Senseable City Lab :.:: Massachusetts Institute of Technology

Transcription

1 Senseable City Lab :.:: Massachusetts Institute of Technology This paper might be a pre-copy-editing or a post-print author-produced.pdf of an article accepted for publication. For the definitive publisher-authenticated version, please refer directly to publishing house s archive system SENSEABLE CITY LAB

2 Care to Share? Using GPS Fleet Data to Assess Taxi Sharing Paolo Santi 1,2, Carlo Ratti 1 1 Senseable City Lab, Massachusetts Institute of Technology, Cambridge, US 2 Istituto di Informatica e Telematica del CNR, Pisa, Italy ABSTRACT GPS technology has been extensively used to optimize operation of taxi systems since the first appearance of commercial GPS devices. Owing to this, data sets generated by taxi fleets are amongst the first and most representative examples of massive GPS data that have been systematically collected. The analysis of these data sets has recently generated a rich literature aimed at, among other things, identifying optimal taxi driver strategies, predicting taxi demand or location of vacant taxis, etc. This chapter focuses on what is a new, exciting field of investigation of GPS taxi data analysis, namely, evaluating the impact of a shared taxi system on the urban environment. After introducing the notion of (taxi) ride sharing, the chapter presents the relevant literature, describing in greater details a methodological approach called shareability network that allows formal characterization of taxi sharing opportunities in an urban environment. Keywords: Global Positioning System, Taxi systems, Dynamic ride sharing, Static ride sharing, Shareability, Sharing Delay, Matching Algorithm, Shareability network. INTRODUCTION In recent years, spatio-temporal data sets have been used extensively to characterize human mobility at the urban, regional, national, and international scale (Calabrese, 2011; Gonzales, 2008; Song, 2010). GPS data has proven especially valuable to this purpose, given its high spatial and temporal resolution compared to other data sets - such as cell phone records. Let s look at the difference between GPS and cell phone data in more detail. A GPS device typically logs the position with a frequency in the order of seconds or, at most, a few minutes, and a spatial accuracy of the order of tens of meters (the latter can be actually much higher if GPS is used in combination with digital maps and map matching algorithms). Conversely, cell phone data typically have a spatial accuracy of the order of hundreds of meters or a few kilometers (depending on the coverage area of cell towers), and a temporal resolution, which is heavily dependent on how active a cell phone user is. Even in case of very active users, however, position is tracked with a resolution of the order of a few minutes. Based on the example above, it is not surprising that GPS data is considered particularly valuable to those interested in studying human mobility. One of the most established collection of GPS data sets that have been analyzed in the literature deals with taxi systems. In their drive to optimize fleet management, taxi companies have been among the first adopters of GPS technology. Vast collections of taxi GPS traces have been collected across the world since over ten years. Such data is particularly interesting for researchers for at least two reasons: 1) it can be used as a sample of individual human mobility in urban environments, contributing to the definition and/or validation of urban mobility models; 2) it can be used to better understand the dynamics of vehicle fleets, which are a very relevant component of urban transportation systems.

3 As a result, the analysis of GPS taxi data has produced a rich literature in the field of GIS, data mining, mobility modeling, and urban transportation. In the realm of traffic and urban mobility modeling, Aslam et al. (2012) show how traffic volume can be estimated in real time through taxi data, while Liu et al. (2011) focus on discovering spatio-temporal interactions in traffic patterns. With the goal of characterizing the dynamics of taxi systems, several authors have studied taxi driver s strategies that maximize profit (Liu, 2010), methods for predicting taxi demand (Huang, 2012;Yuan, 2011; Zhang, 2014), and identification and prediction of vacant taxis (Phithakkitnukoon, 2010). One of the most interesting applications of GPS taxi data analysis is evaluating the impact of ride sharing on the urban environment. In fact, the burgeoning sharing economy phenomenon, i.e., the collaborative consumption of shared resources enabled by the pervasiveness of information technologies and Internet connectivity (Sundararajan, 2013), is rapidly growing also in the context of urban transportation: vehicle sharing companies such as ZipCar and Car2Go are booming, as well as companies offering ride sharing services such as Bandwagon and Uber which recently launched a new UberPool application. New sharing services/companies are popping up in several cities worldwide. What will be the effect of these novel mobility concepts on the urban landscape? Will the increased sharing of mobility resources reduce traffic, thus making cities a better place to live in? Or, will undesired effects such as draining of mobility demand from public transportation services prevail? The answer to these questions is far from being obvious, but an initial glimpse into the potential of massive, urban-level ride-sharing system can be obtained from the analysis of GPS taxi data. This chapter starts by introducing and formalizing the notion of ride-sharing, and reporting on recent literature that deals with the evaluation of ride sharing systems using GPS taxi data sets. More specifically, the chapter will start introducing the notion of static and dynamic ride sharing, and the theoretical framework of dynamic pickup-and-delivery problems that is used to model ride sharing. The chapter will then present instances of heuristic approaches to tackle the dynamic ride sharing problem. A more rigorous treatment of the ride-sharing problem can be achieved in case of static ride-sharing: the recently introduced notion of shareability network allows formal characterization of the maximum possible sharing opportunities arising in a collection of individual trips. The notion of shareability network and its application to a massive data set of GPS taxi traces collected in the city of New York is discussed in the last part of the chapter, together with numerical results. BACKGROUND Ride sharing refers to a form of individual, point-to-point transportation in which at least a portion of the trip is shared with another passenger. Ride sharing should not be confused with carpooling, which is a form of recurrent ride sharing, where typically the entire ride is shared with other passengers who have the same origin and/or destination. To better clarify the difference between the two notions, carpooling typically refers to a situation where a group of passengers (say, co-workers living in a same neighborhood) organize themselves and use a single vehicle for a shared ride, thus saving on transportation costs. The passengers sharing the ride thus have the same destination (or origin, in case of the reverse trip), and very similar origins. Furthermore, the vehicle used for the shared ride is typically owned and driven by one of the passengers. Conversely, ride sharing refers more in general to the occasional sharing of a portion of a ride between two passengers that, in principle, might be perfect strangers. Furthermore, the passengers of a shared ride do not necessarily have the same (or very similar) origin/destination, and they typically do not own nor drive the vehicle. The differences between ride sharing and car pooling are pictorially described in Figure 1. Figure 1. Ride sharing and car pooling

