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On-demand public transportation

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 On-Demand Public Transportation
Claudia Archetti1,a , M. Grazia Speranza1,b , Dennis Weyland2,c
1
Department of Economics and Management, University of Brescia, Italy
2
Universit della Svizzera italiana, Lugano, Switzerland
a
claudia.archetti@unibs.it
b
grazia.speranza@unibs.it
c
dennisweyland@gmail.com

Abstract
In this paper we assess an on-demand public transportation system through a sim-
ulation study. The on-demand system makes use of minibuses that have neither fixed
itineraries nor fixed stops. The minibuses are rerouted online to dynamically accommo-
date the requests received by the users. To use the on-demand service users communicate,
close to their desired departure time, the origin and destination of the trip. If the estimated
arrival time at destination fulfills the user acceptance threshold, it will be chosen. In the
simulation we allow the user to walk, to use the on-demand service, a bus or a private
car. We will consider a large number of scenarios to evaluate the potential costs/benefits
of the introduction of an on-demand service. We will also analyze the scalability and the
responsiveness of the service. The results suggest that an on-demand public transporta-
tion system would be preferred by most users to the private car and to a bus service. This
in turn would imply a more efficient and environmentally friendly transportation system.

1
1 Introduction
A recent analysis on modal split of inland passenger transportation has revealed that in
Europe 15-20% of the passengers’ moves are satisfied by public transportation (motor coaches,
buses, trolley buses and trains), while 80-85% are made through cars (see statistics from
Eurostat [2]). With a moving population of more than 80% of the total, this data implies
that on a daily basis the number of cars on the roads exceeds half of the population.
Traffic congestion is a primary problem everywhere. As stated in [18], the automobile has
had a dramatic impact on the society during the last century. A crucial issue has become
the sustainability of such a growing number of cars on the roads which has led to a renewed
interest in alternative forms of transportation, especially in urban areas. This is witnessed
by the wide diffusion of bicycle and car sharing systems, as well as car pooling. However,
the main issue concerning the scarce use of public transportation means has not yet been
properly addressed.
Why is the public transportation system so unpopular? One of the main reasons that leads
people to use their own private vehicle is the lack of flexibility of the public transportation
system. Mass mobility systems typically work on fixed schedules which in many situations
can not satisfy the dynamic demand of people. The frequency is too low and the average
travel time is much higher than that required by moving privately. A further issue related
to the public transportation system is its inherent inefficiency: buses are too crowded during
peak hours while they are almost empty in other parts of the day. This clearly has a strong
impact on the operational cost and the sustainability of the system. Thus, there is the need
to redesign the public transportation system in order to make it more suited to the users’
needs and, also, to increase its efficiency.
Demand Responsive Transit (DRT) systems (also called dial-a-ride systems) have emerged
in the last decades as an attempt to satisfy the dynamic nature of users’ demands. They rely
on flexible services able to provide almost ‘door-to-door’ transportation in small vehicles,
with the possibility of pre-booking (see [5], [15] and [20]). DRT systems are nowadays mainly
implemented as services for small groups of persons (e.g. elderly or handicapped persons, see
[11], [26] and [16]). However, massive and on-demand services are far from being considered as
a possibility or an alternative to the conventional public transportation system. The literature
is very limited too (see [30], [8], [7], [26] and [25] for studies on the topic and [17] for planning
multi-leg journeys with fixed-route and demand-responsive passenger transportation services).
An excellent review of the literature dealing with DRT systems is presented in a recent
paper [23] where a minibus service is studied to serve low and intermediate density areas (see
also [13] and [12]). The authors propose a classification of DRT systems previously introduced
in [5] as:

• with fixed itineraries and stops, where users must pre-book the service;

• with fixed itineraries and stops with possible detours;

• with unspecified itineraries and predefined stops;

• with unspecified itineraries and unspecified stops.

The first category is the most closely related to the traditional public transportation
service. This category may also include systems with fixed timetables. The difference is that

