An Optimization-based Strategy for Shared Autonomous Vehicle Fleet

Repositioning

Felipe de Souza

, Krishna Murthy Gurumurthy

, Joshua Auld

and Kara M. Kockelman

Argonne National Laboratory, 9700 Cass Avenue, Lemont, IL, U.S.A.

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

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

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

as the number of idle

vehicles at zone i. We also deﬁne f

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

The goal of the strategy is to keep s

higher than

the minimum supply, f

. The repositioning decision

across the region is obtained through the following

optimization problem:

min

i, j

J =

∑

∀i

∑

∀ j

i, j

∑

∀ j

j,i

−

∑

∀ j

i, j

+ s

≥ f

∀i

∑

∀ j

i, j

≤ v

∀i

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

is also inte-

ger. Unimodularity was also exploited in (Hyland and

Mahmassani, 2018).

In addition, depending on the supply, s

, the num-

ber of idle vehicles, v

, a high f

can turn the optimiza-

tion problem infeasible. For example, if there is no

idle vehicles (i.e., v

= 0 ∀i) and at least one zone in

which s

< f

, 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

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

, ..., f

] given s = [s

, ..., s

] and

v = [v

, ..., v

] if:

∑

∀i

(max{ f

− s

, 0}) ≤

∑

∀i

(max{min{s

− f

, v

}, 0}),

(2)

that is, the term max{ f

− s

, 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

as follows. We assume a predicted de-

mand d

for zone i and we set f

as:

= bαd

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

and v

based on the current vehicles’

statuses.

2. Obtain the predicted demand d

(based on histori-

cal data or previous requests).

3. Obtain an α that satisﬁes (2).

4. Instantiate and solve the optimization problem

(1).

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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

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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