Effective Evaluation of Autonomous Taxi Fleets

Philippe Mathieu and Antoine Nongaillard

Univ. Lille, CNRS, Centrale Lille, UMR 9189 - CRISTAL - Centre de Recherche en Informatique Signal et Automatique de

Lille, F-59000 Lille, France

Keywords:

Simulation, Multiagent Systems, Complex Systems, Collective Strategies, Traﬁc Management Systems.

Abstract:

With the advent of autonomous vehicles, self-management of taxis ﬂeet becomes an important issue for the

automotive industry. Designing strategies for taxis turns out to be a difﬁcult task due to a large number of

parameters and metrics involved. Performance evaluation of these strategies is also a complex problem since

effectiveness in some conﬁgurations may become inefﬁciency in others. After formalizing this problem we

propose several strategies based on swarm-computing techniques. Finally, we show that metric uniﬁcation is

necessary and that only a multi-criterion approach illustrated by an economic analysis allows a comparison.

We conclude with a description of the simulator implemented and some examples showing the measurements

made with the proposed strategies.

1 INTRODUCTION

In recent years, research related to autonomous vehi-

cles has been on the rise for car manufacturers as well

as for academics. (Tlig et al., 2012; Cheikh and Ham-

madi, 2014; Dresner and Stone, 2008). Nowadays,

ﬂeets of autonomous vehicles can be created and used

to solve collective tasks. One of them is the establish-

ment of taxi ﬂeets, able to negotiate and effectively

manage customers in a geographical area.

The use of centralised optimisation techniques is

only possible if all requests from clients in a time win-

dow are known, in order to optimise the assignment

of taxis to clients according to their position. Un-

fortunately, in real life, it is not true. Without prior

knowledge on client requests, the system must handle

dynamic data, which is the main advantages of multi-

agent system approaches.

On one side, clients perceive taxis movement in

two steps: waiting to get into the taxi, which must

be carried out efﬁciently according to its own crite-

ria (speed, comfort. . . ) and the transportation phase

to its destination, which must also be carried out ef-

fectively (speed, price. . . ). On the other side, three

major steps structure the behaviour of a taxi. (i) The

positioning strategy, when there is no client. A rea-

sonable attitude requires taxis positioned in the vicin-

ity of future applications if they are known. The

number and position of the various customer requests

vary over time. Depending on the time of the day,

hot spots appear or disappear (arrivals of trains, ex-

its from concerts. . . ) creating varied dynamics of of-

fers and requests. (ii) The selection of a client when

there are several. Which taxi takes which customer?

This choice requires negotiation either between taxis

or with customers or even both. (iii) The transport

of the selected client. This transport requires consid-

ering static information related to the road infrastruc-

ture (in particular speed limitations, positions of traf-

ﬁc lights) and dynamic information on this infrastruc-

ture (e.g., congestion of roads).

The ﬂeet manager wishes of course to maximise

its proﬁts: on the one hand reducing costs (number of

vehicles, inactive vehicles. . . ), maximising the num-

ber of people taken on, on the other hand. Conse-

quently, the number of taxis, their waiting position,

and their coordination become the primary factor (the

distribution of taxis should be based on the prediction

of applications: sometimes all at the same place, but

sometimes all equally distributed). It is necessary to

design vehicle behaviours maximising the effective-

ness of the whole ﬂeet, from the point of view of cus-

tomers, taxis or the manager. Our objective is to iden-

tify collective strategies for the management of taxi

ﬂeets and to know how to compare them.

This article is organised as follows. Section 2

presents the state-of-the-art related to managing ve-

hicle ﬂeets through optimisation and simulation ap-

proaches. Section 3 describes the beneﬁts of us-

ing multiagent systems for this kind of problem and

we describe different positioning strategies of empty

taxis as well. Section 4 presents the assessment

Mathieu, P. and Nongaillard, A.

Effective Evaluation of Autonomous Taxi Fleets.

DOI: 10.5220/0006720002970304

In Proceedings of the 10th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2018) - Volume 1, pages 297-304

ISBN: 978-989-758-275-2

297

method and the comparison of the strategies we pro-

pose. Section 5 concludes and describes the prospects

for future research.

