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Impact of Mobility-on-Demand on Traffic
Congestion: Simulation-based Study
David Fiedler, Michal ˇ
C´
ap and Michal ˇ
Certick´
y
Department of Computer Science, Faculty of Electrical Engineering, CTU in Prague, Czech Republic
Abstract—The increasing use of private vehicles for transporta-
tion in cities results in a growing demand for parking space and
road network capacity. In many densely populated urban areas,
however, the capacity of existing infrastructure is insufficient and
extremely difficult to expand. Mobility-on-demand systems have
been proposed as a remedy to the problem of limited parking
space because they are able to satisfy the existing transportation
demand with fewer shared vehicles and consequently require less
parking space. Yet, the impact of large-scale vehicle sharing on
traffic patterns is not well understood. In this work, we perform
a simulation-based analysis of consequences of a hypothetical
deployment of a large-scale station-based mobility-on-demand
system in Prague and measure the traffic intensity generated
by the system and its effects on the formation of congestion.
We find that such a mobility-on-demand system would lead to
significantly increased total driven distance and it would also
increase levels of congestion due to extra trips without passengers.
In fact, 38% kilometers traveled in such an MoD system would
be driven empty.
I. INTRODUCTION
In many densely-populated urban areas, the use of privately-
owned automobiles as the main mode of transportation is
unsustainable. Private vehicles take up large amounts of space
when parked at a destination, require high-capacity highways,
and significantly contribute to air pollution. Mobility-on-
Demand (MoD) systems can help reduce the parking space
requirements by increasing the utilization of vehicles in the
system. A MoD system consists of a fleet of vehicles shared
by users of the system to realize their mobility needs. Taxi
service, Uber, or Lyft are examples of conventional MoD
systems; the affordability of the service can be further im-
proved by employing the self-driving technology [1]. Since a
typical shared vehicle serves more passengers during a day
than a typical personal vehicle, the same travel demand can
be satisfied with fewer shared vehicles than with personal
vehicles. The work presented here suggests that a properly
designed MoD system can achieve up to fivefold reduction
in the number of required vehicles. Moreover, due to higher
utilization, the cars in the system spend less time parked. Since
MoD systems consist of fewer vehicles, each spending less
time parked, mass adoption of this transportation paradigm
has a potential to drastically reduce demand for urban parking
space.
Despite having the clear benefit of reducing the parking
space requirements, it is also important to understand the
impact of large-scale vehicle sharing on total traffic intensity
and on formation of traffic congestion. Indeed, in order to
transport all the passengers, shared vehicles need to cover
at least the same distance as conventional personal vehicles.
However, unlike personal vehicles, shared on-demand vehicles
must also travel empty between the individual passengers, i.e.,
from the destination of the current passenger to the origin of
the following passenger. On top of that, passenger demands
are not distributed uniformly in time and space, which causes
vehicles to accumulate in some parts of the city and while
other areas may suffer from the shortage of vehicles. To ensure
that the each region of a city has a sufficient number of
available vehicles, the rebalancing has to be implemented,
i.e. vehicles must travel empty from areas with a surplus of
vehicles to areas with a shortage of vehicles [2]. Therefore,
on-demand transportation increases the total amount of traffic
in the system. In this paper, we use micro-simulation to
investigate the extent of this effect by measuring the impact of
empty trips on total vehicular traffic and formation of traffic
congestion.
A. State of the art
The properties and performance characteristics of MoD
systems have been previously studied either using simulation
or by formal analysis of mathematical models of such systems.
In [3], for example, a multi-agent simulation was used to
measure the impact of deployment of a small fleet of MoD
vehicles, and the results suggest that the fleet can be reduced
nearly twelve times, but the total distance traveled increases
by 10.7%. The authors also analyze the environmental impacts
such as the number of cold starts, founding that the emission
savings would be significant. Another simulation study [4]
compares the number of cars needed when using different
vehicle rebalancing methods. In results for offline and online
rebalancing, 28% and 23% fewer cars are needed compared
to the system without rebalancing.
