)
This value can be observed in figure 27, where in the lower plot a strict barrier can be
seen at this distance.
59
2.5 5.0 7.5 10.0 12.5 15.0 17.5
Trip Distance [km]
00:00
00:20
00:40
01:00
01:20
01:40
02:00
02:20
02:40
Trip Duration [hh:mm]
Unchanged car trips
Car to AV
AV from car
2.5 5.0 7.5 10.0 12.5 15.0 17.5
Trip Distance [km]
00:00
00:05
00:10
00:15
00:20
00:25
00:30
Trip Duration [hh:mm]
Unchanged car trips
Car to AV
AV from car
Figure 27: Analysis of the distribution of public transport (top) and car (bottom) trips
in terms of travel distance and duration before and after the introduction of autonomous
vehicles.
60
08:00 10:00 12:00 14:00 16:00 18:00 20:00
0
500
1000
1500
2000
2500
3000
Number of AVs
Pickup
Dropoff
Total
Figure 28: Activities of AVs during the day in the relaxed (8000 AVs) AV baseline scenario.
The solid graphs show the number of vehicles, which are “on tour”, while the shaded area
denotes the number of pickup and dropoff interactions with the passenger.
6.1.3 AV Operation and decreased supply
Finally, figure 28 shows the states of the AVs during the day. While the lines show how
many AVs are currently performing either a pickup or dropoff task, i.e. being “en tour”,
the shaded areas show how many passengers have been picked up or dropped off at a
certain time of the day. In this baseline scenario, only around 3000 cars are actually
active of the available 8000, so from the perspective of an AV operator the scenario would
not be an ideal case, because the usage of the AVs is not nearly close to saturation.
Such a case is depicted in figure 29. It shows the states of the AVs during the day if
only 1000 of them are available. Shaded areas indicate those times of the day where
the dispatchment mode changes from oversupply to undersupply, where there are more
requests than available AVs. At those peak times, one can see that the number of active
AVs goes into saturation. The number does not go to 1000 exactly since only driving AVs
are measured, whereas some might be in the 120s pickup or 60s dropoff activities.
Compared to the high supply case, the share of AV trips drops from 25.19% to 18.92%.
While the travel time stays roughly the same for the AV mode, the average distance
increases slightly from 2.94km to 3.18km, indicating a shortfall of short trips. Around
half the amount of private car users switch to AVs (6.65%, before 13.69%); for public
transport users, the decrease is less significant from 44.29% to 40.29%. From that one can
conclude that the attractiveness of AVs for private car users is decreasing substantially
with a constrained supply while the induced longer waiting times seem to be tolerable by
former public transport users.
61
08:00 10:00 12:00 14:00 16:00 18:00 20:00
0
200
400
600
800
1000
Number of AVs
Pickup
Dropoff
Total
Figure 29: Activities of AVs during the day in the constrained (1000 AVs) AV baseline
scenario. The show the number of vehicles, which are “on tour”, while the shaded area
denotes times where the undersupply dispatchment mode is active.
Figure 30: Comparison of total travel distances in the low and high supply scenarios.
62
From an environmental perspective, this scenario is worse than the former one. While
car users continue using their private vehicles, public transport users switch to additional
cars on the road. In terms of distance (figure 30), the total amount of kilometers driven
increases further because of an increase in excess travel distance of the AVs. Since fewer
agents are using the service, the vehicles have to cover longer distances to get to the next
customer. Such a case is disadvantageous for the service operator, so it will be interesting
to see how the additional costs of excess mileage affect the overall economic evaluation
of the provider (section 6.4). The next chapter will give a more detailed relation of the
supply level on the total traveled distance.
6.2 Supply Analysis
Figure 31 shows the relation of travel distance and supply in a more detailed way. At
around 1000 vehicles, there is a peak of the net driven distance in the network (black),
which is relaxed if the supply is increased. The stable added number of kilometers is then
around 120,000km. However, the peak is only 40,000km bigger than this value, which
itself is a quarter of the initial 400,000km in the base scenario. Looking at the red graph,
which shows the added miles of empty drives in the AV services compared as an offset to
the total number of AV miles, one can see that it shows the same peak, i.e. the excess
mileage is responsible for the increase in total travel distance. In this regard, the service
operator and public administration would have the same priority to avoid this peak (in
terms of profit one one side and regarding environmental policy and congestion on the
other).