2 LITERATURE REVIEW

Numerous works dealing with problems related to

trafﬁc/road simulation are referenced in the literature

as (Bazzan and Klgl, 2014). These problems deal

mostly with two aspects.

Trafﬁc regulation is one aspect in which many

works study multi-agent road simulation. Vehicle co-

ordination for effective intersection management is

carefully explored: using multiagent modelling of in-

tersection and vehicles, the overall behaviour is self-

adaptive in situations such as the appearance of pri-

ority vehicles (Dresner and Stone, 2008), or using

a two-player game modelling to characterise speciﬁc

situations (Mandiau et al., 2008), but also in a more

general framework as in (Badeig et al., 2008).

Other works focus on the design of behaviour: ei-

ther by proposing tools to support this design (Bon-

homme et al., 2014), or by proposing behaviours ded-

icated to enhance the realism of simulations: for in-

stance (Lacroix et al., 2009; Lacroix et al., 2013)

propose generation methods in order to increase be-

haviour diversity as well as the simulation realism

through a normative approach while (Bonte et al.,

2006) introduces heterogeneity in simulation through

two-wheel agents and speciﬁc behaviours in order to

study their impact on the trafﬁc. Finally, other works

propose cooperative behaviours to improve the over-

all efﬁciency of a system by managing conﬂicts lo-

cally, guaranteeing a limited perception of agents as

well as little communication (Tlig et al., 2012).

Studies on the simulation and evaluation of a

transportation system as a whole are numerous (Man-

ley et al., 2014; Yang, 1997; Bonhomme et al., 2016;

Barcel

o et al., 2005). Such works often support the

design and evaluation of road behaviour. Some works

address issues related to the impact of road infrastruc-

ture modiﬁcation while others deal with more spe-

ciﬁc problems such as urban-area parking (Bessghaier

et al., 2012). Recently, other studies have focused

on speciﬁc phenomena as for the vehicle-sharing

(Cheikh and Hammadi, 2014): a hybrid method based

on optimisation techniques and multi-agent systems

allows the parallel assignment of vehicles on demand,

on an environment, divided into distinct geographical

areas within which an optimal assignment is scalable.

(Billhardt et al., 2014) study the dynamic coordina-

tion of a transportation system but focus on the archi-

tecture required to achieve it and not on individual be-

haviour as we propose. They still require centralised

entity to act as a ﬂeet operator, which we claim un-

necessary.

The problem we are interested in, the manage-

ment of taxis ﬂeet, has already been studied under

different aspects. (Lioris et al., 2010) proposes a

discrete-event simulator supporting the design of op-

timal behaviour through learning and systematic test-

ing of many strategies (centralised and distributed).

However, these behaviours cannot adapt themselves

in front of different situations that may arise (peaks

of applications, congestion. . . ). Other studies focus

on the beneﬁts of cooperation between taxis in the

assignment process (Maciejewski and Nagel, 2013).

This approach relies on the existence of a dispatcher

and on the amount of information shared, which

might nevertheless be reduced to a minimum if the

strategy developed becomes complex.

In contrast to approaches based on optimisation

techniques as (Cheikh and Hammadi, 2014) or (Li-

oris et al., 2010), we propose an approach based on

autonomous and adaptive agents, allowing distributed

coordination based on agents with local perception

and reasoning.

3 MULTIAGENT APPROACH

One can easily understand that in such a system, no

client should wait too long, and no taxi should remain

too inactive. Strategy evaluation contains an essen-

tial temporal dimension. This temporality can only be

measured based on real travel time as well as consid-

ering distances and congestion. Therefore, the road

infrastructure must be represented using an GIS (Ge-

ographic Information System) graph or an adjacency

matrix encoding both distances and travel times.

Based on such a representation of the road infras-

tructure, it is possible to simulate congestion, to com-

pute the shortest distance and travel time from one

point to another, and to determine the number of cus-

tomers that can be conveyed for a given period of

time, as soon as their application is regular and in-

ﬁnite. However, as soon as positioning strategies are

necessary, patterns of customer applications are irreg-

ular or, as soon as one seeks to evaluate heteroge-

neous ﬂeets, the notion of behaviour becomes prepon-

derant. It constitutes a complex system, with many

retro-action loops. Moreover, under incomplete in-

formation, notions of perception and neighbourhood

are required: an GIS map with vehicles moving on it

become unavoidable.