The congestion effects of rebalancing in MoD system have
been numerically explored in [5] leading to the following
structural insight: Although the need for rebalancing in MoD
systems generates a significant amount of extra traffic, the
rebalancing vehicles travel in the opposite direction than the
vehicles carrying passengers, and thus they use lanes that
are currently underutilized. Numerical experiments in simple
synthetic networks indeed confirm the observation, suggesting
that if the demand traffic flows (vehicles carrying passengers)
are below road capacity limit, then the rebalancing flows
(rebalancing vehicles) will also not exceed the capacity and
consequently they will not introduce new congestion. Then
in [6] the problem of vehicle routing in congested networks
was modeled to formally study the impact of rebalancing on
formation on congestion. Assuming symmetric network and
time-invariant demand, the authors proved that if the demand
flows can be routed without exceeding free-flow capacity,
then the rebalancing vehicles can be also routed through
the network without exceeding road capacities. Further, they
performed experiments demonstrating that the method remains
effective even in real-world networks that are not perfectly
capacity symmetric. Also, the authors analyzed the system in a
steady state, i.e., they work with the assumption that the travel
demand is time-invariant. Clearly, real-world travel demand
changes over time (e.g., compare travel demand in the morning
peak and the demand at night), but, as the authors point out,
if the demand intensities change slowly relative to the average
trip duration, the model remains reasonably valid. In large
urban areas, however, the traffic intensity may rise drastically
over the time period of a single trip. Consider, for example,
a 30-minute car trip and the difference of traffic intensities
between 6:00 and 6:30, i.e., during the onset of morning peak.
Another aspect that has recently received significant atten-
tion is car sharing. For example, in [7] , authors study the
impact of large-scale ride-sharing and demonstrate that ride-
sharing can further reduce the number of vehicles needed to
satisfy the travel demand and moreover drastically reduce the
total traveled distance by the shared vehicle.
B. Our Contribution
In this paper, we study the impact of large-scale MoD
system deployment on total traffic intensity and formation of
congestion using simulation. Unlike other existing works, 1)
we simulate the system over the period of entire day (24h),
which is important to properly account for the changes in
travel demand intensities, 2) we use real road network of
Prague (cz), which is not capacity symmetric, 3) we use traffic
demand data that is representative of real traffic demand in
Prague both in structure and scale and 4) we simulate the
entire lifetime of an on-demand vehicle including pick-up and
drop-off trips.
This higher-fidelity model allows obtaining new insights
into the impacts of massive deployment of MoD systems. In
particular: 1) the model highlights the contribution of pick-up
and drop-off trips to the formation of congestion in station-
based MoD systems and 2) it suggests that if the demand
cannot be routed through the road network without exceeding
the free-flow capacity, then the deployment of MoD system
may actually worsen the congestion situation.
II. BAC KG ROUND MATERIAL
In traffic engineering, the effects of traffic congestion on
a road segment are modeled by the fundamental diagram of
road traffic [8], which relates traffic density to traffic flow.
Traffic density is the number of vehicles per unit of distance of
the road segment, while traffic flow is the number of vehicles
passing a reference point per unit of time. When traffic density
grows, traffic flow also increases until it reaches a tipping point
after which the flow starts dropping due to congestion. The
tipping point is known as the critical density [9]. The exact
shape of the diagram is typically determined by fitting em-
pirical data from real-world observations of vehicular traffic.
Subsequently, we will use the traffic density as a measure of
utilization of a particular road segment and the critical density
value yc= 0.08 vehicle m−1from [10]. The road segments
with traffic density above critical density ycwill be referred
to as congested road segments.
III. METHODOLOGY
The effect of a hypothetical large-scale deployment of MoD
in Prague is analyzed using simulation as follows. Firstly,
using a demand model, we synthesize a set of trips that
statistically correspond to trips by private cars performed
during a typical work day. Then, we design a MoD system that
is capable of serving those trips with a satisfactory quality of
service. After that, we perform a simulation of two scenarios:
1) In conventional system scenario, all trips are served by
private vehicles. 2) In MoD system scenario, the trips are
served by a large MoD system. During simulation, we record
information about road utilization and the service quality
within the system. Finally, we compare the data collected in
the two simulated scenarios. We will now discuss each step
in detail.
A. Input data
The set of trips that represent the transportation demand is
generated by the multi-agent activity-based model of Prague
and Central Bohemian Region introduced in [11]. In contrast
to traditional four-step demand models [12], which use trips as
the fundamental modeling unit, activity-based models employ
so-called activities (e.g. work, shop, sleep) and their sequences
to represent the transport-related behavior of the population.
Travel demand is then occurring due to the necessity of
the agents to satisfy their needs through activities performed
at different places at different times. These activities are
arranged in time and space into sequential (daily) schedules.