2
users have to pre-book the service which is performed on demand. As specified in [23], the last
type of service, which is the most flexible one, can be considered as the closest to the concept
of shared taxis. The shared taxi system is studied in [22] and is the system where taxis are
used to serve more than one customer at a time. Customers are assigned to shared taxis on
the basis of their origin and destination requests and their service time, while guaranteeing a
predefined threshold of service level. The authors simulate, on the city of Lisbon, the behavior
of a system combining traditional taxis, i.e., taxis serving one person at a time, with shared
taxis. Users can hail for a taxi on the street, go to a taxi stand or phone to a dispatching
company. Shared taxis can only serve customers that place their service request to a dispatch
company. The simulator assigns users to taxis with the objective of minimizing waiting time
for the users and balancing workload (and thus rewards) of taxi drivers. The indicators used
to measure the performance of the system are: waiting time for users, cost for users and
taxi drivers revenues. The results show that passengers may benefit from an average 9%
fare reduction compared with the traditional system. Even if this value may seem low, it is
expected that demand would increase thanks to the fare reduction.
More recently, DRT systems have been referred to as Flexible Transportation Services
(FTS) (see [25]) when used as feeder systems for more traditional public transportation ser-
vices such as buses or trains. From this point of view, DRT are seen as flexible, demand-
responsive transportation services used to ease the user access to massive public transporta-
tion means. A recent paper [3] has introduced a new system called Flexible Mobility On
Demand (FMOD) which provides different levels of service to each passenger request. The
system utilizes three services, taxi, shared taxi and minibus, where the minibus service works
as a regular bus service with fixed schedules. Passengers place their requests to the system
provider and are presented with a menu of choices from which they make a selection based
on their preference. The list of travel services is designed in real time. These services vary
both in terms of flexibility and cost. The authors present a simulation of the system on the
Hino city in Tokyo and compare different scenarios in terms of fleet configuration.
The purpose of this paper is to evaluate, through global performance measures, the impact
of an innovative large-scale on-demand service for public transportation. The service we are
proposing belongs to the last class of DRT systems presented above as it is based on the use
of minibuses with unspecified itineraries and unspecified stops and, thus, is fully flexible. It
is an on-line service in the sense that users place their transportation requests and receive
an answer in a very short time, usually within a few seconds. The system differs from the
shared-taxi system for the following reasons:
• There are no revenues for the drivers. This makes a big difference with respect to the
shared-taxi system where one of the objectives when assigning service requests to taxis
is to keep revenues balanced among drivers;
• Drivers are not traveling around looking for clients as it is typically done by taxi drivers
while they are empty;
• The vehicles are minibuses with a higher capacity than taxis.
• Performance measures of shared-taxi systems are based on fares paid by clients and
revenues gained by drivers. The goal of the proposed system is to attract to a public
transportation service a large portion of the persons that travel with their own car
in urban areas, to reduce congestion and pollution, on one side, and to improve the
efficiency of the public system, on the other side.

3
 The goal of this paper is to present a preliminary simulation study of an on-demand public
transportation system. We will simulate the behavior of the system for different settings of the
road network and of the users requests. The purpose is to study the performance of the system
in terms of average travel time of the users, average distance traveled, fuel consumption and
global system cost. The global system cost is measured as the sum of the cost for the drivers of
the minibuses, cost for fuel and cost for the maintenance and insurance of vehicles (minibuses,
buses and private cars). We do not include fares paid by the users in this preliminary study
and suppose that, if the service level provided by the public transportation system satisfies
the flexibility request of a user, then the user will use the public system, otherwise he/she will
turn to a private car. We will simulate four different scenarios, where in addition to private
cars the following means of public transportation are available: no public transportation
service (i.e., all transportation requests are satisfied by private cars), traditional buses only,
on-demand public transportation only, buses plus on-demand transportation. The simulation
will allow us to compare the behavior of a system where no public transportation is available
with systems where one or more public transportation means are available. In particular,
we will evaluate the potential costs/benefits of the introduction of an on-demand service.
An extensive computational study is made by simulating different road networks, number
of available vehicles and number of requests. The results show that the on-demand service
dominates the conventional public transportation by buses in the sense that it serves a much
higher number of requests with a comparable cost and it remarkably decreases the average
travel time. Moreover, the system performs better when the number of transportation requests
increases, is highly competitive, in terms of cost, with respect to the transportation by private
cars and is much more environmentally friendly.
The remaining part of the paper is organized as follows. In Section 2 we describe a flexible
transportation system on which we base the simulation and present the main ideas behind the
on-demand public transportation service. Section 3 deals with the simulation of the system.
We first define the underlying structures, namely the road network and the transportation
requests. Then, we discuss the simulation of direct trips, i.e. trips performed by walking or by
private cars, of conventional public transportation by buses and of the proposed on-demand
public transportation service. We also give an overview of the parameters and the performance
indicators of the simulation. A comparison between the different modes of transportation is
performed in Section 4. In Section 5 we examine some properties of the proposed on-demand
public transportation service more in detail. Finally, Section 6 contains a discussion of the
results, the conclusions and an outlook of promising research directions.

2 A flexible transportation system

We consider a system where users express transportation requests that can be satisfied by
means of conventional buses, on-demand minibuses or private cars. Each request is charac-
terized by the time at which it is expressed, by an origin and a destination, by a desired
departure time and a flexibility value. The latter value indicates the excess travel time a
user is willing to accept by using public transportation with respect to the usage of a private
car. Note that the desired departure time is the earliest time at which a customer can be
picked up. In our simulations, we fix no maximum waiting time. However, this can be easily
calculated as the difference between the flexibility value and the shortest path to reach the
destination. Moreover, our results show that, in all scenarios, the waiting time is always

4
limited, never exceeding 4 minutes.
Conventional buses work on the basis of a predefined schedule and no deviation is allowed
from their fixed itineraries, stops and timetables.
The on-demand service makes use of minibuses. Any user request is communicated to
a central system together with the trip origin and destination and the desired departure
time. The request will be tentatively assigned to the minibus that best fits the request,
that means the request which minimizes the travel time, and the system will return to the
user the information on the expected departure time from the origin and arrival time at
the destination. If the user accepts the service, the request will be actually assigned to the
minibus that will be rerouted to accommodate the new request.
Private cars are located at the user origin and take the user to the destination through
the fastest path. We additionally take into account walking and parking time.
We model the user behavior as follows. If a public transportation mode, either a conven-
tional bus or an on-demand minibus, is available to satisfy the request within its flexibility
value, then the user will travel using one of these two modes. The underlying assumption
is that the user prefers not to use a private car if a public transportation mode satisfies the
flexibility value. The choice between the conventional bus and the on-demand minibus is
made on the basis of the total traveling time, i.e., the user will choose the fastest mode. In
case no public transportation mean satisfies the flexibility value, then the user will use the
private car.
A user will tend to choose a conventional bus if there is a bus departing from a bus stop
close to the trip origin at the time the user wants to leave (or shortly after) and arriving to a
bus stop close to the trip destination. In such a situation, even when the flexibility value may
be satisfied by a bus and an on-demand minibus, the bus may be faster and, thus, be chosen.
If the bus stops are not conveniently located with respect to the trip origin or destination,
or the bus timetable is not convenient, then the flexibility value may fail to be satisfied by a
bus or, in case it is satisfied, the trip may take longer with a bus than with the on-demand
minibus. In this case the user will choose the on-demand service. If neither a bus nor an
on-demand minibus are available to guarantee the flexibility value, the user will resort to
using a private car.