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298

3.1 A Distributed Solving Required?

While it is quite clear that an GIS map and simulated

vehicles moving on it are required, such a simulation

can be implemented in two ways: centralised compu-

tation that optimises constraints and assigns taxis, or

thanks to a behavioural model in which each taxi has

its own decision model.

The perception halo restricts the volume of infor-

mation which each taxi can access, and also allows a

limited rationality. Three types of information can be

distinguished perception of infrastructure (including

roads, congestion. . . ), perception of customers (inter-

action with customers within the halo), and percep-

tion of other taxis (exchange of information between

close taxis).

A behavioural approach such as the one we pro-

pose allows the test of all these hypotheses based on

the same model: perception radius, halos shape, na-

ture of interactions as well as information exchanged.

The ideal system in which all information would be

public and immediately known to all is directly ob-

tained by considering halos of inﬁnite radius, ac-

counting as a centralised system.

Perception of the

infrastructure

Perception of

clients

Perception of

other taxis

Figure 1: Different perception halos for a vehicle.

Numerous events only have a local impact: a

congestion to the south of Manhattan leads to very

few consequences for vehicles travelling solely to the

north. Broadcasting such information to all is useless.

Any modelling requires choosing the level of

granularity desired. Each business expert decides

what is relevant to his model, for his experiments. Of

course, the ﬁner the granularity, the more important

the number of concepts to consider. It enriches the

model and makes it more complex, impacting its im-

plementation and its effectiveness. All models require

a compromise. For instance, is it required to specify

a behaviour to pedestrians or trafﬁc lights? These al-

ternatives are both possible by extending our model.

However, we choose to only individualise taxis and

customers. Other vehicles will simply be represented

by a ﬂow. Thus, each GIS road segment contains a

speed limit and its level of congestion. Similarly, cus-

tomers do not have their own behaviour, but simply a

place of appearance and a destination.

The use of individual-centred approach guaran-

tees the design of autonomous agents, and a self-

adaptive system as well that is very suitable for this

fundamentally dynamic problem. Taxis automatically

adapt to customer requests, to other taxis, to trafﬁc

congestion. . .

3.2 Description of Strategies

First of all, the way clients are considered must be

detailled. In this study, clients are generated at spe-

ciﬁc places called client generators. Each generator

creates clients according to a predeﬁned probability

distribution, each client is associated with a destina-

tion and a time-to-live. If no taxi picks a client up

before the term of its time-to-life, the request is can-

celled. Generators have been used to simplify mod-

elling assumption, to represent hot spots where clients

appear regularly and to facilitate stategy comparisons.

Of course, if needed, it is possible to generate clients

on any node of a given area.

The distributed management of a ﬂeet of au-

tonomous taxis is based on three distinct tasks men-

tioned above: customer selection, customer transport

and positioning of the taxi when it is empty. The be-

haviour of a taxi should describe these three aspects

for which it is possible to adopt speciﬁc strategies. In

all these strategies, we consider that all agents (clients

and taxis) are cooperative, meaning that they all aim

at contributing to the maximization (or minimization)

of the same objective function.

3.2.1 Client Selection

The question of the customer selection will arise in

two situations: when a taxi receives several requests

for transport and when a customer applies. In the ﬁrst

case, the taxi must decide which customer takes pri-

ority, whereas in the other case the question becomes

which taxi should move and transport him or her. Ob-

viously, an efﬁcient management of the taxi ﬂeet min-

imises unnecessary travel and thus avoids multiple

taxis to move towards the same customer.

The client selection can be managed via a

contract-net-like protocol (Smith, 1980). Indeed,

when a customer appears, he broadcasts a signal to

all taxis in the ﬂeet (e.g., using his or her smartphone

application). Each taxi always answer to all requests

by an arrival time. Taxis decide independently of each

other to answer it or not. Indeed, each taxi has its own

policy based on various elements such as already hav-

ing a customer or not, depending on the distance with

Effective Evaluation of Autonomous Taxi Fleets

299

the client, or depending on the constraints emitted by

this client.