Trip origins, destinations and times are endogenous outcomes
of activity scheduling. The activity-based approach considers
individual trips in context and therefore allows representing
realistic trip chains.
The model used in this work covers a typical work day in
Prague and Central Bohemian Region. The population of over
1.3 million is modeled by the same number of autonomous,
self-interested agents, whose behavior is influenced by de-
mographic attributes, current needs, context, and cooperation.
Agent’s decisions are implemented using machine learning
methods (e.g. neural networks and decision trees) and trained
using multiple real-world data sets, including census data or
travel diaries and similar transportation-related surveys.
Planned activity schedules are subsequently simulated and
tuned, and finally, their temporal, spatial and structural prop-
erties are validated against additional historic real-world data
(origin-destination matrices and surveys) using six-step vali-
dation framework VALFRAM [13]. The model generates over
3 million trips per one 24-hour scenario. For our analysis, we
Fig. 1: MoD system stations in the city of Prague. Stations
are shown as circles. Spatial distribution of origins and desti-
nations of travel demands is depicted using brown dots.
selected the subset of 981 775 trips that were performed in a
private vehicle.
B. On-demand system design
In order to serve the trips generated by the demand model,
we need to determine 1) the size of the on-demand fleet and 2)
a policy for vehicle rebalancing within the system. We adopt
a station-based design of the MoD system [2]. That is, we
partition the city into n= 40 regions using k-means clustering
over the demand data and we assume that there is a station
at the center of each such region. Stations serve as temporary
parking lots for idle vehicles and they also contain facilities
such as refueling/charging and cleaning. When a passenger
requests a ride, a vehicle is dispatched from the nearest station
to the passenger and drives to pick up the passenger. Then,
it carries the passenger to its desired destination, where the
passenger is dropped off. Finally, the vehicle parks again in
the nearest station to the drop-off location. The result of this
process is shown in Figure 1. The number of regions was
chosen such that the average travel time from station to a
passenger is below 3 minutes.
When a passenger requests a vehicle and the nearest station
is empty, the customer cannot be served immediately and
either has to wait for a vehicle to become available or a vehicle
from a distant station must be dispatched, leading to long
waiting time and consequently to customer dissatisfaction.
Unfortunately, existing MoD systems are prone to such events
due to the unbalanced structure of transportation demand. For
instance, during the morning peak, the vehicles are typically
requested for pickup in residential areas, but they subsequently
end up in business districts. In results, the stock of vehicles in
residential areas is shrinking, while unused vehicles are accu-
mulating at business areas. This problem can be mitigated by
continuous redistribution of vehicles from areas with a surplus
Fig. 2: AgentPolis visualization of the traffic in Prague at
07:00.
of vehicles to areas with a shortage of vehicles. This process
is often referred to as rebalancing. In our hypothetical MoD
system, we use linear programming based approach to balance
the vehicle flows in the system [14]. Due to time-varying
demand and significant travel delays in the real-world system,
the flows, however, cannot be balanced perfectly at every time
point and consequently there must be a sufficient number
of vehicles at each station to cover temporary shortages of
vehicles. We determine the initial number of vehicles that
are needed at each station experimentally, by deterministically
simulating the evolution of the system and then by ensuring
that each station has enough vehicles to never become empty.
Using this process, we found that the system requires 51 249
vehicles.
C. Multi-agent simulation
In order to test the impact of the MoD system deployment
on the road network utilization, we have implemented a
multi-agent simulation of vehicular traffic in Prague based on
AgentPolis1simulation framework.
AgentPolis is a large-scale multi-agent discrete-event sim-
ulation over a simulated environment that consists of: a) road
network composed nodes connected by road segments (edges),
b) stations in which on-demand vehicles park, c) on-demand
vehicle agents, d) passengers agents. The visualization of the
whole city of Prague as simulated in AgentPolis is in Figure 2.
A video from the simulation is available at youtube.com2.
The topology of the road network is taken from Open-
StreetMap3, resulting in a road network consisting of 306625
edges and 286009 nodes. The speed limit for all edges was
set to 40 km h−1.
During initialization, we create the vehicles representing
the on-demand fleet and assign them to appropriate stations
(as computed during MoD system design phase). During
1https://github.com/agents4its/agentpolis
2https://youtu.be/e1SNCPrHo7w
3https://www.openstreetmap.org/
simulation, at time points corresponding to travel demand from
the input demand set, we create a passenger agent for the travel
demand. The life cycle of one travel demand in the simulation
is following:
1) A demand agent is created for the demand in the place
where the demand trip starts.