3 Simulation of the transportation system

In this section we will give an overview of the simulation of the transportation system. In
Sections 3.1 and 3.2 we will describe the structure of the road network and of the transporta-
tion requests. The road network represents the topology of a city or a region together with
the relevant transportation properties such as travel times and distances. The transportation
requests represent the travel behavior of the people in the given city or region. In addition
to the usual parameters such as origin, destination and departure time, it is crucial for our
work to also model the willingness to travel by public transportation.
We then present the algorithms used for the simulation of the different modes of trans-
portation. We begin with the simulation of direct trips by private cars in Section 3.3, followed
by the simulation of conventional buses in Section 3.4 and the simulation of the on-demand
transportation service in Section 3.5.
The simulation environment requires the setup of many different parameters. We discuss
these parameters in Section 3.6, together with their standard values which are used in most

5
Figure 1: The grid structure used in the network generator. The thickness of the edges is
proportional to the travel speed.

of the simulations conducted in this work.

Finally, in Section 3.7 we present the performance indicators that are measured during
the simulation.

3.1 The road network

The road network is represented as a strongly connected directed graph G = (V, A) with
vertex set V and arc set A. The arcs are the roads and the vertices are crossroads or could
be used to divide roads into parts with different properties (e.g. travel speed). A function
d : A → R+ assigns distances to the arcs and a function t : A → R+ assigns travel times.
To obtain a variety of road networks with different properties, a network generator has been
implemented. The network generator is based on the grid structure depicted in Figure 1. The
boundary of such a grid consists of roads with high travel speed. The grid is then divided
into cells by roads of medium travel speed and the cells are further divided by roads of slow
travel speed. Clusters of given sizes are then formed by attaching such grid structures next
to each other. These clusters are again attached to other clusters to form the overall road
network. In a last step this network is perturbed in different ways to obtain the final road
network. An example of a network generated is given in Figure 2. Although the generated
networks might differ in some respects from real road networks, we believe that they share
with them the properties which are relevant for our study.

3.2 The transportation requests

The requests are modeled on top of a given road network. Each request has an origin location
and a destination location. Both are defined by a certain edge and the position on that
edge. Additionally, a request has assigned a time at which this request is made and a desired
departure time. For the conventional modes of transportation, bus and private car, the time
at which a request is made is not relevant, but for the on-demand service it is important to
distinguish between these two points of time. A request has also assigned a walking threshold.
In case the distance between the origin and the destination is below the walking threshold,
the person just walks instead of using any other mode of transportation. Otherwise, the
walking threshold is used to determine the bus stops that are sufficiently close to the origin
and destination. Finally, we assign a flexibility value to each request. This value is used to

6
Figure 2: An example of a road network created by the network generator. The thickness of
the edges is proportional to the travel speed.

model the willingness of a person to travel by public transportation. Technically, it is the

maximum ratio between the total travel time using public transportation and the total travel
time using a direct trip by car. For example, a value of 1.5 indicates that the person would
use public transportation even if it would take 50% longer to reach the destination.
The requests for a given road network and a given time horizon are generated in two
different ways. The first approach just generates requests uniformly at random over time and
space. The second, and more realistic, approach uses a time-dependent origin-destination
matrix (OD-matrix). This method assumes that we can partition the whole time horizon
into a set of continuous time windows T = {T1 , T2 , . . . , Tn }, n ∈ N, and the edges of the
graph into a set of cells C = {C1 , C2 , . . . , Cm }, m ∈ N. The latter partition is possible,
since the generated road networks belong to a two-dimensional Euclidean space. A function
p : T × C × C → R gives the probability of travel requests, where p(t, c1 , c2 ) denotes the
probability for a travel request with departure time in time window t from cell c1 to cell c2 .
In this way more realistic sets of requests can be generated, for example by simulating the
typical peaks during rush hours and by having different distributions of requests. Further
details about the request generation are discussed in Section 4.

3.3 Simulation of direct trips

The algorithm used for walking is quite simple. Each request is associated with a walking
threshold and if the shortest distance between the origin and the destination is below the
walking threshold, the person simply walks from the origin to the destination with a certain
average speed. This approach is used in all the simulations and filters extremely short trips.
As there may be persons whose walking threshold is very small or even 0, we think it is
important to include such requests in the simulation.
Direct trips by car are the main point of reference for our comparison with the proposed

7
on-demand public transportation service. The algorithm used for such trips is as follows.
For each request we compute the fastest path between the origin and the destination. This
might not be the shortest route, but since the main indicator for efficiency is time, we decided
for such an approach. In fact, in many situations people prioritize time over distance while
traveling. We then additionally consider the time required to walk from the origin to the car,
the time required to find a parking spot close to the destination and the time required to
walk to the destination. Several studies have shown that these amounts of time substantially
contribute to the overall travel times. A nice overview about this issue is given in [27].
According to different studies that are cited in this paper, the average search times for a
parking spot are several minutes for different major cities around the world: between 7.9 and
13.9 minutes in different areas of New York (according to a study from 1993), 6.5 minutes in
San Francisco (according to a study from 1997) and 6.5 minutes in Sydney (according to a
study from 2001). These values do not even include the time which is necessary to walk to
the actual destination or back to the parking spot.
We consider the driving time from the origin to the destination, although the car might
not be parked at the origin and although it might be impossible to park at the destination.
Thus, the total travel time is given by the sum of the driving, walking and parking time.