In terms of waiting time it has been found that per 1000 AVs around 4% of initial car
trips in the scenario could be replaced with static demand in section 5.4.4. Looking at
the waiting times on top in figure 32 one can see that the mean value as well as the 90%
quantile of the waiting time tWis under the threshold of 10 minutes, which has been
examined before. Furthermore, the middle of figure 32 shows P(tW≤10min), i.e. the
probability of having a waiting time of less than 10 min in the simulated supply scenarios.
While this probability clearly decreases with small fleet sizes, it still stays rather high at
90%. That is the case, because due to high waiting times, fewer trips are being made.
For higher supplies, the quantile finds an equilibrium-like state at around 97%, which
can be interpreted as a measure of how tolerable increased waiting times are in a certain
scenario.
63
5k 10k 15k 20k
Supply of AVs
20k
40k
60k
80k
100k
120k
140k
160k
Excess Distance [km]
Figure 31: Evaluation of the total added travel distance of all vehicles compared to the
base scenario without AVs (black) and excess driving distance for AVs for the respective
supply (red).
Additionally, the bottom plot in figure 32 shows the replaced percentage of trips dependent
on the amount of available AVs. Because of the preferences that are induced through the
utility-based learning, considerably fewer trips are converted to AVs although staying in
the waiting time limits. While in the static analysis 5000 AVs can replace 20% of private
car trips, in the dynamic one it is only 15%. For the static case 60% are simulated at
15,000 AVs, but here the replacement fraction remains at 15%. This shows that the
usefulness of the mode, which is quantified by the utility, is the restricting factor, despite
a large available margin in waiting time efficiency.
6.3 Cost Dependencies
Intuitively, the behavior of the utility parameters should be quite clear: If the utility is
increased, the AV mode gets more favorable, if it is decreased, less people will use it.
However, in such a complex traffic system there are secondary effects, which influence the
adaptation of AVs.
Figure 33 shows the share of the AV mode in the baseline scenario (top) with different
pricing schemes, given through a price per kilometer and a price per trip. For near zero
cost services, the share reaches 90%, while for a combination of $7 per trip and $3 per
kilometer the share drops down to under 10%. It can be seen that for a very low travel
utility (lower left) the threshold in the shares gets steeper while it dilutes for very high
travel utility (i.e. acceptance) of the AV mode (lower right). This hints at the fact that
64
5k 10k 15k 20k
Supply in AVs
2
3
4
5
6
7
8
9
Waiting Time [min]
Average
90% Quantile
5k 10k 15k 20k
Supply in AVs
75%
80%
85%
90%
95%
100%
Cumulative Probability
P(t≤10min)
P(t≤5min)
0k
0% 5k
7% 10k
15% 15k
22% 20k
30%
Supply in AVs
10%
20%
30%
40%
Percentage of replaced trips
Car Public Transport
Figure 32: Top: Mean value and 90% quantile of waiting time for different supply levels.
Bottom: Cumulative probability of observing a waiting time less than 10 minutes.
65
the more accepted AV technology is in the population, the more people will use it while
the pricing scheme can have a huge impact on adaptation if there is a considerable amount
of skepticism towards the technology.
The shaded areas in figure 33 show those parameter combinations, where P(tw≤10min)≥
0.9, i.e. where the probability to wait less than 10 minutes for an AV per trip is higher
than 90%. Taking that as another criterion to assess the performance of an AV service,
one can see that it puts a restriction on how low the prices can drop to allow for a smooth
operation of the service. In fact, if waiting time is a constraint, only moderate shares of
AVs can be reached on any level of acceptance.
What needs to be kept in mind here is that no further investigations on the disutility of
waiting time have been performed here, but it is rather based on an assumption taken
from Chakirov and Fourie (2014). Nonetheless, the result is surprising since, in extreme
cases, agents accept a waiting time of 30 minutes or more in 90% of trips, as can be seen in
figure 34. Mainly, this depends on all the utility parameters in the scenario, also the utility
of performing an activity, the disutility of using other means of transport and so forth.
Accepting such a high waiting time might be an indicator that the utilities in the Sioux
scenario should be further improved to lead to better results. However, the interpretation
is tricky for very low prices, since they also resemble quite unrealistic situations, where
only times are weighed against each other: If there are no monetary costs, a trip in terms
of utility costs as much as not performing an activity for the travel time.
