1782 IEEE TRANSACTIONS ON KNOWLEDGE AND …sma/Papers/taxisharing_TKDE...Real-Time City-Scale Taxi Ridesharing Shuo Ma, Yu Zheng, Senior Member, IEEE, and Ouri Wolfson, Fellow, IEEE

Real-Time City-Scale Taxi RidesharingShuo Ma, Yu Zheng, Senior Member, IEEE, and Ouri Wolfson, Fellow, IEEE

Abstract—We proposed and developed a taxi-sharing system that accepts taxi passengers’ real-time ride requests sent from

smartphones and schedules proper taxis to pick up them via ridesharing, subject to time, capacity, and monetary constraints. The

monetary constraints provide incentives for both passengers and taxi drivers: passengers will not pay more compared with no

ridesharing and get compensated if their travel time is lengthened due to ridesharing; taxi drivers will make money for all the detour

distance due to ridesharing. While such a system is of significant social and environmental benefit, e.g., saving energy consumption

and satisfying people’s commute, real-time taxi-sharing has not been well studied yet. To this end, we devise a mobile-cloud

architecture based taxi-sharing system. Taxi riders and taxi drivers use the taxi-sharing service provided by the system via a smart

phone App. The Cloud first finds candidate taxis quickly for a taxi ride request using a taxi searching algorithm supported by a

spatio-temporal index. A scheduling process is then performed in the cloud to select a taxi that satisfies the request with minimum

increase in travel distance. We built an experimental platform using the GPS trajectories generated by over 33,000 taxis over a period

of three months. A ride request generator is developed (available at http://cs.uic.edu/�sma/ridesharing) in terms of the stochastic

process modelling real ride requests learned from the data set. Tested on this platform with extensive experiments, our proposed

system demonstrated its efficiency, effectiveness and scalability. For example, when the ratio of the number of ride requests to the

number of taxis is 6, our proposed system serves three times as many taxi riders as that when no ridesharing is performed while saving

11 percent in total travel distance and 7 percent taxi fare per rider.

Index Terms—Spatial databases and GIS, taxi-sharing, GPS trajectory, ridesharing, urban computing, intelliegent transportation systems

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1 INTRODUCTION

TAXI is an important transportation mode between publicand private transportations, delivering millions of pas-

sengers to different locations in urban areas. However, taxidemands are usually much higher than the number of taxisin peak hours of major cities, resulting in that many peoplespend a long time on roadsides before getting a taxi.Increasing the number of taxis seems an obvious solution.But it brings some negative effects, e.g., causing additionaltraffic on the road surface and more energy consumption,and decreasing taxi driver’s income (considering thatdemands of taxis would be lower than number of taxis dur-ing off-peak hours).

To address this issue, we propose a taxi-sharing sys-tem that accepts taxi passengers’ real-time ride requestssent from smartphones and schedules proper taxis topick up them via taxi-sharing with time, capacity, andmonetary constraints (the monetary constraints guaran-tee that passengers pay less and drivers earn more com-pared with no taxi-sharing is used). Our system savesenergy consumption and eases traffic congestion whileenhancing the capacity of commuting by taxis. Mean-while, it reduces the taxi fare of taxi riders and increasesthe profit of taxi drivers.

Unfortunately, real-time taxi-sharing has not been wellexplored, though ridesharing based on private cars, often

known as carpooling or recurring ridesharing, was studiedfor years to deal with people’s routine commutes, e.g., fromhome to work [1], [2]. In contrast to existing ridesharing,real-time taxi-sharing is more challenging because both riderequests and positions of taxis are highly dynamic and diffi-cult to predict. First, passengers are often lazy to plan a taxitrip in advance, and usually submit a ride request shortlybefore the departure. Second, a taxi constantly travels onroads, picking up and dropping off passengers. Its destina-tion depends on that of passengers, while passengers couldgo anywhere in a city.

In this paper, we report on a system based on the mobile-cloud architecture, which enables real-time taxi-sharing in apractical setting. In the system, taxi drivers independentlydetermine when to join and leave the service using an Appinstalled on their smartphones. Passengers submit real-timeride requests using the same App (if they are willing to sharethe ride with others). Each ride request consists of the originand destination of the trip, time windows constraining whenthe passengers want to be picked up and dropped off (inmost case, the pickup time is present). On receiving a newrequest, the Cloud will first search for the taxi which mini-mizes the travel distance increased for the ride request andsatisfies both the new request and the trips of existing pas-sengers who are already assigned to the taxi, subject to time,capacity, and monetary constraints. Then the existing pas-sengers assigned to the taxi will be inquired by the cloudwhether they agree to pick up the new passenger given thepossible decrease in fare and increase in travel time. Onlywith a unanimous agreement, the updated schedules will bethen given to the corresponding taxi drivers and passengers.

We place our problem in a practical setting by exploitinga real city road network and the enormous historical taxitrajectory data. Compared to existing carpooling systems,our proposed ridesharing model considers more practical

� S. Ma and O. Wolfson are with the Computer Science Department, Uni-versity of Illinois at Chicago, Chicago, IL 60607.E-mail: {sma, wolfson}@cs.uic.edu.

� Y. Zheng is with Microsoft Research, Beijing 100080, P.R, China.E-mail: [email protected].

