An Optimization-based Strategy for Shared Autonomous Vehicle Fleet
Repositioning
Felipe de Souza
1
, Krishna Murthy Gurumurthy
2
, Joshua Auld
1
and Kara M. Kockelman
2
1
Argonne National Laboratory, 9700 Cass Avenue, Lemont, IL, U.S.A.
2
Department of Civil, Architectural and Environmental Engineering, University of Texas at Austin, Austin, TX, U.S.A.
Keywords:
Shared Autonomous Vehicles, Repositioning, Agent-based Simulation, POLARIS, Bloomington.
Abstract:
With the emergence of autonomous technology, shared autonomous vehicles (SAVs) will potentially be the
prevalent transportation mode for urban mobility. On one hand, relying on SAV fleets can provide several op-
erational benefits. On the other hand, SAVs can increase travel distance and add congestion due to unoccupied
trips such as pickup and repositioning trips. One important aspect for a SAV fleet’s success is to serve the
incoming requests at reasonably low waiting time. This is achieved by an adequate fleet size that is spatially
distributed thoughtfully so that incoming requests can be served by a nearby vehicle. Unfortunately, it is chal-
lenging to keep a satisfactory spatial distribution of vehicles due to imbalances in the origin and destination
patterns of incoming requests. This paper focuses on the impact of SAV relocation on traveler wait times
using a novel optimization-based algorithm for repositioning. POLARIS, an agent-based tool, is used for a
case study of Bloomington, Illinois to quantify the benefits of allowing SAV repositioning. On average, the
wait times were around 20% lower with repositioning for all adequate fleet sizes. SAVs were available more
uniformly across the region’s zones, and proportional to trip-making at different times of day. In addition,
enabling repositioning led to a higher share of demands being served. These benefits, however, are achieved
at the expense of 6% added vehicles miles traveled.
1 INTRODUCTION
With the emergence of autonomous vehicles, trav-
elers may relinquish their own private vehicles and
rely on a fleet of shared autonomous vehicles (SAV’s)
(Spieser et al., 2014; Fagnant and Kockelman, 2014;
Fagnant and Kockelman, 2015; Bischoff and Ma-
ciejewski, 2016; Stoiber et al., 2019) operating sim-
ilarly to current Transportation Network Companies
such as Uber and Lyft. On one hand, this shift
can bring advantages such as the reduction of num-
ber of vehicles and lower the need for parking and
garage spaces (Fagnant and Kockelman, 2015). On
the other hand, the operation of SAV fleets can lead
to significant unoccupied travel which can poten-
tially worsen congestion, despite the increased capac-
ity expected by autonomous vehicles (e.g., (Shladover
et al., 2012)). Therefore, the operational strategies of
SAV fleets should be such that they minimize empty
travel while serving travelers in a timely manner.
Empty trips occur or empty vehicle miles traveled
(eVMT) in the current human-driven TNC services,
as well as with SAV fleets, in three different ways.
First, the pickup trip for an assigned vehicle from its
current location to the traveler location. Second, the
trip performed at the beginning and end of a driver’s
shift from and to home, or a depot in the case of a
SAV vehicle. Third, a repositioning trip from an area
of low demand to an area with higher demand. In the
case of human drivers, these trips are undertaken with
the goal of reducing the time to serve a request and
thereby increasing revenue at the expense of the addi-
tional empty trip’s cost. In the case of autonomous ve-
hicles, these trips occur to better serve future requests.
There is some uncertainty on the share of empty travel
in previous studies, and the extent to which dynamic
ride-sharing can help. Recent literature has found that
around 40% of the current TNC (Uber and Lyft) travel
is empty (Henao and Marshall, 2019).These estimates
are much lower for SAVs. Berlin study suggests the
percent empty travel time as 17% (Bischoff and Ma-
ciejewski, 2016), whereas Austin scenarios, with and
without pooling, averaged between 6 and 15% eVMT
(Simoni et al., 2019; Gurumurthy et al., 2019).
Repositioning trips are important even though
they add empty miles. The necessity of such trips
370
de Souza, F., Gurumurthy, K., Auld, J. and Kockelman, K.
An Optimization-based Strategy for Shared Autonomous Vehicle Fleet Repositioning.
DOI: 10.5220/0009421603700376
In Proceedings of the 6th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2020), pages 370-376
ISBN: 978-989-758-419-0
Copyright
c
2020 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
arise from an imbalance between the origin and des-
tination locations of incoming requests. Areas that
are common trip destinations (i.e, dropoff location)
but not common origins accumulate vehicles while
a dearth of vehicles is observed in areas that have
many trip origins. The strategy proposed by (Alonso-
Mora et al., 2017) found that 20% more trips can be
served when repositioning is allowed. Another study
proposed an assignment strategy that concurrently as-
signs vehicles to travelers while also dispatching vehi-
cles to areas with high demand based on the expected
future demand (Dandl et al., 2019). The share of repo-
sitioning miles ranged from 3 to 6% across all the
simulation scenarios while the pickup miles remained
around 12% of total miles.