2) A vehicle from the nearest station is assigned to serve
the demand. We plan the shortest path to the passenger
and the vehicle drives it moves to the pick-up location.
(pick-up trip).
3) The vehicle picks up the passenger agent and carries the
passenger to the desired destination location. (demand
trip).
4) The passenger agent is removed from the simulation.
5) The vehicle returns to the nearest station. (drop-off trip).
If there is no available vehicle in the nearest station in point 2,
the passenger agent is removed from the simulation, and it is
considered as an unsatisfied demand.
Rebalancing schedule is computed at the on-demand phase
and prescribes the number of empty vehicles to be moved
between every two stations in each 10-minute time slice. Based
on the rebalancing schedule, we order the required number of
vehicles to drive between the two stations along the shortest
path (rebalancing trip).
Every ten minutes, we count the number of vehicles of each
category (pick-up, demand, drop-off, rebalancing) that drive
on every road segment, which can be used to compute traffic
density at those segments.
IV. RES ULTS
In this section, we discuss the result of our simulation. We
will focus on the analysis of traffic patterns between 7:00
and 8:00, which is the time period with highest road network
utilization. Figure 3 shows heat maps depicting traffic densities
on all roads in Prague for selected trip types. In particular,
Figure 3-a shows the overall traffic density in the MoD system.
Figure 3-b to 3-e shows the traffic density contributions of
different trip types. Note that Figure 3-c, in fact, shows the
traffic density in the conventional system because the demand
trips are the same trips that are driven by privately owned
vehicles. Comparing the Figure 3-a to 3-c, we can clearly
see that deployment of the MoD system would increase traffic
intensity within the road network. Figure 3-f shows the conges-
tions introduced by the MoD system, i.e., the road segments
that were below critical density in the conventional system
(only counting contributions of demand trips), but exceeded
critical density when we add the contribution of empty trips
(pick-up, drop-off, and rebalancing). The number of lanes on
each road segment was considered when computing the critical
density, and the critical density was computed separately for
each direction.
In Table I, we list the share on the total distance traveled for
each trip type. Note that the three MoD system specific trip
types (rebalancing, pick-up, and drop-off trips) are responsible
for more than a third of the total distance traveled (37.7%).
TABLE I: The share of the trip types on total travel distance
and on congestion (share on traffic density on roads with traffic
density higher than 50% of the critical density).
Trip type Avg. km/vehicle/day Share on dist. Share on cong.
Demand trip 159 62.3% 61.3%
Pick-up trip 31 12.1% 17.3%
Drop-off trip 31 12.0% 14.4%
Rebalancing trip 35 13.6% 6.9%
Figure 4 shows the histogram of traffic density levels in
the conventional system, before the MoD system deployment.
For the simplicity of presentation, we excluded all road
segments with traffic density lower than 1% of the critical
density (0.0008 vehicle m−1) from all histograms because they
represent roads that are rarely ever used. These road segments
represent 86.3% and 82.3% of all road segments for the con-
ventional system and the MoD system respectively. To show
a reasonable detail of the traffic density levels, there is also a
focused histogram that contains only edges with traffic density
greater than 50 % of the critical density (0.04 v ehicle m−1).
Figure 5 shows the histogram after deployment of the MoD
system. It indeed confirms that there is a considerable increase
of the traffic density. To investigate how different trip types
contribute to the increased traffic density, we measured the
share of traffic density per trip type for each edge and sep-
arated these shares into stacks. The data from this histogram
was aggregated into Table I for easier interpretation.
A. Rebalancing
We will now focus on rebalancing trips. The general in-
sights into the congestion effects of rebalancing stipulating
that rebalancing does not contribute to congestion because
the rebalancing trips have the opposite direction than other
traffic and thus the rebalancing vehicles use underutilized road
lanes was partially confirmed. As we can see in our results,
rebalancing has only 6.9% share on congestion, despite having
13.6% share on total distance driven (Table I).
B. Pick-up and drop-off trips
Pick-up and drop-off trips have a significant effect on both
travel distance and congestion. Our results show that these
two trip types together are responsible for almost quarter
(24.1%) of the total distance traveled and more importantly,
they have nearly a third of the share on total congestion (31.7%
– Table I). Although this number can be probably reduced by
increasing the number of the MoD stations, it is clear that the
contribution of pick-up and drop-off trips cannot be ignored
when designing an MoD system.