Furthermore, the results of the simulation are surprising when looking at the share of
public transport in figure 35. The general tendency makes sense: Lower prices lead to
lower shares of public transport because using an AV gets more advantageous. Also,
having very high prices, the public transport share stays at its initial baseline level.
Nevertheless, one would expect people to react more abrupt to the pricing scheme on
the per-trip side than on the per-km side. So far each trip in the Sioux Falls scenario
costs $2. Imposing no per-trip fee for AVs, but different per-km fares should show a
smooth transition as can be seen in figure 35: The shares should change depending on the
price and the trip distance distribution. On the other hand, if no per-km fare is imposed,
but only per-trip payments, the transition should be more abrupt. This effect, however,
might be smoothed out by AVs taking less travel time.
This is only true though if people can make rational decisions about the total costs of
travel. When looking at the beforementioned plots, one can see that there is are quite
linear nivau lines, meaning that if a per-km cost is given, one can easily obtain the per-
trip cost in order to stay at a certain level of service. For instance, this means that for
66
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Cost per km [$]
1
2
3
4
5
6
7
Cost per ride [$]
10%
20%
30%
40%
50%
60%
70%
80%
90%
0.0 0.5 1.0 1.5 2.0 2.5 3.0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0
1
2
3
4
5
6
7
Figure 33: Dependency of the AV mode share on the pricing scheme. Top: Baseline
scenario. Left: Low utility of traveling (βtrav,av =−0.5). Right: High utility of traveling
(βtrav,av = 0.5). Shaded areas show parameter combinations where the waiting time for
an AV is shorter than 10 min in 90% of the cases.
67
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Cost per km [$]
1
2
3
4
5
6
7
Cost per ride [$]
3min
6min
10min
13min
16min
20min
23min
26min
30min
Figure 34: 90% quantile of the waiting time in the baseline scenario with different pricing
schemes. The scale is truncated at 30 minutes.
the agents, paying $5 per trip and $1.60 per km is equal to paying $3 per trip and $1.90
per distance. In reality, the perception of the high per-trip fare might be different to the
lower per-km fare, especially compared to the initial $2 per trip.
Combining the results of this section, it becomes apprent that in the given scenario, also
the share of public transport has a lower bound if a specific service level in terms of
waiting time should be maintained. On the other hand, the introduction of AV services
will diminish the share of public transport in any case. As one conclusion it can be
therefore stated that without any policy-based incentives, it is not possible to maintain
the level of public transport while motivating private car owners to switch to AVs.
Another point that has to be taken into account regarding these considerations is the
profitability of the service for the operator, which will be the subject of the next section.
6.4 Economic Analysis
The operator model for the net income zproposed in this thesis can be stated as follows:
68
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Cost per km [$]
1
2
3
4
5
6
7
Cost per ride [$]
5%
7%
10%
12%
15%
17%
20%
22%
Figure 35: Share of public transport trips. Shaded areas indicate not completely relaxed
simulation runs with stuck agents.
z=pkm ·ddropof f +ptrip ·ntrips
|{z }
GrossIncome
−
$6 ·nveh +cpd ·nveh +γd,car ·dtotal
| {z }
Expenses
(13)
On the income side of the operator, there is the total distance of dropoff (i.e. occupied)
trips ddropof f , multiplied by the price per km and the number of AV trips ntrips, multiplied
by the price per trip. The expense side has been modeled to be comparable with the car
mode in the Sioux-16 scenario. It involves a cost for parking ($6) as well as running costs
per km for private cars multiplied by the combined total distance for pickup and dropoff
trips. Of course, this choice bears a lot of uncertainty, it might be a reasonable guess
though, since increased costs for insurance and decreased costs for (electric) operational
costs might weigh out each other (Chen et al.,2015). Finally, a cost per day cpd is
introduced for each supplied AV taxi.