4 Ride sharing typically comes along with some delay that passengers experience as a consequence of the shared ride. Let us refer to Figure 1 and let us take Passenger s 1 perspective; in case Passenger 1 takes an individual ride from P 1 to D 1 (top left), she will arrive at destination D 1 at an estimated time t 1. In case of ride sharing (top right), though, a detour is needed to pickup and drop off Passenger 2 along the way to D 1. As a consequence of this, the estimated arrival time of Passenger 1 at D 1 is t 1 S > t 1, and Δ= t 1 S - t 1 is called the sharing delay. Note that the sharing delay is, in a sense, an intrinsic effect of ride sharing occurring whenever origins and destinations of the shared trips are not perfectly aligned in time and space. Sharing delay is a quantifiable measure of the discomfort passengers experience as a consequence of the shared ride, and for this reason it is often included in formalizations of the ride sharing problem. Other forms of passenger discomfort related to lack of privacy, safety, and other psychological barriers to sharing, are more difficult to quantify and, for this reason, are typically disregarded in mathematical ride sharing models. An important distinction in ride sharing models is between static and dynamic ride sharing. In the static model, the taxi service operator collects requests for a shared ride for a short time interval (say, a few minutes), and only trips in the current pool of collected requests are considered for sharing. If two or more individual trips from the pool can be shared, they are matched to form a shared trip, and a single taxi is dispatched for accommodating the combined trip requests. From that time on, and until the time at which the last passenger is dropped, the taxi is considered as occupied and not available for further ride sharing (even if there are still available seats onboard). Thus, similarly to a traditional taxi system, a taxi in case of static ride sharing can be in two possible states: empty, when there is no passenger on board; or occupied, when the taxi is serving either a single or a shared trip. In the dynamic ride sharing model, taxis can be in one of three states: empty, when there is no passenger onboard; shareable, when there is at least one passenger onboard but seats are still available for sharing; and occupied, when all available seats are occupied. In this model, requests for a shared ride are possibly matched not only with currently unserved requests, but also with ongoing shared trips being served by shareable taxis. In case a new trip is assigned to a shareable taxi, the driver is informed of the new passenger to pickup, and a re-route is done to pickup the new passenger, possibly before current passengers are dropped off. Referring back to Figure 1, after trips 1 and 2 are matched, in case of static ride sharing, the shared trip with pickup point P 1,2 and drop off point D 1,2 is considered as an indivisible trip that is served by a single taxi, and no further detour to accommodate additional passengers is allowed on the way from P 1,2 to D 1,2. In case of dynamic ride sharing instead, the trip from P 1,2 to D 1,2 is still considered for sharing with other passengers, as long as there are available seats in the taxi. If other trip requests are matched to the ongoing ride, the taxi might make additional detours on its way to D 1,2 (or to the new destination) to accommodate the additional passengers. To the authors best knowledge, static ride sharing approaches are currently most used in the context of car pooling, while other recently launched services such as Uber Pool are based on dynamic ride sharing. When considered from the system designer, taxi operator, and customer viewpoint, both models have pros and cons. From the system designer and taxi operator s viewpoint, the static model is easier to optimize, implement and operate; on the other hand, static ride sharing is not able to fully exploit potential sharing opportunities offered by partially occupied taxis, as it is instead done by the dynamic model. The dynamic model is however virtually impossible to fully optimize, and more complex to run and operate. From the customer s viewpoint, static ride sharing offers a better travel experience: upon pickup, the customer knows expected travel time to destination (possibly including pickup/drop off of other passengers), and