3.4 Simulation of public transportation by buses

For the conventional public transportation by bus we consider a system of fixed routes which
are periodically traveled. The generation of an efficient bus network and schedule is a difficult
optimization problem. We refer to [28], [29], [21], [10], [9] and [4] as pioneering studies of the
topic and to [6], [19], [32], [14], [24] and [31] for more recent references. For the study in this
paper we use a grid like bus network consisting of horizontal and vertical bus routes. Given
some reference points, the actual route is computed using the paths with the smallest travel
time between the reference points. Along this route, bus stops are created at regular intervals
and all the routes are traveled in both directions with a given frequency. We are aware that a
more efficient bus network and bus schedule may exist. We will discuss this issue in Section 4.
The simulation of the travel behavior for this system is based on the time-dependent fastest
connections between any pair of bus stops. Those values are computed in a preprocessing
step with a time-dependent variant of the shortest path algorithm. To obtain the travel time
for a given request, we consider all bus stops which are within the walking threshold from
the origin and all bus stops which are within the walking threshold from the destination. For
each such pair of bus stops, we compute the total travel time, consisting of the time required
to walk to the bus stop, the time for waiting and traveling (and changing buses) and the time
to walk from the bus stop to the destination. The smallest of these travel times, which means
the travel time corresponding to the fastest connection, is then used as the total travel time
for the given request.

3.5 Simulation of the on-demand public transportation service

For the on-demand public transportation service, we consider a given fleet of vehicles, the
minibuses, with a certain capacity which are distributed over the road network. The route
of each vehicle is initially empty. Once a vehicle is traveling to a location, we do not allow
a change of this part of the route anymore, whereas the remaining route can be altered.
The requests arrive over time, usually slightly before the desired departure time. Whenever a

8
 parameter value
walking speed 5 km/h
high travel speed 50 km/h
medium travel speed 30 km/h
slow speed 20 km/h
fuel consumption private 8 l / 100 km
fuel consumption on-demand 12 l / 100 km
fuel consumption buses 50 l / 100 km
running costs private 1 e/km
running costs on-demand 1.5 e/km
running costs buses 5 e/km
salary for drivers 15 e/h
stopping time on-demand 20 seconds
stopping time buses 30 seconds
lead time for requests 300 seconds
walking times 30-180 seconds
parking times 60-300 seconds

Table 1: The standard parameters used for the simulations.

request arrives, a visit to the origin and a visit to the destination are embedded into the routes
of the vehicles, such that the total travel time of the requests given up to that point of time
is minimized. For our preliminary simulation study, we have decided for this rather simple
algorithm, which can be seen as a greedy algorithm for solving the underlying optimization
problem.

3.6 Parameters
The parameters used in the simulations are the following. The average walking speed is set
to 5 km/h. The travel speeds used during the network generation are 50 km/h, 30 km/h and
20 km/h for the edges with high, medium and slow speed, respectively. The fuel consumption
is set to an average of 8 l / 100 km for private vehicles, 12 l / 100 km for vehicles used
in the on-demand public transportation service and 50 l / 100 km for buses. The running
costs, which are often underestimated by car owners, are set to 1 e/km for private vehicles,
1.5 e/km for vehicles used in the on-demand public transportation service and 5 e/km for
buses. The salary for drivers is estimated in 15 e/h. The average time per stop, which also
includes the time for braking and accelerating, is set to 20 seconds for the on-demand public
transportation service and to 30 seconds for buses. For the on-demand service, the time
difference between the request of a trip and the desired departure time is set to 5 minutes.
We call this time the lead time. Finally, the walking times used for direct trips are sampled
uniformly at random between 30 seconds and 180 seconds and the parking times used for
direct trips are sampled uniformly at random between 60 seconds and 300 seconds. These
values might seem large, but they are in fact quite moderate compared to values reported in
investigations of parking times in urban areas [27]. An overview of these parameters is given
in Table 1.

9
3.7 Indicators of the system performance
During the simulation of the transportation system, we measure several different performance
indicators. First of all, we measure how many of the requests are actually handled by the
different modes of transportation. Here the flexibility value decides whether a request is han-
dled by public transportation or by direct trips. In case of two different public transportation
systems, the faster one is used to handle a request. We will see in Section 4 that this is a
reasonable assumption, since the costs for the two public transportation systems are similar.
For each mode of transportation we measure efficiency indicators, economic indicators and
environmental indicators. The main indicators for the efficiency of a transportation system
are the average distance and the average travel time. The economic indicators are basically
the costs of the transportation system, partitioned into costs for drivers, costs for fuel and
costs for the maintenance and insurance of vehicles. The environmental indicator is the fuel
consumption which is strictly related to pollutant emission.