Manuscript received 28 Oct. 2013; revised 11 June 2014; accepted 11 June2014. Date of publication 30 June 2014; date of current version 1 June 2015.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TKDE.2014.2334313

1782 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 27, NO. 7, JULY 2015

1041-4347� 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

constraints which include time windows, capacity, andmonetary constraints for taxi trips. In addition, our workproposes efficient searching and scheduling algorithms thatare capable of allocating the “right” taxi among tens of thou-sands of taxis for a query in milliseconds. The contributionof this paper is many fold:

� We proposed and developed a taxi-sharing systemusing the mobile-cloud architecture. The cloud inte-grates multiple important components includingtaxi indexing, searching, and scheduling. Specifi-cally, we propose a spatio-temporal indexing struc-ture, a taxi searching algorithm, and a schedulingalgorithm. Supported by the index, the two algo-rithms quickly serve a large number of real-time riderequests while reducing the travel distance of taxiscompared with the case without taxi-sharing.

� Our paper considers and models monetary con-straints in ridesharing. These constraints provideincentives not only for passengers but also for taxidrivers: passengers will not pay more comparedwith no ridesharing and get compensated if theirtravel time is lengthened due to ridesharing; taxidrivers will make money for all the reroute distancedue to ridesharing. The monetary constraints makesour modeling of the taxi ridesharing problem morerealistic.

� We performed extensive experiments to validate theeffectiveness of taxi-sharing as well as the proposedsystem’s efficiency and scalability. According to theexperimental results, the fraction of ride requests thatget satisfied is significantly increased by three timesmeanwhile riders save 7 percent in taxi fare via taxi-sharing when the taxis are in high demand. Further-more 2 million liter of gasoline can be saved each yearin Beijing by taxis alone if taxi-sharing is allowed.

The rest of this paper is organized as follows. In Section 2,we formally describe the real-time taxi-sharing problem. Sec-tion 3 overviews the architecture of our proposed system.Section 4 describes the index of taxis used and the taxisearching algorithm. Section 5 describes the scheduling pro-cess. We present the evaluation in Section 6 and summarizethe relatedwork in Section 7.

Compared with our earlier work [3], this paper claimsfollowing contributions. First, we devised and implementeda cloud-mobile based taxi-sharing system, where the mobileApp for taxi riders and drivers are designed. The detailedinteractions among the mobile Apps of taxi riders, drivers,and the cloud are presented in Section 3. Second, we refinedour taxi-sharing model by introducing the monetary con-straints for both drivers and riders in Section 5.2. This isone crucial step towards a practical deployment of such asystem. In addition, we discussed the time complexity ofreordering the pickup and drop-off locations in the sched-uled route of a taxi at the beginning of Section 5 andshowed that this step is not necessary in practice via experi-ments in Section 6.2.3. Third, we conducted more compre-hensive experiments to validate our system. For example, inSection 6.1.5, we introduce new measurements, such asTaxi-sharing Rate and Seat Occupancy Rate, to evaluate theeffectiveness of ridesharing. We also test the performance of

our approach by changing the parameter of the monetaryconstraints in Section 6.2.1.

2 THE REAL-TIME TAXI-SHARING PROBLEM

The real-time taxi-sharing problem consists of a data model,constraints, and an objective function. We describe eachpart separately below before giving the formal definition ofthe problem.

2.1 Data Model

2.1.1 Ride Request

A ride request Q is associated with a timestamp Q : t indicat-ing whenQwas submitted, a origin pointQ : o, a destinationpoint Q : d, a time window Q:pw defining the time intervalwhen the rider wants to be picked up at the origin point,and a time window Q : dw defining the time interval whenthe rider wants to be dropped off at the destination point.The early and late bounds of the pickup window aredenoted by Q:pw:e and Q:pw:l respectively. Likewise,Q : dw:e and Q : dw:l stand for that of the delivery window.

In practice, a rider only needs to explicitly indicate Q : dand Q : dw:l, as most information of a ride request can beautomatically obtained from a rider’s mobile phone, e.g.,Q : o and Q : t. In addition, we can assume that both Q:pw:eandQ : dw:e equals toQ : t, andQ:pw:l can be easily obtainedby adding a fixed value, e.g., 5 minutes, to Q:pw:e.

2.1.2 Taxi Status

A taxi status V represents an instantaneous state of a taxiand is characterized by the following fields.

� V:ID. The unique identifier of the taxi.� V:t. The time stamp associated with the status.� V:l. The geographical location of the taxi at V:t.� V .s. The current schedule of V , which is a tempo-

rally-ordered sequence of origin and destinationpoints of n ride requests Q1, Q2; . . .Qn such that forevery ride request Qi, i ¼ 1; . . . ;n, either 1) Qi : o pre-cedes Qi : d in the sequence (referred to as the prece-dence rule thereafter), or 2) only Qi:d exists in thesequence.

� V:r. The current projected route of V , which is asequence of road network nodes calculated basedon V:s.

From the definition, it is clear that the schedule of a vehi-cle status is dynamic, i.e., changes over time. For example, aschedule involving two ride requests Q1 and Q2 could beQ1:o ! Q2:o ! Q1:d ! Q2 : d at a certain time. The scheduleis updated to Q2:o ! Q1:d ! Q2 : d once the taxi has passedpoint Q1:o.

2.2 Constraints

The crux of the taxi-sharing problem is to dispatch taxis toride requests, subject to certain constraints. We say that ataxi status V satisfies a ride request Q or Q is satisfied by V ifthe following constraints are met.

� Vehicle capacity constraint. The number of riders thatsit in the taxi does not exceed the number of seats ofa taxi at any time.

MA ET AL.: REAL-TIME CITY-SCALE TAXI RIDESHARING 1783

� Time window constraints. All riders that are assignedto V should be able to depart from the origin pointand arrive at the destination point during the corre-sponding pickup and delivery window, respectively.

