# A high-performance traffic flow microsimulation for large problems

**ABSTRACT** Traffic flow microsimulations are interesting for transport planning problems due to their high temporal and spatial resolution. Unfortunately, most of them involve high computational costs making them impractical for running large scale scenarios. In this paper, we present how we extend our previous event-driven queue-based mircosimulation to run efficiently on parallel computers. Using appropriate load balancing and minimizing communication interfaces, we are able to simulate a test scenario involving 7 million simulated person days on a road net- work with 28k links in 87 seconds on 64 CPUs. Furthermore, we add support for signaled intersections that makes the model well suited for application to urban street networks. Finally, we show that our resulting model reproduces a reasonable relation between traffic flow and density similar to fundamental diagrams extracted from real world counts data.

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A High-Performance Traffic Flow Microsimulation

for Large Problems

David Charypar

Michael Balmer

Kay W. Axhausen

Working paper 509

Transport and Spatial Planning2008

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A High-Performance Traffic Flow Microsimulation for Large Problems2008

Working paper509

A High-Performance Traffic Flow Microsimulation for Large

Problems

David Charypar

Institute for Transport Plan-

ning and Systems

ETH Zurich

CH-8093 Zurich

phone: +41-44-633 35 62

fax: +41-44-633 10 57

charypar@ivt.baug.ethz.ch

Michael Balmer

Institute for Transport Plan-

ning and Systems

ETH Zurich

CH-8093 Zurich

phone: +41-44-633 27 80

fax: +41-44-633 10 57

balmer@ivt.baug.ethz.ch

Kay W. Axhausen

Institute for Transport Plan-

ning and Systems

ETH Zurich

CH-8093 Zurich

phone: +41-44-633 39 43

fax: +41-44-633 10 57

axhausen@ivt.baug.ethz.ch

2008

Abstract

Traffic flow microsimulations are interesting for transport planning problems due to their high

temporal and spatial resolution. Unfortunately, most of them involve high computational costs

making them impractical for running large scale scenarios. In this paper, we present how we

extend our previous event-driven queue-based mircosimulation to run efficiently on parallel

computers. Using appropriate load balancing and minimizing communication interfaces, we

are able to simulate a test scenario involving 7 million simulated person days on a road net-

work with 28k links in 87 seconds on 64 CPUs. Furthermore, we add support for signaled

intersections that makes the model well suited for application to urban street networks. Finally,

we show that our resulting model reproduces a reasonable relation between traffic flow and

density similar to fundamental diagrams extracted from real world counts data.

Keywords

Traffic flow microsimulation, Event driven simulation, Parallelization, Green time fractions,

Large-scale scenario

Preferred citation style

Charypar, D., M. Balmer, and K. W. Axhausen (2008) A High-Performance Traffic Flow Mi-

crosimulation for Large Problems, Working paper, 509, Institute for transport planning and

system (IVT), ETH Zurich, Zurich.

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A High-Performance Traffic Flow Microsimulation for Large Problems2008

1 Introduction

In transport planning, traffic flow simulation plays an important role as it takes the demand

generated by an earlier process as input and produces derived quantities like traffic densities,

flow volumes, speeds, and travel times as output. These quantities are in turn important for

instance to analyze the state of the traffic system or to enable iterative demand generation

based on one or multiple of these values.

There are several choices when it comes to deciding on the type of flow simulation: macro-

scopic aggregated models are available just as mesoscopic and microscopic approaches. For

resolution and accuracy, microsimulation would clearly be the method of choice here. Further-

more, using a microscopic point of view, the advantages of advanced techniques in demand

generation based on the individual, like activity based (e.g. Bowman et al., 1999; Vovsha et al.,

2002) or agent-based(e.g. MATSim-T, 2008) demand models, can be fully exploited by utiliz-

ing the same individuals throughout.

The downside of microsimulation is the computational burden that comes with these methods.

One explanation for this is that data with very high temporal and spatial resolution must be

processed as well as produced. This inevitable property represents a major challenge when try-

ing to use such a method for large scale scenarios. Another disadvantage is arguably the added

complexity in the demand generation process for creating a virtual population: zone-resolution

is no longer sufficient since microscopic flow simulations need the individual traffic objects

(i.e. the cars). On the other hand, tedious procedures known from macroscopic modeling, like

zone definition, placement of connector links, and generation of OD-matrices, can be avoided

this way, . Perhaps as a result of these properties, microsimulations are seldom used for large

scale scenarios today. Instead, mostly macroscopic models and sometimes mesoscopic models

are employed.