4 A comparison of transportation modes

In this section we will perform a comparison of the different transportation modes. For this
purpose we first show that the relative performance of the different transportation systems is
quite stable for different kinds of road networks. We then perform a more detailed analysis on
a representative road network. Here we study the following three scenarios: (1) direct trips
without any public transportation system, (2) direct trips and public transportation by bus,
and (3) direct trips and the on-demand public transportation service. A request is served
by public transportation, when considered, if the flexibility value for the request is fulfilled.
The first scenario is used as a basis of comparison for the other two scenarios. Our goal is to
evaluate the performance of a transportation system which includes a public transportation
mode (either conventional buses or on-demand service) and to compare it with a system
where no public transportation is available. Secondly, we will compare the performance of
the two systems which include public transportation. The results indicate that the on-demand
public transportation service operates in a very efficient way at competitive costs. To further
understand the relationship between the on-demand public transportation service and public
transportation by buses, we additionally analyze the scenario in which all three different modes
of transportation are present. Note that throughout the article we will present the results
for requests generated by time-dependent OD-matrices. The results for uniform demands are
similar and can be found in the additional material in [1].
The goal of our first computational study is to analyze the influence of the road network
on the results of the simulation. For this purpose we created 10 networks with different sizes
and topologies. Additionally, we varied the number of transportation requests per hour and
the size of the fleet of vehicles used in the public transportation scenarios. The simulations
are performed for each of the three scenarios described above and for each combination of
road network and number of requests. We measure the indicators described in the previous
section. As mentioned above, we use the first scenario as the basis and we compute the ratio
between the indicators related to the scenarios 2 and 3, respectively, and the indicators of
scenario 1.
The results show that, while different road networks lead to substantially different results
in terms of absolute values, the impact of different road networks on the relative values (i.e.,
the ratio with respect to scenario 1) turns out to be quite small. This means that the ratio

10
of the costs of two different transportation modes, or the ratio of the average travel times of
two different transportation modes does not significantly depend on the actual road network.
Figure 3 illustrates these findings using the on-demand public transportation service with
300 vehicles and a capacity of 8 and public transportation by bus with a bus network of
average density and a frequency of 3 trips per hour. Each line depicted in the graphics
corresponds to a different road network. The first three graphs report the relative average
cost, the relative requests served and the relative average travel time between the on-demand
public transportation service and direct trips with demands generated by an OD-matrix. The
same indicators are reported in the last three graphs for the public transportation by bus
with demands generated by an OD-matrix. We can see that these relative indicators do
not change much for the on-demand public transportation service. The same holds for the
relative average cost for public transportation by bus. The relative requests served and the
relative average travel time for public transportation by bus is significantly influenced by the
actual road network. However, although these relative values depend on the road network,
the overall picture remains the same: only a small fraction of requests is served by buses and,
moreover, the travel time by bus significantly exceeds the travel time of direct trips and the
travel time obtained by the on-demand service. In fact, comparing Figure 3(b) with Figure
3(e), we see that the average percentage of requests served by the on-demand service goes
from almost 90%, when the number of requests is small, to almost 40% when this number is
high. On the other side, for the conventional bus service this percentage is quite unstable and
never goes above 8%. This percentage is consistent with what is typically observed in many
urban areas. Moreover, when comparing the relative average travel time in Figures 3(c) and
3(f), we see that, for the on-demand service, it increases slowly with the number of requests
and it does not exceed 1.4, which means that the on-demand service never requires more
than 40% of the time spent by traveling with private cars. Furthermore, when the number of
requests is not too large, the on-demand service is faster than private cars. The conventional
bus service presents an relative average travel time with respect to private cars which is never
lower than 1.6 and goes up to 2.3.
In this study we are interested in the overall picture, that is in general trends and in
orders of magnitude rather than in actual numbers. The results about the impact of the road
network on the relative indicators allow us to focus on a representative road network. To keep
the comparison as fair as possible, we have selected for the following analysis a medium size
network which represents the average behavior illustrated in Figure 3, that is a road network
for which the corresponding statistics are always located in between the two extremes reported
in those figures. Using this road network we now analyze more in detail the other scenarios
related to different numbers of requests and different fleet sizes for conventional buses and
minibuses.
We first compare the same three scenarios mentioned above, i.e.: (1) direct trips without
any public transportation system, (2) direct trips and public transportation by bus, and (3)
direct trips and the on-demand public transportation service. For the conventional public
transportation system we use an average density bus network with 2, 3, 4 and 6 trips per
hour per bus line. For the on-demand public transportation service we use a fixed size fleet
of 200, 300, 400 and 500 vehicles. For each of these 9 different settings (1 for scenario 1
and 4 for each of scenarios 2 and 3) we perform a simulation of one hour with uniform
requests and requests generated by an OD-matrix. The number of requests varies from 500
to 5000 in steps of 500. For each simulation we measure the various indicators, in particular
the number of requests that are served by public transportation, the average travel time