5 this travel plan does not change after departure. However, the likelihood of actually being able to share the ride is lower than in case of dynamic ride sharing, due to partial exploitation of ride sharing opportunities. This ultimately results in a relatively smaller number of passengers served with a shared ride in case of static vs. dynamic ride sharing, negatively contributing to the overall quality of service offered to passengers. On the downside, the dynamic model undoubtedly offers a lower quality travel experience to customers, whose arrival time at destination is no longer accurately predictable at pickup time due to possible dynamic re-routing of the taxi. MATHEMATICAL MODELING In the most general case, the ride sharing problem can be modeled as an instance of the class of pickup and delivery vehicle routing problems (Barbeglia, 2010). This is a very ample class of problems in which commodities (objects or people) have to be transported between a set of origins and a set of destinations by a fleet of vehicles. The problem consists of building a set of routes (one for each vehicle in the fleet) in such a way that all commodities are transported to their respective destinations, and some reference metric (e.g., total traveled distance) is optimized, subject to a set of constraints describing, for instance, desired pickup/delivery times, upper bounds on vehicle capacity, etc. Pickup and delivery problems find application in transportation scenarios ranging from optimization of courier deliveries, logistics and long range transportation, pickup and delivery of disabled patients, and so on. Pickup and delivery problems are called dynamic when at least a portion of the input data is revealed or updated during the period of time in which the operation takes place. Dynamic ride sharing is then an instance of dynamic pickup and delivery problem where the commodities to be transported are passengers, the fleet of vehicles is composed of taxis, and input (requests for a shared ride) is revealed during the operation time of the taxi fleet. A typical way of tackling pickup and delivery problems is by use of mathematical programming techniques. Mathematical programming is a process composed of the following steps: 1. formally represent the quantity to be optimized in terms of an objective function. For instance, the objective function could be defined as the total distance traveled by the taxi fleet to serve a set of requests, or the total travel time; 2. define a set of inequalities and equations representing system operational constraints. The defined set of inequalities and equations are collectively referred to as the constraints of the mathematical problem. For instance, inequalities shall be defined to ensure that the vehicle assigned to serve a certain trip request must travel to the passenger pickup location before traveling to the drop off location. Furthermore, inequalities can be defined to bound the sharing delay, etc. 3. solve the mathematical program defined by 1 and 2. Notice that the computational complexity of step 3, and hence the feasibility of computing the optimal solution to the problem at hand, heavily depends on the shape of objective function and of the constraints, as well as on the problem size, i.e., on the number of constraints and variables used to define the problem. Even in the relatively simpler case of linear objective function, linear constraints, and real valued variables, solving a mathematical problem might turn out to be a daunting task if the number of constraints/variables is in the order of thousands or higher, which is typically the case with taxi ride sharing. As an example, the average daily number of taxi rides in the city of New York is in the order of 450,000 (New York Taxi and Limousine Commission, 2014), implying that a hypothetical mathematical program aimed at optimizing ride sharing of a single day of operation in New York should have a number

6 of constraints and variables in the order of 10 5 : solving a problem of this size is unfeasible with current technology. The above discussion has highlighted the computational difficulties related to optimally solving dynamic ride sharing problem at city level. To get around these difficulties, two approaches are possible: a) resuming to heuristic approaches: computationally efficient heuristics can be designed to produce sub-optimal dynamic sharing of rides. b) reducing the problem complexity by considering static ride sharing, and imposing further restrictions on the type of possible sharing options. Both approaches are considered in the remainder of this chapter. First, representative heuristics for dynamic ride sharing are presented. Then, an efficient methodology for computing the static, optimal matching of pair of trips is presented. DYNAMIC RIDE SHARING HEURISTICS This section presents two representative heuristics that have been recently proposed to tackle the dynamic ride sharing problem. Partition based match making The partition based match making approach to dynamic ride sharing has been proposed by Xiao et al. (2013). To tame the computational complexity of the dynamic ride sharing problem, the authors introduce the notion of partition. A partition is a suitably defined closed region of the road network, and it is used to guide the trip match making process. More specifically, partitions are defined based on the classification of road segments in the road network. The authors consider three categories: i) highways, ii) major roads, and iii) minor roads, and build partitions based on highways and major roads, since these typically divide a city into several partitions see Figure 2. As it might be expected, defining partitions based on highway/major roads is not always precise, and Xiao et al. (2013) propose a three step procedure to come up with a well-defined partitioning of the road network. Figure 2. Road network partitioning (digital map courtesy of Hongmou Zhang) Step 1: Basic partitioning This step consists of generating bounding shapes for all major roads by means of buffer and union operations. The buffer operation generates a bounding shape of width α around every single major road, while the union operation combines overlapping bounding shapes in a single shape see Figure 3. By applying buffer and union operations, a buffer zone can be defined which effectively divides the road network into partitions, where the partition is defined by the areas enclosed within the buffer zone. Figure 3. Buffer and union operations used to define partitions Step 2: Partition scaling The outcome of step 1 is a number of disjoint partitions that exclude all major roads. This is not desirable since most taxi trips actually occur along major roads. To get around this problem, in the second step each partition is up-scaled according to a parameter β, until adjacent partitions overlap. This way, also major