After receiving responses from the taxis, the client

then chooses the one that will transport him. Sim-

ilarly, each customer may have a selection process

based on its own criteria (more ecological, faster,

shortest distance. . . , lowest price). By default, a client

always chooses the taxi associated with the closest ar-

rival time. We consider that taxis will not be selected

by the client himself but by its smartphone applica-

tion, which can consider the so-called social criteria

related to the taxi ﬂeet. The radius of the customer

call may vary in order to reach either only close vehi-

cles, or the whole ﬂeet.

3.2.2 Taxi Positioning

The major difﬁculty relies mainly on the positioning

of the vehicles. Indeed, when the number of cus-

tomers is low, taxis should wait for customers. An

inactive taxi must question its positioning according

to the evolution of its knowledge (either by exchange

with others or by direct perception of its environ-

ment): Would it more likely have a client by being

placed elsewhere? All taxis must not position them-

selves and wait at the same place: some forms of co-

ordination is necessary for this purpose. The two ﬁrst

strategies described next do not require any informa-

tion, their decision-making is based on their own in-

formation and the notion of ﬂeet is nonexistent for

each individual. At the opposite, the two last strate-

gies are swarm-based since taxis share information

and use them to make their decision that can be based

either on self-interest or on social motives.

The different positioning strategies considered

are:

• random: when a taxi is empty, it selects randomly

one of the generators and goes there. If there is no

client, the vehicle waits for one.

• closest: as soon as a taxi is empty, it selects the re-

quest generator the closest to its position and goes

there. If there is no customer, the taxi join the

queue.

• probabilistic: when a taxi is empty, it selects a

generator according to the number of requests

pending and goes there. The more pending re-

quests a generator has, the more chances it has to

be selected. If there is no request, the taxi lines

up and waits. Such a strategy assumes that taxis

know the number of customers waiting on all gen-

erators.

• most-requested: when a taxi is empty, it selects

the generator associated with the largest num-

ber of pending requests, according to its knowl-

edge. Without knowledge on waiting clients, it

randomly selects one generator. When taxis inter-

sect, they can exchange information on the status

of applications in order to update their knowledge.

This strategy, based on local exchanges of infor-

mation, constitutes a swarm-based strategy.

This list of strategies does not aim at being ex-

haustive. Each of these strategies can be extended in

different versions according to the amount of infor-

mation that a taxi can recover. Indeed, the exchange

of local information can have an impact on the effec-

tiveness. The strategies described here are primarily

intended to illustrate the range of possibilities.

4 COMPARING STRATEGIES

4.1 Preconception

The comparison of behaviours in such a context raises

a large number of difﬁculties that must be considered

if relevant results are desired. We assume that the

evaluation of such a system relies on the aggregation

of a set C of n criteria C = {c

}

i=1

. The objective

function can be written in a very generic way:

F (c

, . . . , c

) = f (c

, . . . , c

)

The comparison of different ﬂeet management

strategies must imperatively compare them under the

same experimental conditions, these conditions being

scripted in time. This is what we call an execution

scenario and deﬁne as a tuple S = (G, E, S, D) where

G is the GIS graph describing the road infrastructure,

E describes the trafﬁc conditions, S = {s

}

i=1

is the

set of client generators (GIS position and appearance

rate of clients at this point) and D = {d

}

i=1

is the set

of destinations requested by customers.

All these parameters deﬁne a scenario, which

must be the same to allow comparison of strategy ef-

fectiveness. These common experimental conditions

are essential to assess the impact of simulation pa-

rameters and behaviour of taxis: such as the ﬂeet size,

the taxis perception/interaction radius, the positioning

strategy, client selection rules. . .

The effectiveness of strategies is highly dependent

on the scenario used. Indeed, a very effective strategy

on one scenario may perform terribly on another. Fig-

ure 2 illustrates the manipulability of results. Each

simulation was carried out on the same road infras-

tructure, on which a ﬂeet of 10 taxis having complete

information operates. The number of customers trans-

ported is used to measure the ﬂeet efﬁciency. In each

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300

0 500 1000 1500 2000 2500

0 500 1000 1500

time

Nb of accepted clients

Random

Closest

Most requested

Probabilist

0 500 1000 1500 2000 2500

0 500 1000 1500 2000

time

Nb of accepted clients

Random

Closest

Most requested

Probabilist

(a) (b)

0 500 1000 1500 2000 2500

0 200 400 600

time

Nb of accepted clients

Random

Closest

Most requested

Probabilist

0 500 1000 1500 2000 2500

0 500 1000 1500 2000

time

Nb of accepted clients

Random

Closest

Most requested

Probabilist

Figure 2: On the same road infrastructure (Richelieu town), four scenarios makes a different strategy becomes the most

effective.

of the scenarios, client generators are represented by

an orange square while the yellow triangle represents

the destination requested by customers.