In this study, the impact of SAV repositioning
is studied at scale using the POLARIS agent-based
framework. A computationally efficient repositioning
strategy for SAV operation was implemented, and the
operational results for the entire region of Blooming-
ton, Illinois is discussed. The next section discusses
the simulation framework, SAV modeling method-
ology and the repositioning algorithm. This is fol-
lowed by results and discussions for the case study of
Bloomington, Illinois, and finally ends with a conclu-
sion.
2 POLARIS SIMULATION
FRAMEWORK
POLARIS (Auld et al., 2016) is an agent-based
framework for transportation systems that is designed
to simulate large metropolitan areas. Elements of the
simulated area and persons are modeled as individual
agents that take decisions as the simulation evolves
and is often refered to as a discrete event-based simu-
lation. Specifically, POLARIS features an activity-
based-model for the travel demand behavior, along
with traffic flow and dynamic traffic assignment mod-
els. More recently, POLARIS also boasts a module
for SAV simulation (Gurumurthy et al., 2020).
The travel behavior is captured by the ADAPTS
activity-based model (Auld and Mohammadian,
2009; Auld and Mohammadian, 2012) which mod-
els various travel decisions ranging from within-day,
mid-term and long-term choices. The mid-term and
within-day travel behavior decisions include the pro-
cess of individual activity episode planning and en-
gagement. These decisions are constrained by long-
term choices regarding home and workplace choice,
and household vehicle choices, and, in turn, influence
activity and travel planning.
Specific mode choices is modeled as an outcome
of discrete choice models. POLARIS uses three sep-
arate mode-choice models depending on the activ-
ity purpose: home-based work/school, home-based
other and non-home based, similar to traditional mod-
eling. The nested-logit formulation used to model
mode choice include nine modes: drive alone, TNC
use, ride as passenger, walk, bike, bus with walk ac-
cess, bus with drive access, rail with walk access, and
rail with drive access. Among these, drive alone and
TNC use are grouped under the auto nest, and the
two rail modes are grouped under the rail nest. The
model includes a variety of demographic variables,
accessibility information, as well as level of service
(LOS) variables. The demographic variables include
individual demographics such as education, employ-
ment status, possession of driver’s license, and house-
hold demographics such as household income, house-
hold size, and vehicle and bike ownership among oth-
ers. Road-network density and activity density of
the destination zone are used to capture the charac-
teristics of land use and the transportation network.
The TNC-specific Level of Service (LOS) variables
used in the model include in-vehicle travel time and
wait time (obtained from the simulation), and in-
put fare. The TNC fare comprises of a fixed cost
per trip, a distance-varying component, and a time-
varying component. The model is developed and cal-
ibrated against the household travel survey data col-
lected from the local region’s metropolitan planning
organization.
The realized travel times and delays along the
simulation period is an outcome of traffic flow and
dynamic traffic assignment models. The underlying
traffic flow model is based on the link transmission
models (Yperman, 2007) which in turn is based on
Newell’s kinematic wave model (Newell, 1993) with
further adaptation to be able to track individual vehi-
cles along their journey (de Souza et al., 2019). The
dynamic traffic assignment algorithm (Auld et al.,
2019a) assign routes to individual vehicles using a
time-dependent A* shortest path router (Verbas et al.,
2018) based on the prevailing traffic condition, as well
as updated skim travel times. Traveler’s routing be-
havior in response to delays is also captured by al-
lowing re-routing.
The effects of real-time information and impacts
of connected and automated vehicles - from both de-
mand and supply sides - are also captured. This al-
lows for exploratory studies on the impact of con-
nected and automated vehicles in the overall trans-
portation networks (Auld et al., 2019b), as well as the
impact of shared mobility services in the presence of
connected and automated vehicles (Gurumurthy et al.,
2020).
An Optimization-based Strategy for Shared Autonomous Vehicle Fleet Repositioning
371
3 SAV SIMULATION
The shared mobility simulation implemented in PO-
LARIS (Gurumurthy et al., 2020) is extended here to
evaluate the proposed repositioning strategy. SAVs
are modeled to mimic operations that are currently
observed in Transportation Network Companies’ op-
eration. The operator assigns requests to individual
vehicles depending on the assignment strategy and
monitors the spatial distribution of vehicles to de-
termine repositioning decisions. SAVs execute the
pickup, dropoff and repositioning tasks depending on
the instruction received from the operator. SAVs are
able to store requests that are being executed and
those that need to be executed in the future. A de-
tailed overview of the operator and vehicle operations
is available at (Gurumurthy et al., 2020; de Souza
et al., 2020).