7 roads and highways are included in the partitioning, and ride sharing opportunities can be better exploited. Step 3: Problem fixing Steps 1 and 2 being automated processes working on geographical data, the partitioning obtained at the end of these steps might display undesirable features. For instance, in the likely case that partitions have sizes varying across a wide range, it might be possible that small partitions are actually omitted if the value of α used to build the buffer zones in Step 1 is too high. Also, due to border effect, minor roads at the border of the road network might not be included in any partition. Fixing these and similar problems require manual intervention, which is performed in Step 3 of the procedure. After Steps 1 to 3 above are completed, the road network is divided into a number of well-defined, adjacent, non-overlapping partitions. The partitioned road network constitutes the input to the match making algorithm, which works as follows. Given the road network partitioning, a trip from an origin to a destination can be described as a sequence of partitions that must be traversed en route to the destination. Sequences of partitions are called corridors. The match making algorithm compares the corridor of one passenger with that of another passenger: if one corridor is found to be a subset of the other, the two passenger can potentially share the ride. More specifically, if, at any point in time, two passengers reside in the same partition, their corridors are compared in order to see whether one is a subset of the other. If this is the case, the two trips are considered as candidates for sharing. Notice that there are two possible ways in which a passenger can reside in a partition: either the passenger is already sitting in a taxi on its way to the destination, or the passenger is still looking for a taxi. The match making algorithm requires that at least one of the two passengers is still looking for a taxi. This requirement is needed to avoid considering as potentially shareable trips performed by passengers already sitting in distinct taxis. The performance of the match making approach presented by Xiao et al. (2013) heavily depends on how the road network partition is defined: relatively coarser partitions result in more sharing opportunities since the road network is divided into a smaller number of sub-regions, and the conditions for matching two trips are more likely to be fulfilled; on the other hand, coarser partitions result in a relatively higher level of passenger discomfort due to sharing. In fact, relatively larger partitions result in relatively higher value of average inconvenience, where inconvenience is defined by Xiao et al. (2013) as a metric closely related to the sharing delay as defined herein. The reason of this is quite clear: trips can be matched only if one of the respective corridors is a subset of the other; thus, the deviations from a passenger s ideal route to destination incurred as a consequence of ride sharing are confined to happen within the boundary of partitions. Hence, larger partitions imply potentially larger deviations from the ideal route and, consequently, potentially larger sharing delays. Xiao et al. (2013) also present an approach for optimally choosing the α and β parameters used in the partitioning process, so to minimize the inconvenience (averaged over all partitions) subject to an upper bound to the maximum inconvenience. The resulting values of α and β are then used to assess the performance of the match making algorithm in the city of Singapore, where a number of taxi trips is randomly generated using a tool for simulating realistic travel patterns called SEMSim. Defining the sharing potential as the percentage of trips that can potentially be shared according to the above described match making algorithm, Xiao et al. (2013) find a sharing potential ranging from less than 5% to about 27% depending on the time of the day, with an average sharing potential of 15.56%. These results are obtained considering an upper bound to the maximum inconvenience set to 5 minutes. Xiao et al. (2013) also evaluate how the sharing potential varies as a function of the average inconvenience, quantitatively confirming the intuitive observation that relatively larger partitions result in relatively higher sharing potential, at the expense of a relatively higher average inconvenience. T-Share

8 T-Share is a dynamic taxi ride sharing system introduced by Ma et al. (2013), which is specifically designed to be highly efficient and scalable. Ma et al. (2013) aim to build a system that can actually be operated in real-time at the scale of a large city like Bejing. The T-Share system is pictorially represented in Figure 4. The main components of the system are: 1. the communication interface, by means of which passengers, taxis, and the internal components of the T-Share system can communicate; 2. the request queue, which collects all trip requests submitted by passengers, and serves them in a First-Come-First-Served fashion; 3. the taxi searching module, which, given the current request Q, identifies a set of candidate taxis for serving the request according to the procedure described in the following; 4. the scheduling module, which, given a set of candidate taxis output by the taxi searching module, selects the taxi that shall serve Q, and updates the route of the chosen taxi accordingly; 5. a spatio-temporal index module, which, given updates on taxi positions and input from the scheduling module, stores and maintains an efficient spatio-temporal index of each vehicle in the taxi fleet. Figure 4. The T-Share taxi sharing system Requests are defined by a pair of pickup and drop off locations, a request generation time, and time windows for both the pickup and drop off times. A request Q is said to be satisfied if there exists a taxi V with available seat capacity that can pickup and drop off the passenger within the defined time windows, and such that the time constraints for pickup and drop off are still satisfied also for the other passengers already on board V. The dynamic taxi ridesharing problem Ma et al. (2013) attempt to solve can be formally defined as follows: given a taxi fleet composed of a fixed number of taxis and a stream of passenger requests, find a scheduling and dispatching of taxis such that all requests are satisfied, and the minimum total distance on the road network is traveled. By showing a reduction from the Travelling Salesman Problem with Time Windows, Ma et al. (2013) show that the above defined problem is NP-complete, i.e., it cannot be efficiently solved. Ma et al. (2013) then proceed by presenting a computationally efficient heuristic to compute a sub-optimal solution to the dynamic ride sharing problem, which is implemented through the three core components of the T-Share system described above: the taxi searching, the scheduling, and the spatio-temporal index module. Since the two former modules build on functionalities provided by the spatio-temporal index, we start describing this module. The goal of the spatio-temporal index module is providing the taxi searching and scheduling modules with up-to-date and ready to use information about the spatio-temporal location of each taxi. To this purpose, the road network is partitioned using a square grid of a pre-defined size (e.g., 1 1 Km). Within each grid cell, the road network node, which is closest to the geographical center of the cell is selected to be the anchor node of the cell. Then, the travel time t ij and travel distance d ij between any possible pair of cells are estimated computing the shortest path between the respective anchor nodes, and stored in the grid distance matrix. Notice that the grid distance matrix contains static information that can be computed once and for all. The spatio-temporal index module also builds and maintains the following data