According to scenario (a), a large number of

clients (2,400 clients) are waiting on the client genera-

tor the furthest from the destination, the nearest gener-

ator generates 1 client every 240 minutes and the other

10 generators have a higher generation rate (1,200

customers generated in 480 minutes per generator).

Taxis that position themselves according to a random

strategy will mostly take clients from very active gen-

erators (since they represent 10 generators out of 12):

the ﬂeet can thus take over a maximum of applicants.

However, if taxis position themselves according to a

closest strategy, they will stop at the nearest genera-

tor, which only generates few customers and the ﬂeet

can only achieve very limited results. According to a

positioning most-requested strategy, taxis will always

move to the farthest generator (on which a large num-

ber of clients are waiting), therefore limiting the num-

ber of taken clients. A probability strategy encourages

taxis to take clients from the most distant generator

and the 10 closer generators according to the number

of clients, leading the ﬂeet to achieve reserved results.

According to scenario (b), a customer-generator

close to the destination is very active (2,400 cus-

tomers generated in 240 minutes), while the further

one is associated with a lower rate (480 clients in 480

minutes). Taxis following the positioning strategies

random and probabilistic will serve both generators,

reducing the total number of clients that can be ac-

cepted. Taxis acting according to a closest positioning

strategy will only take clients from the closest genera-

tor, maximising the number of clients taken. A most-

requested positioning strategy leads taxis to the near-

est generator until more pending requests appear on

the most distant one, sending taxis to the latter. Such

a strategy does not maximise the number of clients

taken.

According to scenario (c), close to the lone desti-

nation, 1 weak generator (1 client every 240 minutes)

and 10 strong generators (136 customers in 480 min-

utes), while in remote areas rely on a very strong gen-

erator (1,496 customers in 480 minutes) and 11 weak

generators (1 customer in 480 minutes). Follow-

ing the positioning strategy of closest, taxis quickly

exhaust the nearest client-generator and come to a

halt, leading to a low total number of customers ac-

cepted. The random positioning strategy makes taxis

spend time on remote generators containing only a

few clients while the most-requested strategy makes

taxis head to the generator where the largest num-

ber of requests are pending, which is also the fur-

thest, ultimately reducing the total number of cus-

tomers taken. Only the probabilistic strategy dis-

tributes taxis between close generators with numerous

waiting clients.

According to scenario (d), a strong generator is

close to the destination (1,680 customers in 240 min-

utes) while a weak generator is more distant (1,215

Effective Evaluation of Autonomous Taxi Fleets

301

customers in 480 minutes). As before, the strategies

random and probabilist distribute taxis on all gen-

erators, wasting time by taking clients from further

generators while a lot of requests are pending closer.

The nearest strategy quickly exhausts the closest gen-

erator and then immobilises the ﬂeet. Only most-

requested strategy distributes taxis on both client-

generators, but will ﬁrst exhaust the closer one, max-

imising the total number of clients transported.

These 4 scenarios allow us to show that it is pos-

sible to design a scenario speciﬁcally dedicated to

making any strategy the most effective. Moreover,

here we have chosen to look only at the total num-

ber of clients taken to assess the effectiveness of the

taxi ﬂeet, but it is possible to do the same with other

metrics. Indeed, behavioural assessment is also very

sensitive to another aspect: the metrics chosen for the

evaluation. Indeed, even if the scenario (i.e., the ex-

perimental conditions) is the same, the evaluation of

behaviours can lead to opposite conclusions accord-

ing to the metrics chosen for the evaluation. In ad-

dition, some metrics which may seem wise at ﬁrst,

turn out to be perfectly disastrous. Indeed, let us as-

sume that the efﬁciency of a taxi ﬂeet is evaluated

through the waiting time of customers that should be

minimised: F = min(t

). It is then sufﬁcient to match

the number of taxis n

taxi

to the number of applications

r: the waiting time t

tends to zero but taxis will be in-

active most of the time.

taxi

→ r ⇒ t

→ 0 but t

→ ∞

On the other hand, if the effectiveness of a taxi ﬂeet

is evaluated through the inactivity time of taxis which

should be minimised: F = min(t

). It is then sufﬁ-

cient to reduce the number of taxis n

taxi

to one what-

ever the request.

taxi

→ 1 ⇒ t

→ 1 but t

→ ∞

The lone taxi of the ﬂeet would thus always be busy

taking customers. However, the number of accepted

clients would be very low and their waiting time ex-

tremely long.