11
 1.2 0.9

1.1
0.8
1

Relative Requests Served

0.9 0.7
Relative Average Costs

0.8
0.6
0.7

0.6 0.5

0.5
0.4
0.4

0.3 0.3
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made Requests Made

(a) on-demand: relative average cost (b) on-demand: relative requests served

1.4 7

1.3 6

1.2 5
Relative Average Travel Time

Relative Average Costs

1.1 4

1 3

0.9 2

0.8 1

0.7 0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made Requests Made

(c) on-demand: relative average travel time (d) bus: relative average cost

0.075 2.4

0.07 2.3

0.065 2.2
Relative Average Travel Time
Relative Requests Served

0.06 2.1

0.055 2

0.05 1.9

0.045 1.8

0.04 1.7

0.035 1.6

0.03 1.5
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made Requests Made

(e) bus: relative requests served (f) bus: relative average travel time

Figure 3: The relative average cost, the relative requests served and the relative average travel
time for public transportation by bus and the on-demand public transportation service on
different networks.

per request, the average cost per request, the average distance per request and the average
fuel consumption per request. In the scenarios in which a public transportation system is
present, these indicators are measured only for the requests that are actually served by public

12
transportation. The results of these experiments for the requests generated by an OD-matrix
are depicted in Figures 4-8.
The average cost per request served by on-demand transportation system tends to become
competitive with the cost for direct trips once a certain number of requests per hour is reached.
At the same time, the average distance traveled per request and, to some extent, also the
average fuel consumption per request for the public transportation systems is lower than
those for the direct trips, except for the case where the number of requests is extremely
small. On the other hand, the public transportation system using buses is not able to serve a
reasonable number of requests and the average travel time for the requests that are actually
served is much higher than for direct trips. This reflects the current situation with public
transportation systems using buses in many cities around the world. In contrast to that,
the on-demand public transportation service is able to serve the majority of requests while
the average travel time remains competitive with that of direct trips. The results clearly
show that the on-demand service dominates the conventional bus service both in terms of
number of requests served and in terms of average costs and fuel consumption. Thus, a
first important indication provided by these simulations is that an on-demand service can
be provided at a cost which is comparable to the cost which is implied by the conventional
bus service. Moreover, the on-demand service has the advantage of being able to capture a
much higher number of users. Another aspect that is evident from Figures 4-8 is that the
performance of the system strictly depends on the number of transportation requests. This
indicates that, in order for the system to be sustainable, a large number of transportation
requests is needed. This implies that such a system is beneficial when the service is deeply
integrated in the population habits.

5000
direct trips
on-demand, 200 vehicles
4500 on-demand, 300 vehicles
on-demand, 400 vehicles
on-demand, 500 vehicles
4000 bus, 2 trips/h
bus, 3 trips/h
bus, 4 trips/h
bus, 6 trips/h
3500
Requests Served

3000

2500

2000

1500

1000

500

0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 4: The number of requests served.

13
 70
direct trips
on-demand, 200 vehicles
on-demand, 300 vehicles
on-demand, 400 vehicles
60 on-demand, 500 vehicles
bus, 2 trips/h
bus, 3 trips/h
bus, 4 trips/h
bus, 6 trips/h
Average Travel Time (minutes)

50

40

30

20

10
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 5: The average travel time per request.

140
direct trips
on-demand, 200 vehicles
on-demand, 300 vehicles
on-demand, 400 vehicles
120 on-demand, 500 vehicles
bus, 2 trips/h
bus, 3 trips/h
bus, 4 trips/h
100 bus, 6 trips/h
Average Costs (euros)

80

60

40

20

0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 6: The average costs per request.

14
 22
direct trips
on-demand, 200 vehicles
20 on-demand, 300 vehicles
on-demand, 400 vehicles
on-demand, 500 vehicles
18 bus, 2 trips/h
bus, 3 trips/h
bus, 4 trips/h
bus, 6 trips/h
16
Average Distance (kilometers)

14

12

10

2
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 7: The average distance traveled per request.

12
direct trips
on-demand, 200 vehicles
on-demand, 300 vehicles
on-demand, 400 vehicles
10 on-demand, 500 vehicles
bus, 2 trips/h
bus, 3 trips/h
bus, 4 trips/h
Average Fuel Consumption (liters)

bus, 6 trips/h
8

0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 8: The average fuel consumption per request.

15
 To further understand the relation between the two public transportation systems, we
perform experiments using a scenario in which both of them are present. We recall that a
request is served by public transportation if the flexibility value for that request is fulfilled. If
it is fulfilled for both public transportation modes, the request is served by the system which
provides a more efficient service in terms of travel time. Thus, we assume that the travel time
is the only criterion for choosing between the two public transportation modes. We believe
that this is a reasonable assumption, considering that our previous simulations showed that
the costs of the systems are comparable. We use an average density bus network with 6
trips per hour per bus line. According to our previous experiments, this is the most efficient
bus system in terms of average travel time per request and the number of requests that are
served. We then add the on-demand public transportation service with a fixed size fleet of
300 and 500 vehicles. For both scenarios we perform a simulation of one hour with requests
generated uniformly over time and space and with requests generated by an OD-matrix. The
number of requests varies from 500 to 5000 in steps of 500. The results for the requests
generated by an OD-matrix are shown in Figures 9 and 10. We observe that in all cases the
largest number of requests is served by the on-demand public transportation service. This
number increases almost linearly with the total number of requests, up to a point where the
capacity limit of this transportation mode is approached, where the share of requests served
by direct trips suddenly increases faster. In contrast to that, the number of requests served
by the public transportation by bus is almost negligible and much lower than in the previous
experiments. This shows that the public transportation system by bus is strictly dominated
by the on-demand public transportation service.

