Empirical Evaluation of a Dynamic and Distributed ...

Empirical Evaluation of a Dynamic and Distributed Taxi-Sharing System Pedro M. d’Orey, Ricardo Fernandes and Michel Ferreira1 Abstract— Modern societies rely on efficient transportation systems for sustainable mobility. In this paper, we perform a large-scale and empirical evaluation of a dynamic and distributed taxi-sharing system. The novel system takes advantage of nowadays widespread availability of communication and computation to convey a cost-efficient, door-to-door and flexible system, offering a quality of service similar to traditional taxis. The shared taxi service is assessed in a real-city scenario using a highly realistic simulation platform. Simulation results have shown the system’s advantages for both passengers and taxi drivers, and that trade-offs need to be considered. Compared with the current taxi operation model, results show a increase of 48% on the average occupancy per traveled kilometer with a full deployment of the taxi-sharing system.

I. INTRODUCTION An efficient transportation system is vital for any modern society. Nowadays, private cars are clearly the dominant mode of transport. In the EU, the car accounts for 77 % of all motorized passenger transport and is the only mode for which overall demand has increased (14%), according to a study of the European Environment Agency (EEA) [1]. The same document has reported significant increases over the last decade in the price of fuel and in the expenditure for operating personal transport. All these factors combined make personal transport less attractive and can promote the development of an innovative transport modal split. Collective transport is an important alternative mode of sustainable mobility that can compete directly with private transport. A main goal of this type of transport is to reduce the number of vehicles in circulation and to promote efficiency in vehicle use. Car-sharing (decentralized car rental) [2][3] and car-pooling (ride sharing using private vehicles) [4] initiatives have proven successful in many cities in the United States and in Europe as a complement to traditional transport modes. Taxi-sharing has the same philosophy as car-pooling/sharing but instead relies on taxis as a transportation resource and has a more flexible mode of operation. Recently, a number of local initiatives for this last system have emerged: e.g. London [5], NYC [6], Taipei [7]. In this paper we focus our attention on taxi-sharing an advanced, user-oriented form of public transportation *This work was supported by the projects DRIVE-IN: ”Distributed Routing and Infotainment through Vehicular Internet-working”, MISC: ”Massive Information Scavenging with Intelligent Transportation Systems” and VTL: ”Virtual Traffic Lights” under Grants CMU-PT/NGN/0052/2008, MITPT/TS-ITS/0059/2008, PTDC/EIA-CCO/118114/2010, respectively, and by the Portuguese Foundation for Science and Technology under the Doctoral Grants SFRH/BD/61676/2009 and SFRH/BD/71620/2010. 1 The authors are with the Instituto de Telecomunicac ¸ o˜ es, Departamento de Ciˆencia de Computadores, Faculdade de Ciˆencias, Universidade do Porto, 4169-007 Porto, Portugal (e-mail: {pedro.dorey, rjf, michel}@dcc.fc.up.pt).