An intuitive idea could then be to aggregate these

different aspects within the same objective function.

A solution could be to minimise the product of cus-

tomers’ waiting time and taxis’ inactivity time: F =

× t

. The use of a product can be interpreted as

aiming at a compromise between taxis and customers

which can sometimes have opposite interests. Unfor-

tunately, such a function is no more relevant than the

previous ones. Indeed, it is very easy to get a nil value

by playing only on size of the taxi ﬂeet: (i) if the ﬂeet

size tends towards inﬁnity, the client waiting time t

tends towards 0 as well as the whole objective func-

tion; (ii) on the other hand, if the ﬂeet size tends to-

wards 1, the taxis inactivity time tends towards 0 just

like the objective function.

(i) n

taxi

→ ∞ ⇒ t

→ 0 ⇒ F → 0

(ii) n

taxi

→ 1 ⇒ t

→ 0 ⇒ F → 0

Thus, ﬁnding an objective function aggregating

the different aspects of the problem is a difﬁcult task.

It is always possible to design a scenario or manipu-

late a parameter in order to shape the value of the ob-

jective function without achieving a meaningful com-

parison. The different criteria aggregated by the ob-

jective function do not have links between them: each

represents the problem according to a speciﬁc point

of view. Moreover, these aspects have their own

value scales: their comparison often has no meaning.

Thus, in order to evaluate such a complex problem

with multiple facets, it is necessary to create a com-

mon scale of values to allow comparison of strategies.

The more the evaluation metric aggregates various as-

pects, the more difﬁcult the manipulation.

4.2 An Economical Approach to

Compare Strategies

A lot of aspects can be considered as common val-

ues scale for the evaluation: kilometres, time, en-

ergy. . . One a unifying solution: Money. The use of

money as a uniﬁcation of the other parameters is the

conventional projection of R

on to R with the atten-

dant problems of coverage of all the contributory fac-

tors and how to weight their combination. The taxis

are not individually economically autonomous, in the

sense that they do not try to maximize their own util-

ity, even though that may have a negative impact on

their individual welfare. The aim for a manager is

to maximise the efﬁciency of the whole ﬂeet, without

considering individuals.

The effectiveness of such a system must be as-

sessed by considering the different aspects of taxi sat-

isfaction as well as customer satisfaction.

F (w

client

, w

taxi

) = f (w

client

, w

taxi

)

Customer satisfaction is based on various criteria

such as price, waiting time and travel time. Another

possible approach could be to consider a customer

satisﬁed as soon as he is accepted, whatever the time

he waited or the price charged. Such an assumption

clearly focuses on taxis. The objective of such a sys-

tem is to maximise the number of customers taken.

Such a study really makes sense if customers have

limited patience and stop waiting for a taxi a certain

time. They can then be considered as a perishable re-

source of the system.

The satisfaction of taxis must consider the posi-

tioning time (empty-ride) t

empty

, the travel-time t

ride

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

302

the ﬂat rate per customer p

, the price per kilometre

when riding a client p

, the cost per kilometre c

, the

vehicle paying for itself ζ.

The empty-ride time occurs when a taxi moves

without a client, which occurs whenever he has to

reposition itself: the taxi always incurs the costs of

using the vehicle. The more a taxi moves without a

customer, the more it costs and the least proﬁtable it

is. The purchase/rental price of the vehicle is also

considered, which must be calculated on the basis of

the vehicle price and the time needed for the vehicle

to pay for itself. Each customer accepted is charged

and an additional cost per kilometre travelled. Thus,

the proﬁts of taxis depend directly on the number nb

of customers it takes.