9 structures, one for each cell: the temporally-ordered list, the spatially-ordered list, and the taxi list. The temporally- and spatially-ordered lists are lists referring to all the other cells, which are sorted in ascending order of travel time and travel distance, respectively. Since both lists are built from the static information contained in the grid distance matrix, these lists are static as well. Conversely, the taxi list includes dynamically updated records of the IDs of all taxis, which are scheduled to enter the cell in a suitably defined time horizon (set to 1 hour by Ma et al., 2013). The taxi IDs in the list are ordered based on the expected arrival time t a in the cell, with t a =0 indicating taxis already in the cell at present time. The goal of the taxi searching module is identifying a list of candidate taxis for serving a trip request Q. In order to identify candidate taxis, the module scans the temporally-ordered lists of the origin and destination cells of the trip request Q. Let C be a considered cell in the temporally-ordered list of the origin cell C o of Q. The taxi searching module verifies whether it is possible for a taxi located in C to reach C o in the pickup time window of Q. If yes, all taxis in C are included in the origin-side candidate set. A similar procedure is performed starting from the destination cell C d, possibly building the destination-side candidate set. If the intersection of the origin- and destination-side candidate sets is nonempty, then the taxis in the intersection are returned as the candidate set. Otherwise, the taxi search area is expanded by selecting the next cell in the respective spatially-ordered list. The choice of selecting the next cell from the spatially-ordered cell list is motivated by the need of minimizing the total distance traveled by the taxi fleet, which is the optimization objective upon which T-Share is built. The goal of the scheduling module is to identify, within the candidate set returned by the taxi searching module, the taxi which satisfies Q with minimum additional travel distance with respect to the current schedule. This is accomplished by means of two procedures: a procedure for inserting an additional trip to a taxi schedule, and a procedure for lazy shortest path computation. The first procedure identifies, amongst all possible ways of inserting the origin and destination locations of Q into the schedule of a taxi, the one that is feasible and minimizes the additional travel distance. In order to do that, as many as four shortest path calculations are needed for each possible way of insertion. This implies that, if this procedure has to be executed in real time, a very efficient shortest path calculation method must be implemented. This is the goal of the lazy shortest path computation procedure. In a nutshell, the procedure leverages the grid distance matrix, triangle inequality, and caching to delay shortest path calculation until the calculation is really needed. Details on the lazy shortest path calculation procedure can be found in the study by Ma et al. (2013). Ma et al. (2013) evaluate their approach by performing experiments using the real road network of Bejing, which is composed of 106,579 road nodes and 141,380 road segments, and is partitioned into cells. Taxi trajectories are extracted from a GPS data set recorded by over 33,000 taxis during a period of 87 days in the year The total distance traveled by taxis in the data set amounts to more than 400 million kilometers. Taxi trajectories are pre-processed and segmented into trips, and trips further divided into empty and occupied trips. At the end of the pre-processing phase, the data set is composed of about 200 million trips, 46% of which are occupied, and the remaining 54% are empty. The above described data set has been used to generate dynamic travel requests that are as realistic as possible. To this purpose, time is discretized into 5-minute bins, while space is discretized to the level of road segment. The occupied taxi trips recorded in the data set are used to compute the relative frequency for each spatio-temporal bin. Furthermore, the recorded data set is used also to estimate the destination distribution for each possible origin road segment. Travel requests are then dynamically generated as follows: 1) arrival times of requests are generated according to a Poisson process of a certain intensity, and distributed into a spatio-temporal bin according to the relative frequencies computed above; 2) we assume the trip request originates at a certain road segment r o ; the destination of the trip is chosen according to the destination distribution for r o, as estimated from the data set.