� Monetary constraints. These constraints provide cer-tain monetary incentives for both taxi drivers andriders. That is, a rider does not pay more than with-out taxi-sharing; a taxi driver does not earn less thanwithout taxi-sharing when travelling the same dis-tance; the fare of existing riders decreases when anew rider joins the trip. We will further discuss themonetary constraints in Section 5.2.

2.3 Objective Function and Problem Definition

Since multiple taxi statues may satisfy a ride request, anobjective function is usually applied to find the optimal taxi.A variety of objective functions have been used in the exist-ing literature, where a weighted cost function combiningmultiple factors such as travel distance increment, traveltime increment and passenger waiting time, is the mostcommon [4], [5], [6]. In this study, given a ride request, weaim to find the taxi status which satisfies the ride requestwith minimum increase in travel distance, formally definedas follows: given a fixed number of taxis traveling on a road net-work and a sequence of ride requests in ascending order of theirsubmitted time, we aim to serve each ride request Q in the stream

by dispatching the taxi V which satisfies Q with minimumincrease in V ‘s scheduled travel distance on the road network.

This is obviously a greedy strategy and it does not guaran-tee that the total travel distance of all taxis for all riderequests is minimized. However, we still opt for this defini-tion due to two major reasons. First, the real-time taxi-sharing problem inherently resembles a greedy problem. Inpractice, taxi riders usually expect that their requests can beserved shortly after the submission. Given the rigid real-timecontext, the taxi-sharing system only has information of cur-rently available ride requests and thus can hardlymake opti-mized schedules based on a global scope, i.e., over a longtime span. Second, the problem ofminimizing the total traveldistance of all taxis for the complete ride request stream isNP-complete. Please see [3] for a proof.

3 SYSTEM ARCHITECTURE

The architecture of our system is presented in Fig. 1. Thecloud consists of multiple servers for different purposesand a monitor for administers to oversee the running of thesystem. Taxi drivers and riders use the same smart phoneApp to interact with the system, but are provided with dif-ferent user interfaces by choosing different roles, as shownin Fig. 2a.

As shown by the red broken arrow (a), a taxi automati-cally reports its location to the cloud via the mobile Appwhen (i) the taxi establishes the connection with the system,or (ii) a rider gets on and off a taxi, or (iii) at a frequency(e.g., every 20 seconds) while a taxi is connected to the sys-tem. We partition a city into disjoint cells and maintain adynamic spatio-temporal index between taxis and cells inthe indexing server (detailed in Section 4.1), depicted as thebroken arrow (b).

Denoted by the solid blue arrow�1 , a rider submits a newride request Q to the Communication Server. Fig. 2b showsthe corresponding interface on a rider’s smart phone wherethe blue pin stands for the current location of the rider. Allincoming ride requests of the system are streamed into aqueue and then processed according to the first-come-first-serve principle. For each ride request Q, the communicationserver sends it to the Indexing Server to search for candidatetaxis SV that are likely to satisfy Q, depicted as the bluearrow �2 . Using the maintained spatio-temporal index, theindexing server returns SV to the communication server,denoted by the blue arrow�3 .

Fig. 1. The architecture of the real-time taxi-sharing system.

Fig. 2. Screenshots of the mobile client for riders.


Represented by the blue arrow �4 , the communicationserver sends ride request Q and the received candidate taxiset SV to the Scheduling Server Cluster. The scheduling clus-ter checks whether each taxi in SV can satisfy Q in parallel(detailed in Section 5), and returns the qualified taxi V thatresults in minimum increase in travel distance and adetailed schedule, shown as arrow�5 .

Note that in our current implementation, a singlemachine (see Section 6.2.2 for the specs of the machine)instead of a cluster is used to implement the indexing serverand the scheduling servers. The single-machine implemen-tation is able to answer a query in a few milliseconds, i.e.,millions of queries per hour. But we believe in that the clus-ter-based implementation (e.g., using Windows Azure A2virtual machines) can provide a more robust service. Forexample, it prevents system crash in case of unexpectedpower failure of a single machine.

Each rider R who has been already assigned to the taxi Vwill be enquired whether they would like to accept the joinof the new rider, as depicted by blue arrow �6 . The informa-tion, such as the estimated fare saving and travel timeincrease due to Q‘s join, will be displayed on their smart-phones shown in Fig. 2c. Rider R accepts the route change ifshe thinks the fare saving is worth the travel time increase.Otherwise, she can veto the route change by clicking the“Reject” button. The system remembers the rider’s choice,and automatically rejecting a route change in future if theratio of the fare saving to the travel time delay is smallerthan the largest value the rider has ever rejected. Thus, ataxi passenger will not be bothered often.

After all riders R‘s who have been already assigned totaxi V accept the route change, the new rider of Q gets aconfirmation on her smart phone, as illustrated in Fig. 2d.The confirmation informs the new rider the taxi ID, esti-mated pickup time and fare, the scheduled route, and aunique reservation code. The new schedule and the samereservation code are sent to the driver’s phone at the sametime. The reservation code will be used to build a connec-tion between the phones of the new rider and the taxidriver when the new rider gets on the taxi. On the driverside, the smart phone displays a taxi’s schedule, e.g., the

next pickup and destination points as well as the route, asillustrated in Fig. 3.

When a rider’s trip is completed, the rider’s App willshow the exact information, such as the actual fare andtravel time, as illustrated in Fig. 2e. The reservation codewill be used again to confirm the payment to the Cloud as atransaction ID.