3.1 Repositioning Strategy
The repositioning strategy aims to transfer vehicles
from areas experiencing a high supply to areas expe-
riencing a dearth of vehicles. This occurs due to an
imbalance in the origin destination pattern of the in-
coming requests. Areas that are common trip destina-
tions but not common origins tend to accumulate ve-
hicles. Conversely, areas that are common trip origins
experience vehicle shortage. Therefore, it is neces-
sary to relocate idle vehicles into those areas in order
to better serve future requests.
The repositioning strategy is based on zone-level
variables. For each zone i, we define the supply s
i
as the number of idle vehicles on zone i added of the
number the non-idle vehicles whose the destination
of last operation is at zone i (i.e., dropoff at zone i
or repositioning to zone i), v
i
as the number of idle
vehicles at zone i. We also define f
i
as the mini-
mum supply at zone i. This minimum supply is an
input to the proposed method. The minimum supply
should roughly track the incoming demand for a given
zone. In the following paragraphs we provide the ba-
sic guidelines to define f
i
.
The goal of the strategy is to keep s
i
higher than
the minimum supply, f
i
. The repositioning decision
across the region is obtained through the following
optimization problem:
min
x
i, j
J =
i
j
x
i, j
t
i, j
j
x
j,i
j
x
i, j
+ s
i
f
i
i
j
x
i, j
v
i
i
x
i, j
0 (i, j),
(1)
where x
i, j
is the number of vehicles that relo-
cates from zone i to zone j and t
i, j
is the travel time
from zone i to zone j or any zone-to-zone cost that
is deemed appropriate. The optimization problem (1)
is linear and therefore this problem can be efficiently
solved with widely available solvers. Observe that
variable x
i, j
must be integer as each unit is associ-
ated to a given vehicle repositioning from one zone to
another. However, the constraints are unimodular and
the costs are linear which guarantees that the solution
of (1) yields discrete values as long as f
i
is also inte-
ger. Unimodularity was also exploited in (Hyland and
Mahmassani, 2018).
In addition, depending on the supply, s
i
, the num-
ber of idle vehicles, v
i
, a high f
i
can turn the optimiza-
tion problem infeasible. For example, if there is no
idle vehicles (i.e., v
i
= 0 i) and at least one zone in
which s
i
< f
i
, the problem has no solution since there
are no available vehicles to be relocated.
Therefore, there are two prerequisites for the min-
imum supply f
i
when the optimization problem is in-
stantiated: (i) it must be integer; (ii) it should be small
enough so that the optimization problem is feasible.
With respect to feasibility, we can evaluate whether
a particular f = [ f
1
, ..., f
I
] given s = [s
1
, ..., s
I
] and
v = [v
1
, ..., v
n
] if:
i
(max{ f
i
s
i
, 0})
i
(max{min{s
i
f
i
, v
i
}, 0}),
(2)
that is, the term max{ f
i
s
i
, 0} yields the minimum
number of vehicles that needs to be relocated to zone
i while he right-hand-side accounts for the number of
vehicles that zone i can supply to other zones.
We set f
i
as follows. We assume a predicted de-
mand d
i
for zone i and we set f
i
as:
f
i
= bαd
i
c, (3)
with the highest α in the interval [0, 1] that satisfies
the feasibility constraint (2) (bxc is the integer part of
x). Methods such as bisection can be used to find the
highest α that satisfies the constraint. Here we per-
form a line search starting from α = 1 and reducing
with rate β < 1 as α := βα until (2) is satisfied.
In summary, the following steps are performed:
1. Retrieve all s
i
and v
i
based on the current vehicles’
statuses.
2. Obtain the predicted demand d
i
(based on histori-
cal data or previous requests).
3. Obtain an α that satisfies (2).
4. Instantiate and solve the optimization problem
(1).
VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems
372
5. Dispatch vehicles based on the solution x
i, j
.
Here we assume the repositioning decisions are
made at constant time steps (for example, every 5
minutes).
4 SIMULATION RESULTS
The repositioning strategy outlined above was tested
for the Bloomington region in Illinois, USA. The net-
work contains 185 zones, 7000 links, and 2500 nodes.
The mode choice parameters are tuned to the current
travel trends and yielded around 30,000 trip requests
for the 24 hour simulation period. Three different fleet
sizes of 650, 700, and 750 SAVs were tested with, and
without, repositioning.
For all cases, the maximum waiting time is set
to 10 minutes (i.e., the maximum pickup time for a
SAV is 10 minutes as estimated before the start of
the pickup trip. The realized travel time might be
higher if traffic conditions changes). When reposi-
tioning is enabled, repositioning decisions are taken
every 5 minutes, and d
i
is obtained based on the num-
ber of requests on zone i in the previous 30 minutes of
simulation. The GLPK solver (Makhorin, 2001) was
used to solve optimization problem (1) at every step.