4000
direct trips
on-demand, 300 vehicles
bus, 6 trips/h
3500

3000

2500
Requests Served

2000

1500

1000

500

0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 9: The number of requests served (300 vehicles for the on-demand service).

We have to be careful drawing conclusions from these experiments, since some uncertain-

16
 4500
direct trips
on-demand, 500 vehicles
bus, 6 trips/h
4000

3500

3000
Requests Served

2500

2000

1500

1000

500

0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 10: The number of requests served (500 vehicles for the on-demand service).

ties and inaccuracies are involved. However, as we have already pointed out, we are interested
in the general picture, in trends and in orders of magnitude and not in absolute values. We
have seen that both public transportation systems can operate at competitive costs once a
sufficient number of requests per hour is made. The average distance traveled per request is
also reduced for both public transportation systems, which means that they can be effectively
used to reduce traffic. Additionally, the average fuel consumption per request is reduced by
the on-demand public transportation service and, to some extent, also by the public trans-
portation system using buses, which directly implies positive environmental effects. The main
differences between the two public transportation systems can be observed with respect to
the number of requests that can be actually served and the average travel time per request.
The public transportation system based on buses is not able to serve a reasonable number of
requests and the average travel times exceed those of the other systems by far. This result
is consistent with the performance of public transportation systems based on buses in many
cities around the world. In contrast to that, the on-demand public transportation service
is able to serve a large number of requests and the average travel time is competitive with
that obtained by direct trips. Finally, we have seen that in a scenario where both public
transportation systems are present, the public transportation system using buses is clearly
dominated by the on-demand public transportation service. This indicates that a system
based on buses traveling regularly on fixed lines could be partially or completely replaced
by an on-demand service. To summarize, the proposed on-demand service seems to be quite
promising as an alternative to conventional public transportation systems.

17
5 Properties of the on-demand public transportation service
In this section we will further analyze the proposed on-demand public transportation service.
For this purpose, we focus on two important properties of this system: the scalability and
the responsiveness. We have already investigated some aspects of the scalability of the on-
demand service in the previous section, where we have seen that the performance of the
system depends heavily on the number of requests that are made. For a fleet of vehicles with
a fixed size, a certain critical mass has to be reached in order to allow the system to operate
efficiently. Intuitively this is clear, since a certain number of requests is necessary to use the
capacities of the fleet efficiently and, additionally, an increasing number of requests allows for
more synergies in the route planning. In this section we look at this issue from a different point
of view: we keep the ratio between number of vehicles and requests constant and investigate
the performance of the on-demand service using this fixed ratio under increasing number of
requests per hour. After that we focus on another property, which we call in this context
responsiveness. With responsiveness we mean how the system reacts to travel requests which
are made just before the desired departure time. To measure the responsiveness of the on-
demand service, we investigate the performance under different values for the lead time.

5.1 Scalability
In the previous experiments we have seen that the on-demand public transportation service
operates very efficiently as long as the ratio between the number of available vehicles and
the requests made per hour is somewhere in the range between 0.05 and 0.15. We therefore
conduct a series of experiments with the on-demand service, where this ratio is kept constant
to a fixed value, while the total number of requests per hour (and therefore also the size of
the fleet) is varied between 1000 and 10000 in steps of 1000. We simulate the transportation
system for one hour using 6, 8, 10 and 12 vehicles per 100 requests. Again, we measure the
performance indicators, in particular the number of requests that can be served by the public
transportation system, the average travel time per request, the average cost per request and
the average distance per request (which in this particular simulation is also an indicator for
the average fuel consumption per request, because only one mode of transportation with
identical vehicles is used). The results of these experiments are depicted in Figures 11-14.
First of all, we can see that the number of requests that can be served by the on-demand
transportation system increases slightly faster than linear with the total number of requests
per hour. Additionally, the average travel time per request decreases with an increasing
number of total requests. This shows that the overall system scales very well. The situation
for the average cost per request and the average distance per request is similar, although
these indicators decrease more slowly than the average travel time per request. This clearly
reflects the fact that our algorithm is optimizing for the average travel time per request and
not for the other indicators. It seems that a reduction of the average travel time per request
automatically leads to a reduction of the other two indicators, which is a quite desirable
behavior of the overall system. On the other hand, there might be situations in which more
emphasis has to be put on economical or ecological issues and this could be handled by
explicitly using other indicators in the objective function. In any case, the on-demand public
transportation service is capable of handling huge number of requests, and in fact, it achieves
its best performance in such a mass transit scenario.

18
 10000
on-demand, 6 vehicles / 100 requests
on-demand, 8 vehicles / 100 requests
9000 on-demand, 10 vehicles / 100 requests
on-demand, 12 vehicles / 100 requests

8000

7000
Requests Served

6000

5000

4000

3000

2000

1000

0
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Requests Made

Figure 11: The number of requests served.

23
on-demand, 6 vehicles / 100 requests
on-demand, 8 vehicles / 100 requests
on-demand, 10 vehicles / 100 requests
on-demand, 12 vehicles / 100 requests
22

21
Average Travel Time (minutes)

20

19

18

17

16
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Requests Made

Figure 12: The average travel time per request.

19
 9
on-demand, 6 vehicles / 100 requests
on-demand, 8 vehicles / 100 requests
on-demand, 10 vehicles / 100 requests
8.5 on-demand, 12 vehicles / 100 requests

8
Average Costs (euros)

7.5

6.5

5.5

5
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Requests Made

Figure 13: The average costs per request.