characterized by flexible routing and scheduling of vehicles operating in shared-ride mode between distinct pickup and drop-off locations according to passenger needs [8]. From the point of view of the customer, this service combines the advantages of the traditional taxi service (comfortable, door-to-door transportation, flexible) with some of the advantages of public transportation (e.g. reduced cost and minor environmental impact per passenger). The service provider benefits from the increased vehicle occupancy1 (e.g. higher income per trip) and fewer overall trips/traveled distance (e.g. reduced maintenance costs). Previous attempts to address the topic of shared taxis have mainly concentrated in pre-booking of the passenger demand and/or the use of pre-defined routes. More recently dynamic approaches, where requests and assignments are performed in real-time, have been proposed (e.g. [7][10]). Another common feature is the use of a central unit to perform all operations for taxi-sharing (e.g. [7][11]), which can have critical implications on scalability. Initial trials in major cities have not been truly successful since these implementations still suffer from the previously mentioned drawbacks and are not automated (at least some part of the process), implying high human involvement. In this paper we present a novel taxi-sharing system which aims to perform on the one hand coordination between user requests and taxi supply, and on the other hand coordination between user requests. The service is designed to be dynamic (no reservations and immediate assignment), distributed (no central authority), automatic (no human intervention) and door-to-door, in order to be attractive, flexible and costeffective for both passengers and taxi operators. Thus, the main goal is to provide a service with a similar performance to the traditional taxi service but offering additional environmental and cost benefits. Another major contribution of this paper is the evaluation of the system from a number of different aspects using the developed simulation tool and a full data set (e.g. real Origin/Destination (O/D) matrix) environment, which delivers highly realistic results. The remainder of this paper is organized as follows. In Section II, we briefly present a modified version of the Diala-Ride Problem. Section III details the proposed taxi-sharing algorithm’s assumption, functioning and functionality distribution. Section IV provides a simulation methodology for evaluating the operation of a taxi fleet. Section V details the simulation scenario, evaluation metrics and main results. The main conclusions are given in Section VI. 1 In

New York the average number of passengers per ride is 1.4 [9].

II. P ROBLEM S TATEMENT

III. TAXI - SHARING A LGORITHM

This section presents a short formulation of the problem of providing a door-to-door transportation to multiple clients, which is known as Dial-a-Ride Problem (DARP). To model this transportation problem we start by describing the three main entities involved in the main system operations, namely passengers, service provider and road transportation network. Customers present to the system a number of trip requests. Each service request contains pickup/delivery locations (Oi /Di ), seat demand (si ) and a maximum service degradation factor, which has as main function ensuring acceptable Quality of Service (QoS) for passengers. On the other hand, the service provider (e.g. taxi union) possesses a fleet of n vehicles with a capacity of C seats to fulfill trip requests. Usually, the fleet size will vary due to the changing customer demand and taxi-drivers shifts. Finally, the road transportation network provides the infrastructure for vehicle movements with a time-dependent impedance with respect to the number of vehicles, intersection control strategies, etc. The network is represented by a graph G=(V,E) containing a set of vertices (vj ) connected by edges (ej ). The generic DARP consists of designing vehicle routes and schedules for n users who specify pickup and drop-off requests between origin and destinations [12]. The generic problem has been adapted due to the novel characteristics of the algorithm and due to the relaxation of some conditions. In the present statement we consider a distributed and dynamic mode of operation where: i) nodes interact with each other to perform algorithm components computations; ii) requests are accepted at any time without the need for pre-reservation and are assigned immediately. These characteristics have led to a more restricted problem that is the determination of the optimal vehicle to perform a sub-set of services in taxisharing. Prior to the selection of the optimal vehicle, the optimal service sequencing that fulfills both, passengers and service provider’s requirements, needs to be determined for each vehicle. Thus, the main aim is the minimization of a cost function related to weighting of each service sequence. For each new service, the outcome of the problem resolution is the assignment of a route itinerary to a given vehicle. This itinerary contains an ordered set of pickup and delivery locations. The taxi-sharing problem is restricted by capacity, precedence and user constraints. Regarding the capacity constraint, the vehicle can only carry a maximum number of passengers that is updated whenever one user enters or leaves it. The number of allocated seats has to be equal or smaller than the vehicle capacity. Regarding the precedence constraint, whenever calculating routes between O/D, one needs to take into consideration that for each passenger the origin should precede the destination. The user constraint is related to the compliance and violation of the user-defined parameters (e.g. passenger ride time or distance). Whenever at least one of these constraints is not met, the associated service sequence should be discarded.