One way to reduce the computation time of microsimulations is by running them in parallel

on multi-CPU computers and large computer clusters. Unfortunately, it turns out that this

approach cannot be generally applied to each microsimulation model, as often the resulting

parallel performance of such approaches is poor. With the advance of multi-core CPUs in

desktop computers this fact is currently leading to the paradoxical situation that increases in

processing power often do not accelerate traffic flow microsimulations.

Inthiswork, wepresentamicrosimulationprogramthatrealizesdecentsingleCPUandparallel

performance making it suitable for very large scale scenarios. This speed is achieved by bearing

in mind implementation and parallelization issues already during model design. However,

looking at performance only is certainly not sufficient for traffic analysis. We need to make

sure that the model also shows reasonable flow properties. Analysis of such properties therefore

forms an important part of this work. The third focus of this paper is the functional extension

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A High-Performance Traffic Flow Microsimulation for Large Problems2008

of introducing traffic lights into the model. This extension allows the transport modeler to cope

with the intrinsic heterogeneity of simulating large scale scenarios with rural as well as urban

areas.

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2 Traffic Flow Simulation Approaches and Related Work

In this section, we give a brief overview of different classes of traffic flow simulation ap-

proaches. Their level of abstraction has strong influence on the resulting accuracy, resolution

and simulation speed.

2.1 Physical Microsimulation Models

Physical microsimulation models represent the most accurate and expensive type. Their aim

is generally to mimic real traffic dynamics by imitating human car following, simulating lane

changing behavior, employing sophisticated intersection dynamics, etc. Space is often repre-

sented continuously and simulated time is advanced in small time-steps. Examples are AIM-

SUN (Barceló et al., 1998; AIMSUN, 2006), MITSSIM (Yang, 1997; MITSIM, 2006), and

VISSIM (VISSIM, 2006). Barceló et al. (1998) demonstrated a parallel implementation using

globally accessible data which ran 3.5 times faster on 8 processors.

For large scenarios however, physical simulation methods are still too expensive; to become

faster, one has to “trade in” some of the accuracy and resolution for speed.

2.2 Cellular Automata

In cellular automata (CAs, see e.g. Nagel and Schreckenberg, 1992; Chowdhury et al., 2000;

Brilon and Wu, 1998), roads are discretized in cells each of which can be either empty or

occupied by a car. Each car controlls its driving speed based on the available head space to

the front of it. CAs are faster than physical models while retaining a fair amount of spatial

resolution.

A CA is adopted for example in TRANSIMS (Nagel et al., 1998; TRANSIMS, 2006). Nagel

and Rickert (2001) and Rickert and Nagel (2001) showed a parallel version using message

passing between processors, running midsized scenarios on 32 CPUs. Although the running

times were about ten times faster than real time, ethernet latency problems and speed handicaps

due to the use of cellular automata were reported.

What limits CAs’ speed is the necessary update of each car’s position in every time-step. This

becomes impractical for large numbers (>1 million) of cars.

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2.3Queue-Based Simulations

The model can be further simplified and thereby accelerated by representing links as queues.

This approach was followed in MATSim-T (e.g. Cetin, 2005; MATSim-T, 2006). The com-

putational advantage comes from the shift from the cars being the main simulated elements to

links that “process” the cars. This reduces the number of simulated units (links vs. cars) and

thus simulation performance increases by a factor of 10 to 100, depending on network reso-

lution. The links collaborate to move the cars through the network while adhering to various

constraints (capacity, free speed travel time, intersection precedence, and space availability).

Using message passing between cluster nodes, the queue-based model presented in (Cetin,

2005; Cetin et al., 2003) achieved a speed-up of 32 using 64 CPUs when simulating a peak

period. Charypar et al. (2007) presented a single processor queue-based simulation based on

Cetin (2005), that replaces the constant time-steps by an event-driven approach improving effi-

ciency by more than a factor of 10. The idea of advancing time as necessary from event to event

can be found in Mahut (2000) as well, where the entry and exit times of vehicles are computed

directly.

2.4 Mesoscopic Models

In contrast to microsimulation, mesoscopic models (e.g. METROPOLIS (Marchal, 2001;

de Palma and Marchal, 2002), DynaMIT (Ben-Akiva et al., 1998; DynaMIT, 2006), DYNAS-

MART (Chang et al., 1994; DYNASMART, 2006), DYNEMO (Schwerdtfeger, 1984; Nökel

and Schmidt, 2002), ORIENT/RV (Axhausen, 1988)) use aggregates to compute travel times

and speeds.