10 Ma et al. (2013) evaluate the performance of T-Share with increasing request arrival rates. The main performance metrics that are considered are the satisfaction rate, i.e., the fraction of requests that can be successfully served, and the relative distance rate, which measures the amount of distance that is saved compared to the case where no ridesharing is practiced. The results presented by Ma et al. (2013) show that ridesharing can increase the satisfaction rate of as much as 25%, and that it can save as much as 13% in traveled distance. Considering that there are 67,000 taxis in Bejing and each taxi runs on the average 480Km per day, Ma et al. (2013) estimate reductions in total traveled distance in the order of 1.6 billion kilometers per year, corresponding to a decrease in fuel consumption in the order of 120 million liters of gasoline. Figure 5. Missed ride sharing opportunities with partition-based match making Discussion Both approaches described in the previous section implement a sub-optimal dynamic ride sharing system. The partition based match making heuristic presented by Xiao et al. (2013) is sub-optimal under the following respects: 1. partial exploitation of ride sharing opportunities. Due to the requirement that one of the corridor must be a subset of the other, only ride sharing opportunities of type I, as reported in Figure 5, can be exploited. Sharing opportunities of type II are not considered, since neither corridor is a subset of the other. 2. inaccuracies in the matching process caused by coarse spatial granularity. Since the partition based match making approach works at the relatively coarse granularity of partition, trips that are good candidate for sharing (because their respective origin/destinations are very close) might not be considered in the match making process. Conversely, trips with a much longer distance between respective origin and destinations, and hence causing a relatively high sharing delay, might be considered for match making. These inaccuracies in the match making process caused by the coarse spatial granularity are pictorially represented in Figure 6. Figure 6. Inaccuracies in ride sharing with partition-based match making: trips on the right are shared, while those on the left are not. The T-Share system presented by Ma et al. (2013) is sub-optimal under the following respects: 1. similarly to the partition-based match making approach of Xiao et al. (2013), T-Share operates at a relatively coarse spatial granularity, namely, that of square cells. Hence, inaccuracies in the trip matching process similar to the ones described for partition-based match making can occur also with T-Share. 2. sub-optimal selection of taxis. T-Share implements a greedy, sub-optimal algorithm for selecting which taxi should serve the currently considered request: in accordance with the greedy paradigm, the selected taxi is the one that ensures the best local solution i.e., the one that minimizes the distance added to the route as a consequence of serving the additional passenger. In principle, a better global solution could be obtained by, e.g., collectively analyzing all the requests currently in the request queue. However, this approach would be substantially more cumbersome to implement in terms of computational running time, impairing T-Share s design goal of running in real time. STATIC RIDE SHARING AND SHAREABILITY NETWORKS

11 Due to the intrinsic complexity of dynamic ride sharing, the computationally efficient approaches presented in the previous section are sub-optimal under a number of respects. This section presents a methodology that, instead, allows computationally efficient calculation of the optimal ride sharing solution (Santi et al., 2014a). This is achieved by reducing the complexity of the ride sharing problem in two ways: 1) by considering only static ride sharing; and 2) by allowing combination of at most two trips in a shared ride. Thanks to this, the otherwise unstructured and gigantic search space of the type explored in dynamic pick up and delivery problems becomes combinatorially structured. The key of the approach presented by Santi et al. (2014a) is the notion of shareability network: a network where nodes represent trips, and where a sharing opportunity between trips T 1 and T 2 is represented by a link between the respective nodes. According to Santi et al. (2014a), two trips can be shared if and only if there exists a route connecting the respective origin and destinations such that each passenger is picked up and dropped off with a sharing delay of at most Δ, where Δ is a parameter of the shareability network. Notice that, in order for the two trips to be considered shareable, the route must fulfill also the following conditions: 1) each origin should precede the respective destination; and 2) the single trips must be actually overlapped and not concatenated. The notion of shareability network is pictorially represented in Figure 7: trip T 2 can potentially be shared with trip T 3 and T 5, and the corresponding links are included in the shareability network. The overall shareability network, reported on the right end of the figure, is obtained similarly. Notice that the network is undirected, since the conditions to be fulfilled in order for any two trips to be shareable are symmetric. Figure 7. From taxi trips (left) to shareability networks (right) Having defined the shareability network, Santi et al. (2014a) show that optimally solving the static ride sharing problem becomes equivalent to finding a maximum matching in the shareability network. Since the maximum matching problem can be solved in polynomial time, the optimal solution can be efficiently computed even for problems of very large size. For instance, the analysis reported by Santi et al. (2014a) refers to the data set composed of over 150 million taxi trips performed in the city of New York in year 2011 by the 13,586 officially registered taxis 1. Santi et al. (2014a) present two different versions of the shareability network, which differ in terms of the optimization goal of the ride sharing process. In the first version, the shareability network is unweighted, and finding the maximum matching on the shareability network is equivalent to computing the maximum number of trips that can be shared, i.e., to maximizing shareability. In the second version, each link (T 1,T 2 ) in the shareability network is assigned a weight that equals the difference between the total travel time needed to complete the two single rides, and the travel time of the shared ride that combines T 1 and T 2. The maximum weighted matching of the shareability network then becomes equivalent to the matching of trips that minimizes the total traveled distance. It is important to observe that the parametric nature of shareability networks, which are defined in terms of the sharing delay Δ, allows a quantitative characterization of the tradeoff between passenger discomfort and sharing opportunities: relatively higher values of Δ result in relatively denser shareability networks, i.e., networks with relatively higher average node degree. Since the cardinality of the maximum matching is positively correlated with the average node degree, a relatively higher value of Δ ultimately results in a relatively higher percentage of shareable trips. Santi et al. (2014a) further investigate this trade off by analyzing the shareability networks defined starting from the New York taxi trip data set. The larger such network, obtained for Δ =10min, is composed of about 150 million nodes and 100 billion links. The results show a shareability ranging from