4.4
on-demand, 6 vehicles / 100 requests
on-demand, 8 vehicles / 100 requests
on-demand, 10 vehicles / 100 requests
4.2 on-demand, 12 vehicles / 100 requests

4
Average Distance (kilometers)

3.8

3.6

3.4

3.2

2.8

2.6
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Requests Made

Figure 14: The average distance per request.

20
5.2 Responsiveness
Another important property for the on-demand public transportation system is the respon-
siveness, which describes how well the system can cope with requests that are made very
close to the desired departure time. In the previous experiments, the lead time was fixed to 5
minutes. In this section we will perform a series of experiments where the lead time is fixed
to values of 0, 2, 4, 6, 8 and 10 minutes. For each of these settings we perform a simulation
where the total number of requests is varied from 500 to 5000 in steps of 500. We measure
the same performance indicators used in the previous section with the addition of the average
waiting time per request which is defined as the interval between the desired departure time
and the actual pickup time. This is clearly an indicator that remarkably depends on the
lead time. The results of this series of experiments are shown for requests generated by an
OD-matrix in Figures 15-19.

4500
on-demand, no lead time
on-demand, 2 minutes lead time
on-demand, 4 minutes lead time
4000 on-demand, 6 minutes lead time
on-demand, 8 minutes lead time
on-demand, 10 minutes lead time
3500

3000
Requests Served

2500

2000

1500

1000

500

0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 15: The number of requests served.

We can see that the number of requests that are served by the on-demand service and the
average cost per request are only slightly influenced by the lead time, whereas the average
travel time per request and the average waiting time per request are significantly influenced
by the lead time. The average distance per request depends quite strongly on the lead time
for a small number of requests per hour, but the difference vanishes for a large number of
requests per hour. A lead time of 0, which means that the requests are just made at the
desired departure times, leads to a significantly worse average travel time per request and
average waiting time per request, while the difference among the other lead times is not that
large. This is due to the fact that a lead time of 0 does not allow an efficient reassignment of
requests among drivers. In any case, the results show that the on-demand service is highly

21
 19
on-demand, no lead time
on-demand, 2 minutes lead time
on-demand, 4 minutes lead time
on-demand, 6 minutes lead time
18 on-demand, 8 minutes lead time
on-demand, 10 minutes lead time

17
Average Travel Time (minutes)

16

15

14

13

12
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 16: The average travel time per request.

30
on-demand, no lead time
on-demand, 2 minutes lead time
on-demand, 4 minutes lead time
on-demand, 6 minutes lead time
on-demand, 8 minutes lead time
25 on-demand, 10 minutes lead time
Average Costs (euros)

20

15

10

5
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 17: The average costs per request.

22
 8
on-demand, no lead time
on-demand, 2 minutes lead time
7.5 on-demand, 4 minutes lead time
on-demand, 6 minutes lead time
on-demand, 8 minutes lead time
7 on-demand, 10 minutes lead time

6.5
Average Distance (kilometers)

5.5

4.5

3.5

3
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 18: The average distance per request.

220
on-demand, no lead time
on-demand, 2 minutes lead time
200 on-demand, 4 minutes lead time
on-demand, 6 minutes lead time
on-demand, 8 minutes lead time
180 on-demand, 10 minutes lead time
Average Waiting Time (seconds)

160

140

120

100

80

60

40

20
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Requests Made

Figure 19: The average waiting time per request.

23
responsive and that already small lead times of 2 minutes lead to a very efficient system with
small waiting times for the users. On the other hand, it seems that the current algorithm is
not able to properly exploit larger lead times. It would be very interesting to understand if
a more sophisticated algorithm could make use of larger lead times and in this way further
reduce the average travel time and the average waiting time per request. This is left to future
research. All in all, the analysis suggests that the on-demand public transportation service
offers a great flexibility for the users, which can barely be found in other public transportation
systems that are currently used.

6 Conclusions and future research

Traffic congestion is a primary problem in most urban areas, also due to the constantly
increasing size of cities. A crucial issue has become the sustainability of the ever growing
number of cars on the roads which has led to a renewed interest in alternative forms of
transportation. This is witnessed by the wide diffusion of bicycle and car sharing systems, as
well as car pooling. However, the main issue concerning the scarce use of public transportation
means has not yet been properly addressed.
In this paper we have assessed a public transportation system that includes, besides the
conventional buses, an on-demand service with no fixed itineraries that allows users to commu-
nicate the desired departure time, origin and destination of the trip. A minibus, if acceptable
in terms of arrival time to destination, will pick up the user at the origin and deliver him/her
to the destination. In case the public system, conventional bus or on-demand minibus, does
not satisfy the acceptance threshold set by the user, the user will resort to using a private
car.
A large number of scenarios have been tested in the simulation study. The analysis
performed suggest the following conclusions:

• the on-demand service is dominating conventional public transportation by buses, in

terms of number of requests attracted, travel time and cost;

• the on-demand service is more environmentally friendly, can reduce traffic, pollution
and congestion.

There are several directions that are worth of further research, such as the usage of
more sophisticated algorithms for the routing and rerouting of minibuses, the usage of more
complex objective functions and a detailed analysis of the ecological impacts of the proposed
on-demand public transportation service.

Acknowledgements
The third author’s research has been supported by the Swiss National Science Foundation as
part of the Early Postdoc.Mobility grant 152293.

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