METROPOLISisabletosimulate largescenariosefficientlybyusingaparallelimplementation

based on threads. DynaMIT does not parallelize the traffic flow simulation itself but uses task

parallelization i.e. different modules are run in parallel. DYNEMO was run in parallel (Nökel

and Schmidt, 2002) by using a message passing technique on 19 CPUs for simulating small

scenarios. Larger numbers of CPUs were reported to be inefficient.

2.5 Macroscopic Models

The highest level of abstraction can be found in macroscopic models that compute all traf-

fic quantities on an aggregated level. One example of a traffic simulation model as a one-

dimensional incompressible fluid is NETCELL (Cayford et al., 1997).

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3 Traffic Flow Model

This section summarizes the traffic flow model we presented in Charypar et al. (2007), which

forms the base for the extensions presented in the follwing three sections: support for traffic

lights, analysis of the flow properties of the model, and the parallelization of the model to run

efficiently on many CPUs.

3.1Event-Driven Queue-Based Model

Themainover-allaimduringthedevelopmentofthepresentedmodelwascomputationalspeed.

As mentioned earlier, we are targeting very large scenarios with up to 10 million simulated

agents. It is important to realize that in this range of size we are competing mostly with macro-

scopic models and not with high resolution microsimulations of the physical or cellular au-

tomata type. For this reason, it was decided to develop a queue-based model to achieve the

maximal possible speed.

At the base of the simulation model there are the road segments which represent the built

infrastructure and a population of agents that represent the people inside cars that use the in-

frastructure. Between agents there exist gaps which are represented explicitly:

• The road segments are directed links between a starting and an end point. They have a

length, an amount of available space, a minimum travel time and two flow capacities, for

in- and outflow, respectively.

• Each agent has a complete 24-hours activity plan and represents a person traveling by

car. The plan consists of an ordered list of activities, corresponding activity start times

and durations, and the route to travel between subsequent activity locations.

• The population of virtual agents together with their activity plans represent the travel

demand.

• In the opposite direction of agents gaps move upstream to produce the necessary delays

between a car leaving a congested link at the end and a new car entering that link at its

starting point.

During the course of the simulation agents and road segments work together by means of mes-

sage passing. The basic idea is simple: In order to enter or leave a specific road segment, each

agent needs to ask the segment for approval first. Approval is not given until execution of the

corresponding action will not violate any of the following requirements:

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• Agents can only leave the road segment in the same order as they entered.

• The road segment must not hold more agents than a certain maximum.

• There is a minimum gap between two consecutive cars according to inflow capacity.

• Outflow is constrained analogously.

• To enter a road segment, there must be a gap available at the inlet. Gaps travel upstream

at a constant predefined speed.

• An agent cannot leave the road segment before the free speed travel time has elapsed.

If a road segment has available space, an agent’s request is accepted immediately. Only if the

road is full, approvals are delayed, thereby leading to a reduction in travel speed.

One crucial observation with queue-based models in general is that basically all information

about the course of simulation is contained in the entry and exit events. Between subsequent

entry and exit events for a given car, its exact position is unknown. As a result, simulating the

time between such a pair of events with time-steps only increases simulation costs.

Furthermore, on a heavily loaded link, one can even say that one event triggers the next. As-

sume for example an agent trying to enter a road segment that is completely filled with cars.

The agent sends an entry request message to the road segment and waits until the next space

becomes available. At some point in time, the leaving event of the front car produces a gap

that travels upstream at constant speed. When it reaches the upstream end, it becomes avail-

able for the new car to enter the link. This predetermination between subsequent events can

be exploited for simulation efficiency. It makes it possible to avoid constant time-steps and

instead use variable time-steps to advance time from one event to the next. This has a couple

of advantages:

• Computational events correspond to traffic events. That means, that computation time is

spentproportionallytothetrafficflow. Thisdenotesanadaptiveassignmentofprocessing

resources according to instantaneous traffic flow.

• Since the event processing rate is more or less constant on a given machine it is easy to

predict how long it will take to simulate a given traffic demand.

By using variable time-steps based on events, one can realize an overall speedup factor of at

least 10 over the time-step-based implementation.