12 about 50% when Δ =30sec to nearly 100% when Δ =5min. In the case of reducing the total travel time as the optimization goal, results show savings ranging from about 13% when Δ =30sec to about 40% when Δ=5min. As observed by Santi et al. (2014a), these results should be considered as an optimistic upper bound to the performance a practical ride sharing system could achieve, since they are obtained under the assumption that the entire shareability network is known at the time the matching is computed. In reality, trip requests are revealed over time, and so is the shareability network. To account for this, Santi et al. (2014a) introduce the notion of online shareability network, which is a shareability network in which only links between trips T 1 and T 2 whose difference in starting times is at most δ are retained. The notion of online shareability network is representative of a scenario in which a passenger using an e-hailing application issues a taxi request reporting pickup and drop off locations, and after at most δ units of time, receives feedback from the taxi management system whether a shared ride is available. From the viewpoint of the taxi fleet operator, trip requests are collected for a time δ, and then collectively processed to find the best possible matching among them. There is a clear trade off in how to set the value of δ: while a relatively larger value of δ is desirable to group together more requests and hence increase ride sharing opportunities, its value cannot be increased too much in order to preserve passenger quality of service. Santi et al. (2014a) suggest setting δ=1min, and evaluate the resulting sharing performance. While reduced, sharing performance is still impressive: when Δ=5min, more than 98% of the trips can be shared, and total travel time reductions are in the order of 30%. The notion of shareability network is amenable to further generalization. In particular, Santi et al. (2014a) show how a shareability network can be defined for representing sharing opportunities between groups of up to k>2 trips. Unfortunately, as soon as k=3, the shareability network becomes a shareability hypernetwork, for which maximum matching is solvable only in approximation using a heuristic algorithm which is computationally feasible for networks of relatively small size. Another difficulty lies in the fact that the number of possible routes between all origin and destination points of a candidate shared trip, which have to be considered during the construction of the shareability network, jumps from 4 when k=2 to 60 when k=3, and increases exponentially with k. For these reasons, Santi et al. (2014a) have been able to evaluate sharing performance with k=3 only with the online shareability network model. The results show that when Δ=5min, the total traveled time can be reduced of about 40% when k=3, as compared to about 30% when k=2. A final analysis reported by Santi et al. (2014a) is aimed at understanding the effect of a sparser demand of taxi rides on sharing performance. The authors randomly delete a fraction x% of trips from the data set, with x ranging from 1 to 95, and evaluate the resulting shareability values. The results reveal that the relation between the average number of daily trip and shareability can be approximated very well by a saturation function known as Hill equation. The fast, hyperbolic saturation of this curve implies that taxi sharing could be effective also in cities with taxi densities much lower than New York, or when the willingness to share is low. FUTURE RESEARCH DIRECTIONS The ones reported in this chapter should be considered only initial steps along the way towards gaining a deeper understanding of the city-level impact of ride sharing. Further work is needed along several directions. An open question regards whether shareability performance similar to those reported in this chapter could be expected in cities different from the ones analyzed therein (namely, Bejing, Singapore, and New York). Although answering this question requires further research and analysis of other data sets, the observation made in (Santi, 2014a) that shareability performance is constant across a wide range of trip density values seems to suggest a certain generality of the analysis reported therein. Effects of the urban