The system administrator oversees the taxi-sharing sys-tem via the monitor. The monitor provides two views: onefor ride requests, the other for taxis. Fig. 4a shows a screen-shot of the ride request view, where all requests are dis-played on the map at their corresponding pickup point,with scheduled requests in red and unscheduled requestsin blue. On the right, two boxes list the detail information ofscheduled and unscheduled ride requests respectively. Thesearch box allows the administrator to quickly locate arequest on the map via a request ID.

Fig. 4b shows a screenshot of the taxi view of the monitor.Each taxi is represented by a yellow taxi symbol on the map.The locations of these symbols on themap are updatedwhilethe corresponding taxis upload new statuses. Similarly, thesearch box is used to quickly locate and track a taxi via que-rying a specific taxi ID.

4 TAXI SEARCHING

The taxi searching module quickly selects a small set of can-didate taxis with the help of the spatio-temporal index. Inthis section, we will first describe the index structure andthen detail the searching algorithm.

4.1 Index of Taxis

The spatio-temporal index of taxis is built for speeding upthe taxi searching process. Specifically, we partition theroad network using a grid. (Other spatial indices such as Rtree can be applied as well, but we envision that the highdynamics of taxis will cause prohibitive cost for maintain-ing such an index.) As shown in Fig. 5a, within each gridcell, we choose the road network node which is closest tothe geographical centre of the grid cell as the anchor nodeof the cell (represented by a blue dot in Fig. 5a. The anchornode of a grid cell gi is thereafter denoted by ci. We com-pute the distance, denoted by dij, and travel time, denotedby tij, of the fastest path on the road network for eachanchor node pair ci and cj. Both the distance and traveltime is only computed once. (Alternatively, travel time canbe updated dynamically, i.e. calculated once in a while(e.g., every 10 minutes) by leverageing historical data

Fig. 3. Screenshot of the mobile client for drivers.

Fig. 4. Screenshot of the monitor.

Fig. 5. Grid partitioned map and grid distance matrix.


archives, and travel time estimation techniques e.g., T-Drive [7], [8], [32]. However since the effectiveness oftravel time estimation is not a focus of this work, we donot discuss it in details here.) Intuitively, we can use thecomputed travel time to quickly filter out a large numberof taxis whose schedule is “far away” from a given riderequest. The distance and travel time results are saved in amatrix as shown in Fig. 5b. The matrix is thereafterreferred to as the grid distance matrix.

The distance between any two arbitrary nodes is approxi-mated by the distance between two corresponding anchornodes. In other words, the grid distance matrix provides anapproximation of the distance between any two nodes ofthe road network. These approximated distances avoid theexpensive computation cost of frequent fastest path calcula-tions at the stage of taxi searching.

As illustrated in Fig. 6, each grid cell gi maintains three

lists: a temporally-ordered grid cell list (gi : ltc), a spatially-order

grid cell list (gi : lsc), and a taxi list (gi : lvÞ : gi : ltc is a list of other

grid cells sorted in ascending order of the travel time fromthese grid cells to gi (temporal closeness). Likewise, gi : l

sc is

a list of other grid cells sorted in ascending order of thetravel distance from these grid cells to gi (spatial closeness).The spatial and temporal closeness between each pair ofgrid cells are measured by the values saved in the grid dis-tance matrix shown in Fig. 5b. For example, t2i measures thetemporal closeness from g2 to gi, and d2i measures the spa-tial closeness from g2 to gi. The spatial grid cell list is onlycomputed once. The temporal grid cell list is computedeach time when travel times tij‘s are updated. It is worthmentioning that cells that are neighbours in the grid maynot be the neighbours in a grid cell list because the distanceis measured in the road network instead of a free space.

The taxi list gi : lv of grid cell gi records the IDs of all taxiswhich are scheduled to enter gi in near future (typicallywithina temporal scope of 1 or 2 hours). Each taxi ID is also tagged

with a timestamp ta indicating when the taxi will enter thegrid cell. All taxis in the taxi list are sorted in ascending orderof the associated timestamp ta : gi:lv is updated dynamically.Specifically, taxi Vj is removed from the list when Vj leaves gi;taxi Vk is inserted into the list when Vk is newly scheduled toenter gi. If taxis are tracked (see [9]), when new GPS recordsare received from taxis, taxi lists need to be updated. Specifi-cally, when a new GPS record from Vm is received, denote bygn the current cell in which Vm is located, the timestamp asso-ciated with Vm in the taxi list of cell gn and cells to be passedby Vm after gn need to be updated.

4.2 Searching Algorithms

4.2.1 Single-Side Taxi Searching

Now we are ready to describe our first taxi searching algo-rithm. For the sake of the clarity of description, please con-sider the example shown in Fig. 7. Suppose there is a queryQ and the current time is tcur : g7 is the grid cell in whichQ : o is located. g7‘s temporally-ordered grid cell list g7 : l

tg is

shown on the right of Fig. 7. g7 is the first grid cell selectedby the algorithm. Any other arbitrary grid cell gi is selectedby the searching algorithm if and only if Eq. (1) holds, whereti7 represents the travel time from grid cell gi to grid cell g7.Eq. (1) indicates that any taxi currently within grid cell gican enter g7 before the late bound of the pickup windowusing the travel time between the two grid cells (if weassume that each grid cell collapses to its anchor node)

ti7 þ tcur � Q : pw : l (1)

To quickly find all grid cells that hold Eq. (1), the single-sidesearching algorithm simply tests all grid cells in the order-preserved list g7 : l

tc and finds the first grid cell gf which fails

to hold Eq. (1). Then all taxis in grid cells before gf in list

g7 : ltc are selected as candidate taxis.