To coordinate the necessary variable time-steps, we introduce a centralized clock object. All

agents and road segments use this clock to register timers as necessary for the event handling

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Figure 1: The traffic flow protocol: the vertical lines indicate how time runs during the course

of the simulation; the arrows between these lines represent messages sent between the

objects of the simulation; the numbers in circles denote the corresponding protocol

step of the message.

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process described above. When such a timer expires, the corresponding object gets informed

and is then able to take the corresponding action. The rules that define these objects’ interac-

tions form the so-called flow-protocol, which is illustrated in Figure 1 for the case of an agent

traveling along a line of road segments.

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4 Green Time Fractions

The simulation of 24 hours scenarios on urban networks with many signaled intersections often

involves a special problem: The observable link flow capacities on crossing roads do not always

keep a fixed ratio as the signal control parameters may be time of day dependent. This type

of intersections cannot be handled correctly with constant flow capacities. To alleviate this

problem, we introduce green time fractions that modulate the links outflow capacity. These

greentimefractionscanbevaryingovertime, enablingthesimulationofdifferenttrafficcontrol

schemes over the day.

4.1Model Extension

The general idea is to introduce on each link an explicit representation of the outgoing capacity

reduction based on the fraction of time the associated traffic light is switched to green. We

simply assume the average capacity realized on such a link is proportional to the relative green

time. For example on a link with its traffic light switched to green during 30% of the time on

average, we expect to observe an average realized capacity of 30% of the free flow capacity.

Admittedly, there probably is no linear relation between green time fractions and realized ca-

pacity. Still we choose this model to make the simulation easy to understand. After all, we can

switch to an interpretation of the data where we replace relative green time by relative useable

green time, rendering our linear model correct.

In our model, the green time fractions per link are not constant but are merely modulated, each

individually, by a piecewise linear function of time. Other models would have been possible

(including piecewise constant modulation functions), but we think it is a beneficial property to

have a continuously changing capacity on the links to avoid undesired shocks in the system.

After all, if desired, very quick changes in capacity can still be realized.

The question might arise why we model averaged green time fractions instead of individual

green phases. There are multiple reasons to mention:

• The necessary data is difficult to obtain and process, especially for very large scenarios

with hundreds or even thousands of traffic lights. These scenarios often cross adminis-

trative boundaries resulting in a lot of heterogeneity in the input data.

• The data cannot be easily made up and small errors in these numbers may produce totally

different realized flows on crossing links.

• For similar reasons, it is very difficult to test new policies using individual green phases

compared to the relative ease of adapting the average green time fractions on a road

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Figure 2: Plot of example green time fractions for one link.

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

green time fraction

time [h]

during some time of day.

Note, that if there is, for some reason, the need to simulate individual green phases on certain

intersections, our model is flexible enough to mimic such a behavior by changing the green

times fraction periodically. For example, a link’s green time fraction can be set to alternate from

100% green for 73 seconds to 0% green (i.e. red) for 128 second by defining a corresponding

modulation function in the input data.

This input data is provided as a separate file (the green time fraction file) in a human readable

XML format. In this file, for each link incorporating traffic lights, there is a list of data points,

specifying the green time fraction on that link at a given point in time. Furthermore, the simu-

lation assumes that the values repeat periodically according to a period defined in the same file.

In Figure 2 you can see a plot of example green time fractions for one link.

4.2Technical Description

Internally, for each of the road segments holding green time fractions data an instance of a

special modulator object is created. Apart from holding the data, this object is also responsible

for computing the car waiting times on the associated road segment.

The data is stored in a sorted data structure allowing quick access to any data point needed

during computations. Each data point consists of a time stamp and a green time fraction.

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When a car wants to leave a signaled road segment, just as before without signalling, it requests

the next available time slot. This value depends on the time when the last car left the link and

on the out flow capacity of the road segment, which is now time dependent. Technically, the

car has to wait until the integral of the time dependent capacity reaches 1[car]. This integral of

the piecewise linear capacity function q(t) is the piecewise quadratic volume function V (t). If

tlis the time when the last car left the road segment, the requested next leaving time tncan be

computed by solving the equation

V (tn) − V (tl) = 1

(1)

for tn. This involves inverting the volume function which is not trivial, since it is a piecewise

quadratic function, and it is not clear which piece will contain the tnto be computed. Our im-

plementation solves this problem by starting at tland integrating each piece of q(t) sequentially

until the integral exceeds the required 1[car]. At this point, it is clear that the last covered piece

contains the tnin question and this can be easily found by solving a quadratic equation.