13 layout (rivers partitioning a city, density of the built environment, etc.) on shareability performance shall also be investigated. Another open question is providing a more detailed assessment of the psychological limitations of taxi sharing, to understand the conditions and appropriate incentive systems under which individuals are willing to be seated in the same vehicle. A primary incentive mechanism is pricing, which in the context of shared taxi systems is a largely unexplored field to date. While the authors of T-Share have proposed a method for faring a shared ride (Ma et al., 2013), the effect of such a pricing model on taxi supply and demand is not discussed, as well as the interplay between taxi and other urban individual and mass transportation systems. As observed by Lopez et al. (2014), a complete evaluation of the environmental sustainability of a taxi ride sharing system requires considering not only direct impacts such as percentage of shared trips and total travel time reduction, but also indirect impacts linked to this new transportation mode. Ride cost reductions implied by sharing might trigger substitution and income effects, possibly resulting in an increased demand for taxi service at the expense of more environmentally efficient modes such as public transportation. Motivated by Lopez et al. (2014), Santi et al. (2014b) suggest that the strategy used to price a shared taxi system should be carefully evaluated, in order to quantitatively characterize the interplay between taxi and other urban transportation systems, and identify socially desirable solutions. Such a micro-economic analysis is, to the best of the authors knowledge, still lacking so far. CONCLUSION This chapter illustrates how a relevant type of spatio-temporal data - namely, the GPS traces collected and recorded by taxi fleets - can be used to estimate the potential of ride sharing in urban environments. The computational challenges underlying ride sharing have been identified, and two approaches for solving them have been presented: heuristic, sub-optimal solutions to the dynamic ride sharing problem; and an optimal, network-based solution to the relatively simpler static ride sharing problem. The application of such approaches to massive GPS data sets demonstrates the enormous potential of ride sharing in urban environments: the vast majority of trips can potentially be shared, with benefits in terms of reduced number of traveled miles. However, as discussed in the last section of the chapter, further research is needed to better understand the interplay between a shared taxi system and other forms of urban transportation: private vehicles, bikes, public transportation, etc. Depending on this interplay, desirable social, city-level goals such as high quality individual transportation, low carbon footprint, reduced vehicular traffic, etc., could or could not be achieved. How to act on fares, policies, city regulations, etc., in order to obtain a desirable social outcome from the transformations brought along by ride and vehicle sharing is still an open question. ACKNOWLEDGEMENTS Thanks to ENEL Foundation, Volkswagen Electronic Research Lab, the MIT SMART program, and all the members of the MIT Senseable City Lab Consortium for supporting this research. REFERENCES Aslam, J., Lim, S., Pan, X., & Rus, D. (2012). City-Scale Traffic Estimation from a Roving Sensor Network. In Proceedings 10 th ACM Conference on Embedded Networked Sensor Systems (SenSys 2012). Toronto, Canada: ACM. Barbeglia, G., Cordeau, J-F., & Laporte, G. (2010). Dynamic Pickup Delivery Problems. European Journal of Operational Research, 202 (1), 8-15.

14 Calabrese, F., Di Lorenzo, G., Liu, L., & Ratti, C. (2011). Estimating Origin-Destination Flows using Mobile Phone Location Data. IEEE Pervasive Computing, 10 (4), Gonzales, M., Hidalgo, C., & Barabasi, A.L. (2008). Understanding Individual Human Mobility Patterns. Nature, 453, Huang, Y., & Powell, J.W. (2012). Detecting Regions of Disequilibrium in Taxi Services under Uncertainty. In Proceeding 20 th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2012). Redondo Beach, CA: ACM. Liu, L., Andris, C., & Ratti, C. (2010). Uncovering Cabdriver s Behavior Patterns from their Digital Traces. Computers, Environment and Urban Systems, 34 (6), Liu, W., Zheng, Y., Chawla, S., Yuan, J., & Xing, X. (2011). Discovering Spatio-Temporal Causal Interactions in Traffic Data Streams. In Proceedings ACM Conference on Knowledge Discovery and Data mining (ACM KDD 2011). San Diego, CA: ACM. Lopez, L.A., Domingos, T., Cadarso, M.A., & Zafrilla, J.E. (2014). The Smarter, the Cleaner? Collaborative Footprint: A Further Look at Taxi Sharing. Proceedings National Academy of Science, 111 (51). Ma, S., Zheng, Y., & Wolfson, O. (2013). T-Share: A Large-Scale Dynamic Taxi Ridesharing Service. In Proceedings IEEE Conference on Data Engineering (IEEE ICDE 2013). Brisbane, Australia: IEEE. New York Taxi and Limousine Commission (2013). Phithakkitnukoon, S., Veloso, M., Bento, C., Biderman, A., & Ratti. C. (2010). Taxi-Aware Map: Identifying and Predicting Vacant Taxis in the City, Lecture Notes in Computer Science, 6439, Sundararajan, A. (2013). From Zipcar to the Sharing Economy. Harvard Business Review. Santi, P., Resta, G., Szell, M., Sobolevsky, S., Strogatz, S.H., & Ratti, C. (2014a). Quantifying the Benefits of Vehicle Pooling with Shareability Networks. Proceedings National Academy of Science, 111 (37), Santi, P., Resta, G., Szell, M., Sobolevsky, S., Strogatz, S.H., & Ratti, C. (2014b). Reply to Lopez et al: Sustainable Implementation of Taxi Sharing Requires Understanding Systemic Effects. Proceedings National Academy of Science, 111 (51). Song, T., Wang, P., & Barabasi, A.L. (2010). Modelling the Scaling Properties of Human Mobility. Nature Physics, 6, Xiao, J., Aydt, H., Less, M., & Knoll, A. (2013). A Partition Based Match Making Algorithm for Taxi Sharinh. In Proceedings IEEE Conference on Intelligent Transportation Systems (IEEE ITS 2013). The Hague, Netherlands: IEEE. Yuan, J., Zheng, Y., Zhang, L., Xie, X., & Sun, G. (2011). Where to Find My Next Passenger. In Proceedings ACM International Conference on Ubiquitous Computing (ACM UbiComp 2011). Bejing, China: ACM.