The on-line, on-demand taxi-sharing system is responsible for the efficient and real-time matching of user requests to available resources (taxi seats). On the other hand, it handles the coordination between requests in such a way that resources are shared by users in real-time. The proposed service has been designed to be costefficient and to provide a QoS similar to the traditional taxi service. The service is dynamic since user requests can be made on the fly and taxi assignments for passenger pickup are immediate. To ensure early acceptance, and an additional advantage over public transportation, we consider a doorto-door service. Furthermore, human intervention is reduced to the minimum in the proposed system, since the majority of the tasks are automated; the user solely needs to create a request containing the destination and the total number of passengers. Other distinguishing characteristics of the system are self-organization and distributed operation. The nodes involved in problem solving (taxis and users) interact with each other using wireless communications and perform distributed computation tasks (e.g path cost calculation) to select a taxi to serve a given client. By introducing selforganization, planning is done locally by peers without the need for a central authority. Distributed computing implies shorter processing times since the most complex tasks are performed in each vehicle instead of at a central location. Before providing more details on the algorithm, we outline the main requirements for vehicles and passengers: • position can be determined accurately from location sources (e.g. GPS); • computation and wireless communication capabilities (e.g. on-board computer, smartphone) are available; • routing and navigation is installed in vehicles. These requirements can be easily overcome since currently there is a widespread use of smartphones and modern taxi dispatching system include on-board computers with incorporated communication capabilities, which is in favor of the applicability of the system. Consider a typical urban scenario with a number of taxis (moving while or after servicing passengers or at taxi stands waiting for new passengers) and customer posing requests for immediate transportation. When a client needs to be transported from his current location (Oi ) a pickup request is made, which also includes his destination (Di ), the allowed service degradation factor and seat demand (si ). In the taxisharing setting end users can require taxi services in a number of ways. Due to the widespread use of smartphones one possible and straightforward implementation is the use of an application running on these devices. The request is received by all or a subset of moving taxis, which compute the distributed vehicle algorithm and communicate back to the user the cost associated with the trip. For each taxi this distributed algorithm is responsible for checking whether the new request can be associated to the current service(s) using a route cost criteria. The end user terminal receives the request responses, determines the least-cost admissible

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filtered making use of the service degradation factor, which is relative to the optimal path (shortest path in terms of distance or time). Each permutation is then considered valid if the conditions are acceptable to all passengers, either current or new. By offering a lower fare, the system ensures that passengers are compensated by the service degradation. In this step, vehicle capacity constraints are also verified: service sequences are discarded if, for any O/D pair, the total passenger number surpasses the maximum taxi capacity. Different service sequences result in distinct number of onboard passengers between O/D points, which can result in unacceptable solutions in terms of vehicle capacity. Usually, constraint assessment results in a reduced number (Y) of valid routes as illustrated in Fig. 1. The last component of the system then selects the minimum-cost service sequence whose cost is communicated back to the passenger (if applicable). The passenger request and the resulting best service sequence description, path and cost are stored during a certain period for future use (in case the user is assigned to this taxi). B. Distributed Algorithm - Customer

Fig. 1: Taxi-Sharing component installed at vehicles.

solution for taxi-sharing and selects a taxi to do the service. If there is no admissible taxi-sharing solution, the nearest available taxi is assigned (e.g. at the closest stand or the closest free taxi). Each of the algorithm’s main components, namely Vehicle Algorithm (III-A) and Passenger Algorithm (III-B), are explained in more detail in the following sections. A. Distributed Algorithm - Taxi In this section the distributed taxi-sharing algorithm executed at each taxi is given in more detail. The main objective of this component assemble is to calculate the best service sequence permutation, which can later be used to select the best vehicle for taxi-sharing. Fig. 1 depicts the main components of the algorithm installed at the computation device available in vehicles. The main inputs for the execution of the algorithm are the new service requirements (O/D pair, seat demand and user constraints) received from the customer and the current taxi state, namely the current number of passengers and the remaining service sequence. Making use of these service sequences (new and remaining), the first step in the algorithm is the concatenation of these sequences followed by the determination of all possible permutations between O/D points of the corresponding services. Some of these permutations will not be considered since the precedence constraint is not met: origins are preceded by the corresponding destinations. The resulting set of N service sequences is fed to a distance-based cost calculation function, that calculates the shortest path distance or time between all points in the sequence, in order to minimize the total travel distance. However, in order to take into consideration user constraints, these permutations are