In Fig. 7, grid cell g3, g5 and g9 are selected by the searchingalgorithm. Then for each selected grid cell gs, the algorithmselects taxis (in gs : lv) whose ta is no later than Q :wp:l� ts7.For instance, Fig. 8 shows how taxis are selected from gridcell g7 and g3.

The taxi which can satisfy Q with the smallest increase intravel distance must be included in one of the selected gridcells (under the assumption that each grid cell collapses).Unfortunately, this algorithm only considers taxis currently“near” the pickup point of a query (thus called single-sidesearch). As the number of selected grid cells could be large,this algorithmmay result inmany taxis retrieved for the laterschedulingmodule (therefore increasing the entire computa-tion cost), which is certainly not desirable for a rigid real-time application like taxi ridesharing. Actually, the

Fig. 6. Spatio-temporal index of taxis.

Fig. 7. The single-side taxi searching algorithm.

Fig. 8. Choose taxis from the selected grid cells.


spatiotemporal factor on the destination point of queries alsoprovides us with opportunities to reduce the number of gridcells to be selected. Along this idea, we propose a dual-sidesearching algorithm as an effort for striking a balancebetween the distance optimality and the computation cost.

4.2.2 Dual-Side Taxi Searching

The dual-side searching is a bi-directional searching processwhich selects grid cells and taxis from the origin side andthe destination side of a query simultaneously.

To dive into the details of the algorithm, consider the riderequest illustrated in Fig. 9 where g7 and g2 are the grid cellsin which Q : o and Q : d are located respectively. Squaresfilled with stripes stand for all possible cells searched by thealgorithm at Q : o side. These cells are determined by scan-

ning g7 : ltc, the temporally-order grid cell list of g7. That is,

each grid cell in g7 : ltc which holds Eq. (2) is a candidate cell

to be searched at the origin side. Eq. (2) indicates that anytaxi currently within grid cell gi can enter g7 before the latebound of the pickup window using the latest travel timebetween the two grid cells (assuming each grid cell collap-ses to its anchor node). The red number in each such gridcell indicates its relative position in g7 : l

sc, the spatially-

ordered grid list of g7

tcur þ ti7 � Q : dw : l: (2)

Squares filled with dots indicate the candidate grid cellsto be accessed by the searching algorithm at Q : d side. Like-wise, each such grid cell gj is found by scanning g2 : l

tc to

select all grid cells which holds Eq. (3), which indicates thatany taxi currently in gj can enter the g2 before the late boundof the delivery window (assuming that each grid cell collap-ses to its anchor node). In this example, g6 is the only satisfy-ing grid cell as shown by Fig. 9

tcur þ tj2 � Q : dw : l: (3)

Fig. 10 then illustrates the searching process step by step.The algorithm maintains a set So and a set Sd to store thetaxis selected from Q : o side and Q : d side respectively. Ini-tially, both So and Sd are empty. The first step in the search-ing is to add the taxis selected from taxi list g7 : lv to taxi setSo as depicted in Fig. 10a, and add the taxis selected fromtaxi list g2 : lv to taxi set Sd as depicted by Fig. 10b. Then thealgorithm calculates the intersection of So and Sd. If the

intersection is not empty, the algorithm stops immediatelyand returns the intersection set. Otherwise, it expands thesearching area by including one other grid cell at each sideat a time.

To select next cells, we use the following heuristic: for ataxi V , the closer a cell to be passed by V is to g7 and thecloser a cell to be passed by V is to g2 (measured in the dis-tance between the anchor nodes of the cells), the smaller V ‘sscheduled travel distance increases after the insertion of theride request. For the purpose of minimizing increased traveldistance, the next grid cell included at Q : o side is alwayschosen as the next element in the spatially-ordered grid listg7 : l

sc which holds Eq. (2). Similarly, the next grid cell

included at Q : d side is always chosen as the next elementin the spatially-ordered grid list g2 : l

sc which holds Eq. (3).

In this example, since So and Sd produces an empty inter-section, the algorithm expands at Q : o side to include g3(indicated by the broken red rectangle) and add taxisselected from g3 : lv as depicted in Fig. 10c. At Q : d side, thealgorithm covers g6 and adds taxis as indicated in Fig. 10d.Unfortunately, the intersection set of So and Sd remainsempty. Consequently, the algorithm needs to continueexpanding the searching area at both sides. g9 is then selectedat Q : o side; but no grid cell can be further included at theQ : d side. After adding the taxis selected from g9 : lv into setSo as shown in Fig. 10e, we find Taxi10 and Taxi17 as theintersection between So and Sd. Hence, the searching algo-rithm terminates.

Compared to the dual side searching algorithm, the dis-advantage of the single side searching algorithm is that thenumber of selected grid cells could be large and thus itresults in many taxis retrieved for the later scheduling pro-cess. In other words, it increases the overall computationcost, which is certainly not desirable for a rigid real-timesystem like taxi-sharing. Though the dual-side searchingalgorithm may result larger increase in travel distance forthe given ride request, as a compensation for the small lossin distance optimality, the algorithm selects far fewer taxisfor the schedule allocation step, reducing the computationcost and ride request processing time. We found in theexperiments that the number of selected taxis is reduced

Fig. 9. Overview of the dual-side taxi searching algorithm.