That cost has been modeled as follows: Chen et al. (2015) states predictions of (electric)
AV taxi prices of around cv eh = $62,000 (converted to AUD) and states lifetimes of around
69
dmax = 370,000km. From the simulation the average driven distance of one day is known
as davg =dtotal/nveh per vehicle. Those values can be used to obtain a vehicle lifetime,
assuming that the amount of kilometers driven stays constant over the lifetime τ:
τ=davg
dtotal/1d=km
km/d = [d](14)
Then the costs per vehicle per day can be stated as:
cpd =cveh
τ=davg ·cveh
dmax
=davg ·ν
=ν·dtotal
nveh
(15)
with
ν= 0.17 $
km .(16)
Inserting this equation into equation (17) effectively cancels out the number of available
AVs from the investment costs and integrates them into the per distance costs:
z=pkm ·ddropof f +ptrip ·ntrips
| {z }
GrossIncome
−
$6 ·nveh + (ν+γd,car )·dtotal
| {z }
Expenses
(17)
Therefore the net income is characterized by a complex relation of the total distance
driven, the occupied distance, the number of cars and the number of AV trips. Applying
this model to the previously introduced pricing scheme map gives the result in figure 36.
For very low prices the service clearly is not profitable in the proposed model, while it is
possible to maintain the service in a moderate price range. In fact, the area with most
profit is covered by the formerly introduced condition on waiting times (hatched area).
However, from an administrative perspective, one might also want to maintain a certain
share of public transport. Here, a arbitrary share of 15% is chosen, which should be
maintained. In that case the operator would need to offer the service in the crossed area.
There the profit is decreasing because of a smaller number of users.
70
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Cost per km [$]
1
2
3
4
5
6
7
Cost per ride [$]
$-450k
$-300k
$-150k
$0k
$150k
$300k
$450k
Figure 36: Net income of the AV operator. The shaded areas represent acceptable waiting
times (bigger area) and public transport mode shares of more than 15% (smaller area).
For the baseline scenario, the operator scenario has been tested with different supply
levels. The results in figure 37 show that over the whole range of AVs there the service
is profitable, especially at 4000 AVs. Over the whole depicted range the constraints on
waiting time and public transport are fulfilled. In that sense those scenarios are quite
optimal cases, where the share of public transport stays above 15%, the waiting times
are usually less than 10 minutes and the operator has a large margin. Incorporating the
results from section 6.1, the right-most cases are the best because additionally the overall
excess mileage is smallest.
The large margin is an indicator that the baseline scenario is a setup that could “work” in
a city similar to the Sioux Falls network. Contrary to the financial analysis in Chen et al.
(2015), here infrastructure costs have not been included in the analysis, which could be
covered by that profit of the operator.
71
5k 10k 15k 20k
Supply of available AVs
$180k
$200k
$220k
$240k
$260k
$280k
$300k
Operator Net Income
Figure 37: Dependency of the operator net income in the baseline scenario on the number
of supplied AVs.
72
7 Conclusion
In the previous chapters a simulation of autonomous vehicles in a multi-modal traffic
network has been developed and assessed. The development started out with the extension
of the existing Sioux Falls traffic network for MATSim to a more finegrained resolution,
with comparable traffic characteristics as the original scenario.
Furthermore, a the new AgentLock framework for the simulation of dynamic agents in
MATSim has been developed, providing a decreased computational time for a wide range
of simulation configurations, compared to the existing DVRP extension of MATSim. Ad-
ditionally, a layer for the easy programming of state-based agents, AgentFSM has been
created and used in the subsequent simulations.
For the simulation of AVs, a basic agent logic has been shown, a dispatching strategy has
been assessed and different ways of routing AVs through the network have been analyzed.
Finally, behavioral parameters for the simulation of AVs have been defined and quan-
titative results of the AV simulation have been demonstrated in detail. However, the
simulation at hand is by nature more suited for giving qualitative insights into the traffic
system rather then quantitative since it is based on a virtual test scenario.
One of the first results, which could be obtained, is that AVs in the test scenario will
lead to an increased overall milage, which is an adverse effect looking from an environ-
mentally perspective, but is also disadvantageous in terms of congestion in the network.
Implementation-wise it has been found that considerable work needs to be put into intelli-
gent ways of making AVs facilitate the existing infrastructure in order to avoid artificially
made traffic jams, which is a problem that gets crucial with an increasing number of AV
trips and therefore increasing mileage.
In that regard the introduction of AVs plays against one positive effect of public transport:
to have fewer vehicles one the road. As could be shown in the results, former public
transport users are the main adapters of autonomous vehicles in the given scenario. While
private car users have a financial motivation to switch to the AV mode and accept longer
travel times, public transport users mainly do the switch to reduce their accumulated
travel time consisting of the walking to the stop facilities and the ride itself, possibly with
several line switches.