The first task of the customer algorithm is to issue a service request with the parameters presented previously. Depending on the characteristics and size of the taxi the fleet, requests can be sent to specific taxis or to all taxis. This can be achieved by selecting specific geographical areas for information spreading. Afterwards, this algorithm receives, within a certain time window, route permutation cost values from several vehicles. The passenger algorithm then selects the best corresponding taxi for sharing. The present algorithm considers a simple technique where route permutation values are ranked and the highest value is selected (max RS). The selected taxi is then informed of the selection by means of wireless communications. If taxi-sharing is not feasible, the closest empty vehicle, either at the closest taxi stand or in the free state, is allocated to this service. IV. S IMULATION M ETHODOLOGY Analytical studies, field-trials and/or simulations are conducted whenever the feasibility and performance of Intelligent Transportation Systems (ITS) needs to be studied. In the specific case of collective transport we had to resort to simulation due to the dynamism of the proposed algorithm and due to the infeasibility to implement a complete field-trial. Besides, the system dynamism associated with the mobility of taxis makes the development of analytical models complex. Furthermore, simulation allows the study of different system configurations. Due to its performance and open-source nature, Development of Intervehicular Reliable Telematics (DIVERT) has been selected as the simulation platform to build upon the needed extra functionality. DIVERT [13] is a sophisticated microscopic simulator based on the Intelligent Driver Model (IDM) [14] with a validated mobility model [15]. The lanechanging model is based on the Minimizing Overall Braking decelerations Induced by Lane changes (MOBIL) model

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Fig. 2: Actual service points mapped into the road network of the city of Porto. The blue and red dots represent pickup and drop-off locations, respectively.

proposed by Kesting et al. in [16]. The implementation includes all the common features of a road transportation network (e.g. traffic signals). To mimic the functioning of a taxi fleet two main aspects have to be modeled in great detail, namely taxi operation and passengers requests. Taxi operation corresponds to the sequence of stages (e.g. leave taxi stand) that taxis follow to service clients and thus can be modeled as a state machine in which state transitions occur under certain conditions. In the simulator we have selected to explicitly model the taxi stop states and implicitly model the Movement state by updating the taxi path. Due to this the following states have been included: OnEnterTaxiStand, OnLeaveTaxiStand, OnEnterRouteStop and OnLeaveRouteStop. The transition between the OnEnterRouteStop and the OnLeaveRouteStop states occurs after a pre-defined timeout has been reached (e.g. 20 s). On the other hand, passenger requests corresponds to modeling the demand for taxi services and, consequently, for available capacity in vehicles. As input to the simulator we have used a list of real taxi requests obtained from a taxi fleet in the city of Porto. Since each request O/D is given by a GPS coordinate, the tool first matches this to the closest road segment in the map (see Fig. 2). After this procedure is completed, the result is stored in a file. A conceptual representation of the simulation platform is depicted in Fig. 3. The function of the service scheduler is to emit service requests at the defined time stamp. As previously explained, the taxi operation algorithms were build on top of the DIVERT platform, which models the microscopic behavior of vehicles and the communications between vehicles and/or infrastructure. The taxi operation component (including taxi-sharing) receives the pre-defined request events from the scheduler and starts the taxi-sharing algorithm described in section III. In case there is no reasonable sharing alternative, the Taxi Operation Algorithm is called. This last algorithm replicates the traditional taxi operation where there is solely one service per O/D pair. Given any service sequence, the Taxi Routing component is responsible for providing the shortest path and associated