Fig. 10. Calculation of the taxi set in the taxi searching process.


by 50 percent while the increase in travel distance is just1 percent over the single-side search algorithm.

5 TAXI SCHEDULING

Given the set of taxi statuses SV retrieved for a ride requestQ by the taxi searching algorithm, the purpose of the taxischeduling process is to find the taxi status in SV which sat-isfies Qwith minimum travel distance increase.

To this end, given a taxi status, theoretically we need totry all possible ways of inserting Q into the schedule of thetaxi status in order to choose the insertion which results inminimum increase in travel distance. All possible ways ofinsertion can be created via three steps: (i) reorder the pointsin the current schedule, subject to the precedence rule, i.e.,any origin point precedes the corresponding destinationpoint (we refer to this step as the schedule reordering there-after); (ii) insert Q : o into the schedule (iii) insert the Q : dinto the schedule. The capacity and time window con-straints are checked in all three steps, during which theinsertion fails immediately if any constraint is violated. Themonetary constraints are then checked for the insertion afterall three steps have been done successfully. Finally, amongall insertions that satisfy all constraints, we choose the inser-tion that results in minimum increase in travel distance forthe given taxi status.

Consider a schedulewith n points, amongwhichm pointsare pickup points. After the first step, i.e., the schedule reor-dering step, there will be as many as n!=2m sequences whichcomply with the precedence rule. (n! is the total number ofsquences of all n points. Since each pickup point mustprecede the correspoinding destination point, so the totalnumber of squences needs to be divided by 2m.) Thoughreordering the schedule is theoretically necessary for findingthe optimal insertion way, we find that it is not the case inpractice via experiments (see Section 6.2.3). Therefore, forthe sake of simplicity, we do not consider the schedule reor-dering step here.

Next we describe how to check the feasibility of eachinsertion possibility, subject to the capacity and time win-dow constraints first (Section 5.1) and then the monetaryconstraints (Section 5.2), given a pair of Q and V . A com-puter cluster can be employed to parallelize the computa-tion by assigning taxi statuses to different computers in thecluster, so the constraints checking for multiple taxi statusescan be performed simutaneously.

5.1 Time Window Constraints

Given a schedule of n points, there is clearly O n2ð Þ ways toinsert a new ride request into the schedule. For example,Fig. 11 shows one way of inserting a request into a schedulewith four points. To insert Q3:o after point Q1:o optimally,the algorithm needs to find the first path (starting from the

shortest path) from Q1 : o to Q3 : o which allows the taxi toarrive at Q3 : o during Q3 : pw given the scheduled arrivaltime at Q1 : o. Since the shortest path is often not the fastesttone when considering real road traffic, it is likely that multi-ple paths needs to be calculated before finding the first satis-factory path from Q1 : o to Q3 : o: Similar process is requiredfor other connecting paths, as illustrated by the dash linesin Fig. 11. As a result, the overall computation load can beextremely high for checking just one insertion way. To easethe computation load, here we only consider using the fast-est path from one point to another during the insertion,though the new route may not be the shortest one in theory.

Denote by ! the travel time of the fastest path from onelocation to another location, and tw represents the time spentwaiting for the passenger if the taxi arrives Q3 : o ahead ofQ3 : pw : e. Eq. (4) gives the travel time delay, denoted by tdafter insertingQ3 : o betweenQ1 : o andQ2 : o

td ¼ Q1 : o ! Q3 : oð Þ þ Q3 : o ! Q2 : oð Þþ tw � Q1 : o ! Q2 : oð Þ (4)

If td results in the late arrival at point Q2:o or any pointafter Q2:o in the original schedule, then the insertion fails.For this purpose, we introduce the notion of slack time.Denote by ap and ad the projected arrival time at a pickuppoint Q : o and a destination point Q : d, respectively. Thenthe slack time at Q : o and Q : d, denoted by ðQ : oÞst andðQ : dÞst respectively, is calculated by Eq. (5) and Eq. (6),respectively

ðQ : oÞst ¼ Q : pw : l� ap (5)

ðQ : dÞst ¼ Q : dw : l� ad (6)

Thus, we can use slack times as a shortcut to checkwhether the delay incurred due to an insertion destroys thetimely arrivals at any subsequent point in the schedule. Inthe example shown by Fig. 11, if td � Minf Q1:dð Þst;Q2 : dð Þstg, then the insertion fails. If Q3:o is inserted success-fully, the system proceeds to insert Q3 : d in a similar way.Algorithm 1 summaries the process of computing a newroute for a possible insertion way, represented by a pairði; jÞ. This algorithm is run for all possible insertionways.

Fig. 11. One possible insertion of a ride request into a schedule.


5.2 Monetary Constraints

The new schedule after the insertion, so far, has only beenchecked against the capacity and time window constraints.It should also meet the monetary constraints. In this sectionwe formulate the monetary constraints of taxi-sharing.

On one hand, we impose two constraints which encour-age riders to participate in taxi-sharing by rewarding themwith certain monetary gains. The first rider monetary con-straint says that any rider who participates in taxi-sharingshould pay no more than what she would pay if she takes ataxi by herself. The second rider monetary constraint saysthat if an occupied taxi V is to pick up a new rider Q, theneach rider P currently sitting in V whose travel time islengthened due to the pickup of Q, should get a decrease intaxi fare; and the fare decrease should be proportional toP ’s increase in travel time.

On the other hand, we enforce one constraint which givesthe driver motivation to participate in taxi-sharing. Thisconstraint says that a driver should charge for all distancesshe has travelled. Intuitively the driver should make moneyfor the distance of reroutes incurred by the join of any newpassenger.