4.3Demonstration of New Simulation Possibilities

If inclusion of new links into existing road networks is considered, for instance the creation

of a city by-pass, accompanying measures are often investigated. Changing the timing and

prioritization of traffic lights is often one of these measures tested and the presented extension

of our traffic flow model provides a way of rendering such ideas in the simulation.

Our model was used at our institute in a recent project where the effects of opening a city

by-pass tunnel around the city of Zurich, Switzerland, were investigated (see Balmer et al.,

forthcoming). Thescenarioinvolvedaroadnetworkwith60klinks, usedbyaround670kagents

each of which executing its 24-hours activity plan. One of the questions under investigation was

how changes in traffic flow patterns could be influenced by modifying the traffic lights policies

aroundrelevantpointsinthenetwork. Figure3visualizeshowpeakhourtrafficvolumeschange

if traffic flow into and out of the city center is restrained by using traffic lights. The section

shows an area around the freeway exit “Wollishofen” near the east entrance of the tunnel under

investigation. One can see clearly that traffic starts to avoid the restrained road and starts to use

alternative routes.

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Figure 3: Effect of changing traffic lights policy near the freeway exit Wollishofen. The num-

bers indicate the change in hourly traffic volumes of the peak hour. The circle in the

center indicates where the traffic lights were changed, thickness of the roads indicates

the number of lanes.

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Figure 4: In our queue-based microsimulation model with gaps the average density and flow

ratio show a clear trapezoidal relation. This property is independent of network reso-

lution.

5 Flow Properties

To be able to use our model in a way that it produces the best possible simulation results, it is

important to know its inherent properties. One especially important property is the relation be-

tween traffic density and traffic flow and how much this relation depends on external properties

like the network resolution and the travel demand. With this information available, it is pos-

sible to tell if and how the model should be applied to certain classes of simulation problems.

Can the model be used for the simulation of freeway traffic? Does the accuracy of the result

change if we split long links into pieces? Such questions are ultimately under investigation in

this section.

5.1Averaged Characteristics

To find the relation between average flow and average density, we perform a virtual experiment

on a circular test network. This circle is loaded accordingly to produce all relevant average

traffic densities. The average traffic flow is then measured and the corresponding values plot-

ted against each other. In Figure 4, we show the resulting flow-density plot. The graph has

a trapezoidal shape, the left, upper, and right edges of which can be clearly associated with

independent parameters of our queue-based model with gaps: The slope of the left edge is con-

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trolled by the free speed defined on a road segment, the height of the top flat part corresponds

to the flow capacity on the link, and the cut-off point together with the slope of the right edge

are a result of the maximum density (fully congested density) and the backward traveling gap

speed. Interestingly, increasing the network resolution by a factor of 500 does not change the

average flow-density relation at all. Another interesting observation: all observed states on

the network lie on the border of the graph. No state of medium average density together with

medium average flow was observed in any of our tests. It seems that our model is not only able

to produce the limit values, but it also will produce exactly these limit values if used on a ring

topology.

5.2 Instantaneous Flow Characteristics

We are not only interested in the relation between average flow and average density: We also

want to know, how these values relate locally and on a short time scale. To extract the desired

values, the test setup was slightly modified by introducing a short measurement strip. Sub-

sequently, density and flow at any time were measured on this sensor strip and no temporal

smoothing was applied. For this test setup, the demand was left the same as in the previous

case. Interestingly, the resulting instantaneous flow-density plot looked very similar to the av-

erage flow-density plot. The only noticeable difference was a certain clustering at high an low

densities, so it seems medium densities are rare local observations. Maybe this can be explained

through transitions from congested flow conditions (high density) to free flow conditions (low

density) back again to congestion. This maybe can be interpreted as stop-and-go traffic.

5.3 Stochastic Flow characteristics

With the test scenario describe above we have found that our traffic flow model basically re-

produces the envelope of what could be termed a stylized fundamental diagram.

Interestingly, the “inner” states, as they are often seen in real wold fundamental diagram are

never observed. To figure out if this is a property of our model we have created a new test

case, basically an isolated short road segment that is fed by two stochastic and independent

processes: On the upstream end, one such process is randomly producing cars trying to enter

the road segment and at the downstream end another one is randomly producing outflow slots

for cars arriving. This setup corresponds to the (admittedly unrealistic) situation where cars

enter and leave a road segment with the highest possible fluctuation.

The resulting flow and density patterns show the same trapezoidal envelope as before, but now,

the inner states are realized regularly.

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