This choice behavior goes along with a high tolerance for waiting times for the AV mode.
Because public transport users are used to having a long travel time, the performance
that could be reached in the given network was clearly enough to serve the demand.
73
Nevertheless, the public transport users are not the audience that a policy maker would
want to attract with AVs. From the findings in the simulations one can state (at least
for the Sioux network), that it is very hard to impossible to maintain a certain level
of public transport while getting private car owners to using the AV service. In fact,
applying pinpointed incentive or taxation schemes might be necessary to reach at the
desired results.
In terms of pricing it has been found that the more inclined people are to spend time in an
AV, the less constrained the financial structure of the service needs to be in order to reach
certain AV shares. For the baseline scenario it has been found that it is possible to operate
an AV service in a profitable way while still maintaining a share of %15 public transport
and providing waiting times of less than ten minutes. While doing this, there would be
a financial margin available on the side of the operator to cover necessary infrastructural
expenses.
The final conclusion is that AVs without administrative regulation are likely to attract
public transport users rather than private car owners. Further research needs to be done
on how AV usage can be incentivized for private car owners to reach at a beneficial traffic
situation.
Finally, it remains to state that the proposed model is built on a manifold of assumptions
in the initial Sioux Falls scenario, in the operation of the AV agents and on the financial
model for the operator. While for the latter future predictions will become better and
better, it would be highly interesting to apply the developed model to a real-world scenario
with a higher confidence in the estimated utility parameters and relative factors such as
current taxi pricing.
8 Outlook
During the course of this thesis a versatile and extentable basis model for the simulation
of autonomous vehicles has been developed. Many topics in the field which would be
interesting to investigate were not part of the scope of this thesis. The following sections
will present the most important and interesting ones and give directions on how to simulate
them with the framework.
74
8.1 Infrastructure Extensions
The adaptation of autonomous vehicles will take great advantage of the ongoing electri-
fication in the automotive industry. While the “distance anxiety”, which makes people
refrain from using electric vehicles due to the limited driving range, is a major barrier
for the introduction of electric vehicles, autonomous vehicles might be able to solve this
problem by providing reliable trips through an operator (Burmeister et al.,2016;Chen
and Kockelman,2016). Therefore the availability of the respective electrification infras-
tructure is one factor which has to be taken into account when predicting the adaption
of autonomous vehicles.
Given the right amount of resources to create such an infrastructure, a big question that
arises is how many recharging facilities are needed and where they should begin located in
order to serve certain sizes of AV fleets (Chen,2015). Furthermore, how can a combined
infrastructure for ordinary owned EVs, private AVs and publicly provided AV services be
designed?
As a first step one could assume that AVs recharge at dropoff locations, where they are
artificially put to rest for a certain minimum idle time in order to simulate the recharging
process. This would already lead to results on the customer acceptance side, but would
ignore effects on congestion if AVs would actually need to take long trips to the next
charging facility. Previous studies using MATSim already gave interesting results on the
implementation of eletrified taxis in Berlin with distributed charging facilities over the
network (Bischoff and Maciejewski,2014). Such research could be combined with the
AV framework developed here. The modular AgentFSM component would make it easy
to add specific new points in the state chains of an AV to drive to a charging facility.
Then again, the simulation framework could be used to get insights in which scheduling
strategies would be optimal for an AV fleet if recharging has to be taken into account.
Another idea to improve the simulation is to introduce means of simulating maintenance
and parking. So far it has been assumed that autonomous vehicles will reside where
the last dropoff has taken place. This assumption is quite optimistic, since parking space
might be rare. In consequence, the driven kilometers per AV in the unoccupied state could
be quite off the actual distance. More mileage would be needed to find a parking space
in between tasks. This rises a whole range of questions on how an optimal AV scheduling
would look like, maybe depending on the demand level, it might be even interesting to
run studies on whether the search for parking space might be inferior to roaming around.
75
This could be done in combination with intelligent repositioning, where in between peak
hours taxis could be intelligently moved to likely pickup positions and thus minimize the
waiting time for customers, increasing the acceptance and reducing operator costs at the
same time because less unoccupied miles might be travelled.