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cost to the remaining blocks. The Taxi System State stores relevant information for the algorithm functioning (e.g. current taxi state (e.g. busy), current service position). V. P ERFORMANCE A NALYSIS A. Scenario We evaluate the taxi-sharing algorithm using realistic input parameters and a large-scale scenario. The replicated scenario is the city of Porto, which is the second largest in Portugal, spanning an area of 41.3 km2 . Fig. 2 represents the road network of the city, which comprises 965 km of extension and has 328 (out of 1911) intersections managed by physical traffic signals. Porto is the central city in a metropolitan area with 1.3 million inhabitants. In the city there are 63 taxi stands and the main taxi union has a fleet of 441 vehicles. The capacity of the vehicle was set to 4 passengers since in Porto all taxis have 5 seats. This union has recently installed a dispatching and fleet management system, which allows to constantly monitor taxi locations and taximeter information. Thus, services’ O/D points can be determined by combining relevant data (see Fig. 2). In the present analysis we resort to 3 hours of taxi operation, which corresponds to 864 services, as input to the simulation request scheduler. The services file contains data of peak hours of a working day. In this city supply clearly exceeds demand since taxis spent a great amount of time idling. Another important simulation parameter is the number of passengers per trip. Since these values cannot be obtained from the taxi management system, we conducted in collaboration with taxi drivers a survey to determine the average number of passengers per trip, which resulted in the following distribution: i) 82% - 1 passenger, ii) 13% - 2 passengers, iii) 4% - 3 passengers and iv) 1 % - 4 passengers. To be able to isolate the benefits of the proposed taxisharing system a number of parameters had to remain constant. Firstly, we chose to solely simulate the vehicles in the taxi fleet; as future work we intend to study the performance of the algorithm under varying traffic conditions. Furthermore, a reasonable service degradation factor of 1.2 has been selected.

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B. Metrics To study the benefits of the taxi-sharing system, two distinct perspectives need to be considered: taxi operator and passenger. For the taxi operator, one of the main goals is related to the reduction of the operational costs or an increase in revenue. Yet for passengers, performance can be more related to costs, service duration or waiting time. Here, we analyze these two different perspectives using a number of aggregate variables that measure the overall system performance: • (taxi) total travel distance; • (taxi) number of taxi stand departures; 2 • (passenger) average waiting time ; 3 • (passenger) average service time . In this paper we also aim to study the influence of partial deployment of the taxi-sharing system. Accordingly, in the following analysis we present results for a varying taxisharing penetration rate. To obtain an estimate of each metric, twenty simulation runs were performed and later on averaged for each taxi-sharing penetration rate. In this study, we have also computed 95% confidence intervals for the mean of each metric using the bootstrap method (see Fig. 5 and Fig 6). C. Results & Discussion In this section, we present the main simulation results that were obtained using the simulation platform given in section IV. The simulator was configured with the settings provided in section V-A. Using the metrics defined in V-B the main simulation results are reported. Fig. 4 presents the total travel distance for various number of on-board passengers. From the analysis of the plot, the first fact to notice is the predominance of 2 Time 3 Time

elapsed between request and vehicle arrival to client’s origin point. elapsed between client’s origin and destination points.

0 (free), 1 and to some extent 2 passengers. However, as the system penetration ratio increases, the evolution of these plots changes differently. For the free state and for the 1 passenger case there is a sharp reduction since with this system vacant seats can be shared. In the opposite direction, for two or more passengers there is a significant increase on the total number of traveled kilometers. As a corollary from the results plotted in Fig. 4, we have computed the average occupancy per traveled kilometer (driver and free state included). For a 0% taxi-sharing penetration rate, the average occupancy is 1.89, while for 100% taxi-sharing enabled vehicles this value raises to 2.32, which corresponds to a 22% increase. If we count the driver as an inherent part of a moving vehicle, the increase is of 48%. These results show that the introduction of taxi-sharing leads to increased average passenger occupancy reducing the “empty seats traveling” problem. Fig. 5 depicts the number of vehicle departures from taxi stands needed to perform all services. In the opposite direction, this metric can also be used to understand the number of moving taxis. For a scenario with the traditional taxi operation (0% taxi-sharing), the number of exits is similar to the number of services. However, these values do not match exactly since services can be assigned to vehicles in the free state. As the percentage of taxi-sharing enabled taxis increases, the number of taxi stands exits diminishes. This result indicates that a smaller number of vehicles is needed to fulfill a given service demand and that the taxis that are moving should spend less time idling. In the following part we consider some additional aspects strictly related to customers. Fig. 6 depicts the average passenger waiting, service and total transit times. For all settings, average waiting and service times are small since the closest free taxi to each passenger is assigned, and real service