Now let us consider these three monetary constraintstogether in the scheduling context: given a taxi status V anda new ride request Qn, under what conditions will V satisfythe above three monetary constraints with respect to Qn.

Denote by Q1; . . .Qn�1 the riders involved in the currentschedule of V before the join of Qn. Also denote by di thedistance between Qi:o and Qi:d on the road network; i ¼ 1; . . . ; n. Denote by fi the taxi fare of rider Qi if V picksup Qn. Denote by F : Rþ ! Rþ the fare calculation function,which maps the travelled distance to the taxi fare. FunctionF can be defined by some transportation authority or taxicompany. Then the first monetary constraint can beexpressed by Eq. (7)

fi � F ðdiÞ; i ¼ 1; . . . ; n: (7)

Denote by M the revenue of the driver if she picks up Qn

and by D the travel distance of the new route after thepickup. Then the driver monetary constraint is expressed byEq. (8)

M � F ðDÞ: (8)

Since M ¼ Sfi, we then have Eq. (9) by bridging the twoequations above

F ðDÞ � M ¼ Sfi � SF ðdiÞ; i ¼ 1; . . . ; n: (9)

M can take any value between F ðDÞ and SF ðdiÞ in orderto make Eq. (9) hold. In this paper, we take the lower boundF ðDÞ in order to minimize the total taxi fare of riders. There-fore, we haveM ¼ F ðDÞ.

Then we need to distribute the total fare M to each indi-vidual rider. Denote by Dfi the decrease in taxi fare for riderQi, and DTi the increase in travel time of rider Qi due to thepickup of Qn, i ¼ 1; . . . ; n� 1. The fare is determined in theway expressed by Eqs. (10) and (11), where fn is the taxifare of rider Qn, DD is the travel distance increase of the taxiroute due to the pickup of Qn and f � 0 is some constant

fn ¼ F ðdnÞ � f; (10)

Dfi ¼ DTiPn�1

i¼1 Ti

½ðF ðdnÞ � fÞ � F ðDDÞ�; i ¼ 1; . . . ; n� 1: (11)

Eq. (10) says that the new rider pays by f less than what-ever she would pay if she rides alone. Eq. (11) says that(i) existing riders collectively save an amount which equalsthe difference between the charge of the new rider and thedriver’s expected fare increase due to the increase in traveldistance; and (ii) existing riders split the total saving pro-portional to their individual travel time delay (the secondrider monetary constraint). Since it requires Dfi � 0, there-fore, we have Eq. (12)

F ðdnÞ � F DDð Þ þ f: (12)

Eq. (12) by itself is the sufficient and necessary conditionfor taxi V to satisfy all three monetary constraints withrespect to Qn.

Fig. 12 illustrates how to apply the monetary constraintswith a concrete example. Fig. 12a shows the schedule of ataxi before the second rider boards. The fare of the first rideris f1 ¼ F ðd1Þ. Themonetary constraint for picking up the sec-ond rider is F ðd2Þ � F DDð Þ þ f , where DD is the increase intravel distance due to the join of the second rider. If the aboveconstraint stands, then we have Df1 ¼ ½F ðd2Þ � f� � F ðDDÞand f2 ¼ F ðd2Þ � f . Likewise, Fig. 12c shows the schedule ofthe taxi after the second rider joins and before the third riderjoins. Similarly, the pricing constraint for picking up thethird rider is F ðd3Þ � F DD0ð Þ þ f , where DD0 is the increasein travel distance due to the join of the third rider. If this con-

straint stands, then we have Dfi ¼ DTiDT1 þDT2

½F d3ð Þ � f� �F ðDD0ÞÞ; i ¼ 1; 2 and f3 ¼ F ðd3Þ � f .

Some riders may think the taxi fare decrease is not worththe increase in travel time and thus rejects the pickup deci-sion. We thus introduce a parameter Qi:r for each rider Qi,which presentsQi‘s acceptable money-to-time rate. That is tosay, Qi supports the pickup of a new rider only when theratio of the fare decrease to the travel time increase is largerthanQi:r. The above constraint is expressed by Eq. (13). Andan insertion satisfies the monetary constraints only when allcurrent riders on the taxi support the pickup decision

Dfi=DTi � Qi : r: (13)

Fig. 12. An example of the pricing constraint.


6. EVALUATION

6.1 Setting

6.1.1 Data Set

Road networks: We perform the experiments using the realroad network of Beijing, which contains 106,579 road nodesand 141,380 road segments.

Taxi Trajectories: The taxi trajectory data set contains theGPS trajectory of over 33,000 taxis during a period of87 days spanning from March to May in the year of 2011.The total distance of the data set is more than 400 millionkilometres and the number of points reaches 790 million.After trip segmentation, there are in total 20 million trips,among which 46 percent are occupied trips and 54 percentare non-occupied trips. We map each occupied trip to theroad network of Beijing using the map-matching algorithmproposed in [10]. Fig. 13 shows the distribution of pickupand destination points of the ride requests in the data setover road segments in a day (note that long tails, i.e., roadsegments with large number of requets, are not shown inthe figures due to space limitation). It is clear that riderequests are distributed sparsely over the road network.