With the parallelization of customer trips the presented framework already shows by
example how such an algorithm could be incorporated into the existing infrastructure
without having too much impact on the computation times. In general, doing “some”
intelligent repositioning should always be more beneficial than doing none. In this regard,
the repositioning could be computed in parallel to the ongoing traffic simulation, while
still offering the ability to restrict it if it slows down the main loop of MATSim.
8.2 Usage and interaction with the AV service
The AV service in the developed model so far is very basic in the way customers are
able to interact with it. One obvious advantage of AV fleets is, that up to five people
could be transported in ordinarily shaped cars and even more in autonomous minibusses
or full-sized busses. Intelligent routing and scheduling algorithms would make it possible
to pick up passengers at arbitrary locations, not being bound to a fixed public transport
schedule.
Due to the extensible structrue of the AV extension, its would be easy to add such
behaviour in principle. However, the problem of optimizing the trips of more than one
passenger, probably while already on a ride, is a highly complex problem and heuristics
are still an important research subject. Adding such functionality to the AV framework
would make it possible to test such strategies in near-realistic scenarios and measure the
performance of different heuristics.
Additionally, autonomous vehicles are likely to relax the last mile problem, where people
are not motivated to opt for public transport, because the last mile from the trans-
port facility to their home is too long. An AV could bridge this distance, maybe being
prescheduled to pick up the passenger according to the current expected arrival times.
Implementing this behaviour would need only small changes in the MATSim framework.
Generally, a public transport trip is generated as three legs: One transit_walk leg in
order to get to the stop facility, one pt leg for the actual residual time in the bus and
another transit_walk. A first attempt would be to replace some of the transit_walk
legs during the planning phase with av trips, which could already lead to a convincing
simulation of AVs feeding the public transport network. A probable requirement for this
76
to work well would be to have prescheduled AVs to give a higher reliability on these
connections.
Prescheduled autonomous vehicles would be easy to implement in the existing infrastruc-
ture. In fact, test have already been done, but abandoned due to the fact that in a first
approximation delays from the scheduling can be modeled using worse utility values for
the waiting times. In the current state, the AV framework fully supports such presched-
uled trips, though their impact has not been investigated in the scope of this thesis. As
shown in figure figure 15, where the state diagram of the AV is depicted, a “Waiting” state
is already included, which would make an AV which arrives early at a pickup location
wait for the passenger.
An intereting point in the simulation is the spatial dependence. On one side, it would be
interesting to investigate where AV users live, maybe indicating that on specific pricing
strategies, people from the suburbs prefer AVs, while other strategies might encourage
people living in the center to use them.
Heavily related to that is the initial distribution of AVs at the beginning of the daily sim-
ulation. As described before, AVs are currently distributed dependent on the population
density, though that might not be the best approach. Especially if one wants to encourage
suburbians to use AVs, the density there should be higher.
In that regard it would be beneficial to investigate how the initial conditions in the
MATSim simulation influence the result on an abstract level. For the case of AVs, having
initial AV plans mainly assigned to agents from a city center, but not for people from the
suburbs, the relaxed state might settle down in exactly this condition. However, if AVs
are mainly distributed in the suburbs in the initial plans, the main user group might stay
there, just because during the simulations the waiting times are shorter in either case and
therefore these people might stick to their initial plan decisions. Therefore, a thorough
investigation of the distribution behavior of the algorithm would be very interesting.
Furthermore, the research in this thesis has shown that without any incentives, AVs might
lead to adverse effects, which should be corrected by intelligent policy decisions. Chen and
Kockelman (2016) suggests interesting approaches of incentivizing AV usage. In order to
“free” the city center from too much congestion one could for instance in the Sioux Falls
scenario put high monetary fees on using the streets within the highway belt for private
cars, while in parallel increasing the likelihood for AVs to use the highways. This way one
could try to move traffic to the highways, then taking a direct trip to the workplaces in
a perpendicular way.
77
Experiments like these are ready to be done with the existing simulation framework by
adding custom scoring functions for private cars and autonomous vehicles.
Finally, efforts have been made recently to diversify the population in MATSim simu-
lations (Chakirov,2015). This means that people might be constrained or inclined due
to age or income to use certain means of transport. Combining the simulation of AVs
with the introduction of that heterogeneity could give insights on how the availability and
pricing of AVs affect the distribution of users in terms of a richer set of social variables.
78
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