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Sharing of taxi resources is also beneficial for passengers since these will be able to reduce their travel costs and, eventually, will be serviced faster in a high demand scenario. The longer the shared trip distance is and the greater the number of sharing parties is, the lower the cost for each passenger will be. However, the passenger will also pay a cost in terms of transit time (waiting + service) when compared to the traditional taxi system. More specifically, each passenger will spend a small additional amount of time to reach its destination since, usually, a detour will be made to serve other passengers. Yet, passengers can control this additional amount of time since they define the service degradation factor. The operation of a taxi fleet is selfish by nature, since every owner tries to maximize his own profits. However, taxi drivers should take into consideration other aspects of the taxi operation. Simulation results have shown that the total overall number of kilometers can be reduced with the introduction of taxi-sharing, which has a positive impact on the reduction of operational costs and can postpone capital expenditure (e.g. purchase of new vehicles). Other important implication of the implementation of the system is a remarkable diminution of distance driven in the free state; this is particularly important for the taxi driver since no revenue is made in this period. The increased passenger occupancy is also beneficial for the taxi driver since its revenue per traveled kilometer will increase, which will eventually lead to increased profitability. Thus, we believe that taxi unions will be willing to accept this new mode of operation since it can lead to a more efficient operation, to reduced operational expenditure and possibly to increased service demand. Analyzing the reported results, we conclude that the proposed system presents good performance. As illustrated previously, the system performance is strictly related to the penetration ratio of this transportation service. Furthermore, a trade-off between the system efforts and passenger service degradation is observed. VI. CONCLUSIONS

distances are small. Besides it should be emphasized that all these values are inline with the actual taxi performance. Data also shows that, as the system penetration ratio increases, the average transit time increases. The degradation of the QoS is especially clear for the average waiting time as this parameter is solely indirectly constrained. However, the average waiting time and service times are within acceptable limits. Fig. 7 depicts the Cumulative Distribution Function (CDF) of passengers’ waiting, service and total transit times. The analysis of these plots confirms the observations made earlier on, namely that passengers’ waiting and transit times are degraded with the increasing introduction of taxi-sharing. Yet, most passengers (80 %) are picked up within 10 min and its service time is increased only by up to 3 min, which clearly traduces into reasonable transit times. Another interesting fact to underline is that further degradation in waiting and service times is almost negligible for taxi-sharing penetration rates bigger than 50%.

In this paper, we have proposed a novel distributed and dynamic taxi-sharing algorithm enabled by wireless communications and distributed computing capabilities to perform coordination between customers’ requests. Furthermore, we have developed a large-scale and highly realistic simulation environment that makes use of a full data set (e.g. O/D matrix) for evaluating the operation mode of any taxi fleet. Simulation results have demonstrated the feasibility of the taxi-sharing system and added advantages for both taxi driver and passengers. Taxi drivers benefit from this scheme since they can lower their operational cost (lower total travel distance and lower number of taxi stand departures) and can increase their profitability per traveled distance (higher average number of passenger per trip). On the other hand, passengers will be able to lower their transportation cost due to sharing but need to be willing to have longer waiting and travel times. Yet, trip times can by restricted by a service degradation factor.