Table 1 presents the key metrics for each scenario.
Without repositioning, the share of empty miles lies
around 30% and it increased to around 33% in the
cases in which repositioning was enabled. This in-
crease in VMT allowed a lower share of the VMT
in pickup trips since vehicles are repositioned to high
demand areas. This allowed a average wait time 20%
shorter when repositioning is available. Meanwhile,
the share of served trips at peak time has increased
for all fleet sizes.
The share of trips that were served and unserved
over the 24 hr time period for all fleet sizes is depicted
in Figure 1. Blue and orange lines correspond to the
scenario without repositioning, and the green and red
lines correspond to the scenario with repositioning.
The fleet sizes are 650, 700, and 750 from the top to
bottom. In all cases, enabling repositioning led to an
increase in the share of served trips with the difference
being larger for smaller fleets.
The repositioning method also lowers waiting
time. Figure 2 depicts the distribution of waiting time
for fleet sizes of 650 (top), 700 (middle), and 750
vehicles (bottom) with (in red) and without (in blue)
repositioning. The vertical lines in red and blue high-
light the average waiting time for each case, respec-
tively.
The efficiency of an SAV fleet can be observed by
assessing the daily operation profile. Figure 3 shows
Figure 1: Share of Served and Unserved Trips for the Three
Fleet Sizes with and without Repositioning Enabled.
the share of SAVs idle, or performing pickup, dropoff
or repositioning for the two scenarios with and with-
out repositioning. When repositioning is enabled, the
entire fleet is utilized at peak times of day, if neces-
sary. This is not true in the absence of repositioning
when SAVs are idling at low demand areas.
5 CONCLUSIONS
An optimization-based method for SAV fleet reposi-
tioning is proposed. Vehicles in zones with excess
supply are moved into areas where the supply is in-
sufficient to serve the incoming demand. The method
is formulated as a Linear Program with decision vari-
An Optimization-based Strategy for Shared Autonomous Vehicle Fleet Repositioning
373
Table 1: Summary of the Results for the Three Different Fleet Sizes with and without Repositioning. Pickup VMT Is Labeled
as pVMT, Repositioning Vmt as rVMT and Empty VMT as eVMT.
Fleet VMT % pVMT % rVMT % eVMT % Served at Peak Wait Time (min)
Without Repositioning
650 205,475 30.3 0.0 30.3 83.5 4.52
700 206,403 29.6 0.0 29.6 85.3 4.32
750 202,513 28.3 0.0 28.3 88.8 4.07
With Repositioning
650 221,843 24.3 9.2 33.5 92.0 3.49 (-23%)
700 223,002 23.3 10.0 33.2 95.5 3.37 (-22%)
750 220,431 22.5 10.5 33.1 96.3 3.24 (-20%)
Figure 2: Histogram of Waiting Times for Different Fleet
Sizes with (Red) and without (Blue) Repositioning.
ables based at the zone level. This brings two key
advantages: (i) being a Linear Program, the method is
computationally efficient; (ii) the computational com-
plexity does not grow with the fleet size, since the
number of vehicles is encoded as a variable as op-
Figure 3: Fleet Operation Profile without (Left Graph) and
with (Right Graph) Repositioning Enabled for S = 650.
posed to enumerating decisions specific for each ve-
hicle in the network.
In experiments for a medium-sized network, en-
abling the repositioning strategy led to an increase in
the share of served requests, as well as a reduction in
waiting times of up to 20%. The benefits occurs at
expense of higher empty distance traveled. The addi-
tional distance from repositioning partially balances
with the added empty pickup distance, and, therefore,
improves the fleet’s service characteristics. In all, the
results suggest the additional empty miles is signifi-
cant smaller than the strategy introduced in (de Souza
et al., 2020).
For future work, we plan to perform a thorough
performance analysis using larger networks like that
of the Chicago region. In addition, we want to investi-
gate the influence of inaccuracies of the model inputs,
VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems
374
especially with respect to the incoming demands, as
well as the effect of different time steps for perform-
ing repositioning decisions.
ACKNOWLEDGEMENTS
This report and the work described were sponsored by
the U.S. Department of Energy Vehicle Technologies
Office under the Systems and Modeling for Accel-
erated Research in Transportation Mobility Labora-
tory Consortium, an initiative of the Energy Efficient
Mobility Systems Program. David Anderson, a De-
partment of Energy Office of Energy Efficiency and
Renewable Energy manager, played an important role
in establishing the project concept, advancing imple-
mentation, and providing ongoing guidance.
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