V. DISCUSSION
The simulation results indicate that all types of empty trips
contribute significantly to both total traveled distance and
congestion. The impact on traveled distance is inevitable and
can only be reduced by increasing the number of stations,
which shortens pick-up and drop-off trips, or vehicles, which
reduces the need for rebalancing. The impact of the empty
Fig. 3: Traffic density levels between 7:00 and 8:00. a) The traffic density after the deployment of the MoD system. b) Traffic
density – pick-up trips c) Traffic density – demand trips. This image represents the traffic density levels on roads in the current
state, without MoD system. d) Traffic density – drop-off trips. e) Traffic density – rebalancing trips. f) The roads on which
the traffic exceeded the critical density after deployment of the MoD system.
Fig. 4: Histogram of the traffic density in the current state
(demand trips only). Edges with traffic density greater than
200% of critical density (0.16 veh m−1) are represented by
the last bin.
trips on congestion is more interesting. Pick-up and drop-off
trips have a significantly larger share on traffic density than
the share on traveled distance. This effect can be explained
by the fact that these trips are not distributed uniformly, on
the contrary, they are accumulated creating clusters around the
Fig. 5: Stacked histogram of the traffic density after MoD
system deployment, created by the same methodology as the
focused histogram in Figure 4.
MoD system stations (see Figure 3-b and Figure 3-d ).
Although the contribution of rebalancing trips to congestion
is disproportionately smaller than the contribution to total
distance driven, it is still significant. This is perhaps surprising,
since previous numerical and experimental results [5], [15]
may suggest that rebalancing does not increase congestion. We
could attribute this discrepancy to the invalidity of assumptions
used by [15] in our setting, but there are other possible
explanations. First, our routing is not ”congestion-aware”,
vehicles drive to their destination using the shortest path.
This setup is different from the referenced work, where the
routes of rebalancing vehicles are coordinated to prevent the
formation of congestion. Second, the result from [15] states
that if the passenger flows can be routed through the network
without exceeding road capacities, then vehicle rebalancing
can be also routed without exceeding road capacities. As our
results (and everyday experience) shows, the traffic network
is unfortunately significantly congested already at the current
state, i.e., under the conventional system. Therefore, even if
the rebalancing flows were optimally routed, they may exceed
the road free-flow capacities leading to increased congestion.
So far, we can only guess how much is the 6.9% share of
rebalancing on congestion caused by non-optimal routing and
initial congestion, and how much it is caused by the fact that
the simulated scenario does not satisfy the assumptions of the
above theoretical analysis.
Another aspect that we did not model is the congestion
effect in the simulation. In real traffic scenario, congestion
tends to spread over the network and affect roads whose
traffic density is not above the critical density. This effect
is not implemented in our simulation, and thus our results
underestimate the scale of congestion. Moreover, we simulate
the traffic flow as an uninterrupted flow, i.e. we do not model
travel delays on intersections.
VI. CONCLUSION
Large-scale deployment of mobility-on-demand systems in
cities can dramatically reduce the number of vehicles needed
to satisfy existing transportation demand and consequently
reduce the need for parking. The impact of such systems on
road utilization and traffic congestions is however relatively
less understood. In this paper, we studied the impact of large-
scale MoD system deployment on urban traffic patterns using
multi-agent simulation.
We ran a one-day simulation of a hypothetical large-scale
MoD system that serves trips that represent the transportation
demanded currently realized by private vehicles in Prague. We
analyzed the results and compared the road utilization in the
current state (conventional system) and in the MoD system.
Simulation results clearly showed that there would be an
increase in both total traveled distance and traffic density after
switching from conventional vehicles to on-demand vehicles.
The total share of empty trips (i.e., drop-off, pick-up, and
rebalancing) on traveled distance was 37.3% with rebalancing
accounting for 13.6%. The total share of these trip types on
traffic density on the roads with traffic density greater than
50% of critical density was very similar – 38.7%, but here the
rebalancing contributes only 6.9%.