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Fig. 7: Cumulative Distribution Function (CDF) of Waiting, Service and Total Times for different Taxi-Sharing Penetration Rates. Despite the increased travel times with increasing taxi-sharing usage, the values are actually within reasonable limits for passengers.

Apart from the mentioned advantages, the society as a whole will also benefit, namely in terms of reduced pollutant emissions and decreased congestion4 . As future work we intend to study and quantify the environmental impact of the implementation of this type of transportation system. Furthermore, we shall address the problem of defining a fair tariff system for both passenger and taxi driver. Additionally, incentives for the early acceptance and usage of this system need to be investigated. Scenarios where demand exceeds supply need to be further analyzed since the QoS experienced by customers can differ substantially. Further work is also necessary to study the best communication model for the taxi-sharing system. R EFERENCES [1] European Environment Agency, “Laying the foundations for greener transport (TERM 2011),” Copenhagen, Denmark, Tech. Rep. 7, 2011. [2] ZipCar. [Online]. Available: http://www.zipcar.com [3] BuzzCar. [Online]. Available: http://www.buzzcar.com [4] Carpooling. [Online]. Available: http://www.carpooling.com [5] Transport for London. [Online]. Available: http://www.tfl.gov.uk/ gettingaround/taxisandminicabs/taxis/1144.aspx [6] Fare/Share NYC. [Online]. Available: http://faresharenyc.com 4 Metropolis, such as Beijing, China, which has serious congestion problems, have tens of thousands of taxis circulating permanently.

[7] C.-C. Tao, “Dynamic Taxi-Sharing Service Using Intelligent Transportation System Technologies,” in International Conference on Wireless Communications, Networking and Mobile Computing, New York, USA, Sept. 2007, pp. 3209 –3212. [8] “Demand Responsive Transit service (DRTs): PersonalBus - Tuscany,” European Commission Directorate-General for Energy and Transport, Florence, Italy, Tech. Rep. R853, 2009. [9] Southern California Association of Governments, “Maximizing mobility in Los Angeles first and last mile strategies,” Los Angeles, USA, Tech. Rep., 2009. [10] S. Frattasi, H. Fathi, A. Gimmler, F. Fitzek, and R. Prasad, “A New Taxi Ride Service for the Forthcoming Generation of Intelligent Transportation Systems,” in Proc. of the International Conference on ITS Telecommunications, Brest, France, Jun. 2005. [11] P.-Y. Chen, J.-W. Liu, and W.-T. Chen, “A Fuel-Saving and PollutionReducing Dynamic Taxi-Sharing Protocol in VANETs,” in Proc. IEEE Vehicular Technology Conference, Sept. 2010, pp. 1 –5. [12] J.-F. Cordeau and G. Laporte, “The Dial-a-Ride Problem (DARP): Variants, modeling issues and algorithms,” 4OR: A Quarterly Journal of Operations Research, vol. 1, pp. 89–101, 2003. [13] H. Conceic¸a˜ o, L. Damas, M. Ferreira, and J. Barros, “Large-scale simulation of V2V environments,” in Proc. ACM Symposium on Applied computing, Fortaleza, Brazil, 2008, pp. 28–33. [14] M. Treiber, A. Hennecke, and D. Helbing, “Congested traffic states in empirical observations and microscopic simulations,” Physical Review E, vol. 62, no. 2, pp. 1805–1824, Aug. 2000. [15] M. Ferreira, H. Conceic¸a˜ o, R. Fernandes, and O. Tonguz, “Stereoscopic Aerial Photography: an Alternative to Model-Based Urban Mobility Approaches,” in Proc. ACM International Workshop on VehiculAr InterNETworking, Beijing, China, 2009, pp. 53–62. [16] A. Kesting, M. Treiber, and D. Helbing, “General Lane-Changing Model MOBIL for Car-Following Models,” Transportation Research Record, vol. 1999, no. 1, pp. 86–94, 2007.