The satisfaction function that a taxi aims to max-

imise can be formulated as:

taxi



+ (p

− c

charge



nb − c

vide

− ζ

In order to assess the effectiveness of the system,

it is necessary to aggregate the satisfaction of all taxis.

The choice of this aggregation function also has a lot

of serious consequences and must result from an in-

formed choice: the most common choice is the sum

∑

. However, the maximisation of a sum does not

consider the standard deviation: some drivers could

be very proﬁtable while others would be dedicated to

making shorter journeys for example. If the direct re-

muneration of drivers depends directly on the number

of customers taken, aggregation by means of a sum

is not fair. An alternative would be to use a product

∏

, allowing a fairer distribution of the less proﬁtable

rides between different drivers. This small example

shows the need for an informed choice for the selec-

tion of the aggregation functions involved in evaluat-

ing the effectiveness of our complex system.The eco-

nomic approach avoids manipulation thanks to the de-

sign of dedicated scenarios. The probabilist strategy

achieves great results in all scenarios whereas some

of them have been designed to make another strategy

the most effective.

Different strategies have been described in Section

3. The effectiveness of some strategies depends on the

quality of information available. Indeed, the position-

ing strategies random or closest do not required more

information than the place of the client generators.

However, other strategies like probabilistic or most-

requested perform better if the information available

for each taxi is updated in time, to know the number

of requests pending on each client generators. By in-

teracting between each other, taxis can update their

knowledge if a taxi with more recent information en-

ters within its perception radius. The larger the per-

ception radius, the more effective the ﬂeet.When no

information is exchanged between taxis, when a ﬁrst

generator is exhausted, taxis select randomly a new

one since no information is available.The taxi ﬂeet

needs a lot more time to accept all waiting clients.

If information can be exchanged, the speed of client

acceptance will be much greater. A taxi with no infor-

mation has just to interact with one which have newer

information to make a new wiser positioning deci-

sion. The larger the interaction distance, the quicker

all clients are accepted. Depending on the size of the

halo, compared to the size of the road infrastructure

considered, also according to the number of taxis, the

beneﬁt of exchanging information vary.

To run our experiments, the system described in

this paper has been implemented in a powerful simu-

lator. The system is able to simulate up to the whole

of the island of Manhattan (shown in Figure 3) with

a ﬂeet of 3,000 taxis, which is globally the maximal

instance size of all trafﬁc simulators.

Figure 3: Simulation of Manhattan Island, with several

clients sources and destinations and a ﬂeet of 500 taxis sup-

porting customers.

5 CONCLUSION AND FUTURE

WORKS

We have presented in this paper the DCarPool model,

based on a multiagent architecture for distributed

management of autonomous taxi ﬂeets. This centred-

individual model considers the speed limitations and

the congestion of each road, as well as customisable

variations in applications and the deﬁnition of indi-

vidual behaviour for each taxi. The system relies on

a real map (GIS environment). We have shown that

this type of problem constitutes a multi-criteria com-

plex system difﬁcult to evaluate, especially due to its

dynamic nature. We have proposed here a list of cri-

teria to combine as well as a uniﬁed economic eval-

uation function allowing an overall evaluation of this

system. Thanks to the model we have proposed, it is

now possible in a given situation to compare different

strategies in order to obtain a multi-criteria optimum

based in particular on the satisfaction of taxis (costs

Effective Evaluation of Autonomous Taxi Fleets

303

of daily use and depreciation) and the satisfaction of

customers (fares and time spent waiting and travel-

ing). This system and the numerous possible settings

allow the ﬂexible design of a multi-criteria objective

function relevant to any desired optimisation. Next,

the results obtained with the different decentralised

strategies must be compared with the optimal assign-

ment in order to determine the absolute effectiveness

of the proposed approch.

As electric vehicles are becoming more and more

popular, a new dimension similarly becomes essen-

tial. The notable difference between a petrol-powered

vehicle and an electric vehicle is that the latter re-

quires a downtime for its recharging. It is obviously

not desirable for all taxis to recharge at the same time.

A collective energy management policy is thus re-

quired, leading to a modiﬁcation of individual strate-

gies. A taxi must be able to recharge during empty

periods or with an offset during a full period. This

obviously impacts the ﬂeet size: it becomes more and

more important as the longer the recharging time.

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