These results confirmed the hypothesis that the rebalancing
does not contribute to congestion as much as it contributes to
traveled distance because rebalancing vehicle drives against
passenger-carrying vehicles, but still, the impact of the re-
balancing on congestion is significant. Moreover, the results
exposed the importance of the negative impact the station base
model has on congestion. This is probably caused by high
concentration of the pick-up and drop-off trips around the
stations, and thus it can be reduced by increasing the number
of the stations or by using free-floating fleet.
In future, we will focus on the development of more sophis-
ticated congestion models, validation using data from transit
sensors, and investigation of the potential of ride sharing to
reduce road utilization.
ACKNOWLEDGMENT
This work was supported by the Grant Agency of
the Czech Technical University in Prague, grant No.
SGS16/235/OHK3/3T/13.
REFERENCES
[1] Todd Litman. Autonomous vehicle implementation predictions - im-
plications for transport planning. Technical report, Victoria Transport
Policy Institute, 2017.
[2] Kevin Spieser, Kyle Treleaven, Rick Zhang, Emilio Frazzoli, Daniel
Morton, and Marco Pavone. Toward a systematic approach to the
design and evaluation of automated mobility-on-demand systems: A case
study in singapore. In Gereon Meyer and Sven Beiker, editors, Road
Vehicle Automation, Lecture Notes in Mobility, pages 229–245. Springer
International Publishing, 2014.
[3] Daniel J. Fagnant and Kara M. Kockelman. The travel and environmental
implications of shared autonomous vehicles, using agent-based model
scenarios. Transportation Research Part C: Emerging Technologies, 40:1
– 13, 2014.
[4] Marczuk, Katarzyna A., Soh, Harold S.H., Azevedo, Carlos M.L., Lee,
Der-Horng, and Frazzoli, Emilio. Simulation framework for rebalancing
of autonomous mobility on demand systems. MATEC Web Conf.,
81:01005, 2016.
[5] Rick Zhang and Marco Pavone. Control of Robotic Mobility-on-demand
Systems. Int. J. Rob. Res., 35(1-3):186–203, January 2016.
[6] Rick Zhang, Federico Rossi, and Marco Pavone. Routing Autonomous
Vehicles in Congested Transportation Networks: Structural Properties
and Coordination Algorithms. ArXiv e-prints, March 2016.
[7] Javier Alonso-Mora, Samitha Samaranayake, Alex Wallar, Emilio Fraz-
zoli, , and Daniela Rus. On-demand high-capacity ride-sharing via
dynamic trip-vehicle assignment. Proceedings of the National Academy
of Sciences of the United States of America, 114(3):462 – 467, 2016.
[8] Frank A. Haight (Eds.). Mathematical Theories of Traffic Flow.
Mathematics in Science and Engineering. Elsevier Science, 1963.
[9] Boris S. Kerner (auth.). Introduction to Modern Traffic Flow Theory and
Control: The Long Road to Three-Phase Traffic Theory. Springer-Verlag
Berlin Heidelberg, 2009.
[10] Shin-ichi Tadaki, Macoto Kikuchi, Minoru Fukui, Akihiro Nakayama,
Katsuhiro Nishinari, Akihiro Shibata, Yuki Sugiyama, Taturu Yosida,
and Satoshi Yukawa. Critical Density of Experimental Traffic Jam, pages
505–511. Springer International Publishing, Cham, 2015.
[11] M. ˇ
Certick´
y, J. Drchal, M. Cuch´
y, and M. Jakob. Fully agent-based
simulation model of multimodal mobility in European cities. In 2015
International Conference on Models and Technologies for Intelligent
Transportation Systems (MT-ITS), pages 229–236, June 2015.
[12] Button Kenneth J. Hensher, David A. Handbook of Transport Modelling:
2nd Edition. Emerald, Inc., 2007.
[13] Jan Drchal, Michal ˇ
Certick´
y, and Michal Jakob. Data Driven Validation
Framework for Multi-agent Activity-Based Models. In Multi-Agent
Based Simulation XVI, pages 55–67. Springer, Cham, May 2015.
[14] Marco Pavone, Stephen L Smith, Emilio Frazzoli, and Daniela Rus.
Robotic load balancing for mobility-on-demand systems. The Interna-
tional Journal of Robotics Research, 31(7):839–854, June 2012.
[15] Rick Zhang, Federico Rossi, and Marco Pavone. Routing Autonomous
Vehicles in Congested Transportation Networks: Structural Properties
and Coordination Algorithms. arXiv:1603.00939 [cs], March 2016.
arXiv: 1603.00939.