6.1.2 Experimental Platform

In order to validate our proposed system under practicalsettings, instead of generating random ride requests and ini-tial taxi statuses, we mine the trajectory data set to build anexperimental platform. From the historical trajectory dataset, the platform learns information regarding 1) the distri-bution of the ride requests on the road network over time ofday, and 2) the mobility patterns of the taxis. With thislearned knowledge, the platform then generates a realisticride request stream (meaning that the origin-destinationpairs and time windows of ride requests follow the learneddistribution) and initial taxi statuses for our experiments.We envision that this platform (available at http://cs.uic.

edu/~sma/ridesharing/) can be applied to many otherurban and transport computation problems.

Ride request stream. The goal is to generate real-time riderequests that are as realistic as possible. For this purpose,we first discretise one day into small time frames, denotedby fj’s. Denote all road segments by ri’s. We assign all his-torical ride requests into time frames. Assume that the arriv-als of ride requests on each road segment approximatelyfollow a Poisson distribution during time frame fj. Thus,

we can learn �ji , i.e., the parameter of the Poisson distribu-

tion for road segment ri during time frame fj. Specifically,for each road segment ri, we count the number of riderequests that originate from ri within time frame fj, denoted

by cji . Then we calculate �ji based on cji using Eq. (14) (where

lenðfÞ is the length of a frame in time units) and generate aride request stream that follows a Poisson process with

parameter �ji . In order to generate destination of requests

trufhfully, for each cji , we decompose it into an array of

numbers fcji1; cji2; . . . cjimg, where cjik; k ¼ 1; 2; ::m represents

the number of requests which are originated from road seg-ment ri and destined for road segment rk during time framefj, as illustrated by Fig. 14a. Therefore, the transition proba-

bility from ri to rk during time frame fj, denoted by pjik, can

be estimated using Eq. (15). Fig. 14b shows the distributionof destination road segments for requests that originatefrom road segment ri in an hour

�ji ¼ cji=lenðfÞ; (14)

pjik ¼ cjik=cji : (15)

For each ride request Q generated in frame fj with the ori-gin road segment being ri, the destination road segment is

generated according to the transition distribution pjik.

Q : pw : e and Q : dw : e equals to Q : t, i.e., the submitted timeof the ride request. Q : pw : l is calculated by applying a fixedwindow size. Q : dw : l equals to the sum of Q : pw : l and theaverage travel time between the origin and destination pairlearned from the GPS trajectory data set.

Note that the taxi GPS trajectory data set only revealsthe number of ride requests that got served. In reality thereare also many ride requests unsatisfied and disappeareddue to the shortage of taxis. To take such ride requests intoconsideration, we introduce a system parameter D, suppos-ing that the number of real ride requests is D times thenumber of request extracted from the trajectory data set.Figs. 15a and 15b show the supposed number and theextracted number of ride requests that originate from all

Fig. 13. Distribution of ride requests over road segments.

Fig. 14. Transition probability of road segment ri during a time frame fj.

Fig. 15. Inflated and extracted number of ride requests during a day.


road segments and a specific hot spot road segment (i.e.,with a large number of requests), respectively, over time ofa “hot day” (i.e. with more requests than an average day),where the time frame is 1 hour and D ¼ 2.

Initial taxi statuses. To keep the characteristics of the realis-tic scenario, we use the real taxi statuses by slicing the histori-cal trajectories at a certain timestamp. Specifically, we select adate and choose a particular second of day as the timestampwhen the experiment starts, denote it by ts. We scan all theGPS records of the selected date to determine the initial statesof taxis. A taxi status V is set to be occupied if it is recordedoccupied crossing timestampts. The initial schedule of V canbe initialized according to the record. A taxi V is set to bevacant if it is recorded vacant both just before and right afterts. The concept of “just before” and “right after” is controlledby a temporal parameter, which is set to be 10 minute. Allremaining taxis are then considered as not recorded andthus not used in the simulation.

The ride requests and initial states used in all experi-ments are generated with parameters listed in Table 1.

6.1.3 Framework

We study two strategies in the searching algorithm (single-side and dual-side) and two strategies in the schedulingalgorithm (first-fit and best-fit), resulting in four taxi-sharing methods. We compare the performance of thesefour methods with that of a non-taxi-sharing method asthe number of requests (i.e., D) changes. We also test theperformance of these four methods by changing themoney-to-time rate parameter of the monetary constraints,and study the necessity of the schedule reordering step(i.e., considering different pickup and drop-off orders) inthe scheduling algorithm.

6.1.4 Baseline Methods

The Non-Taxi-sharing method (NR) forbids taxi-sharing andassumes that a vacant taxi moves to pick up the rider that itcan pick up at the earliest time.

Taxi searching step. A taxi-sharing method is single-side ifthe taxi searching algorithm retrieves taxis only from theorigin side of a request; otherwise, it is dual-side.

Taxi scheduling step. A taxi-sharing method is called best-fit where the taxi scheduling process tries all candidate taxisreturned by the taxi searching algorithm. Otherwise, iscalled first-fit if the scheduling process terminates once itfinds a taxi that satisfies the ride request.

Because the two choices can be made independently, weget the following four taxi-sharing methods: Single-side andFirst Fit Taxi-sharing (SF), Single-side and Best-fit Taxi-sharing

(SB), Dual-side and First Fit Taxi-sharing (DF), Dual-side andBest-fit Taxi-sharing (DB).

The fare calculation function F ¼ pD, where D is thetraveled distance and p is some constant price for a unittraveled distance. The money-to-time rates of ride requestsare assumed to follow an exponential distribution with amean valuem.

6.1.5 Measurements

The performance of the taxi-sharing system is evaluated intwo perspectives, namely effectiveness and efficiency. Wefirst describe following effectiveness measurements.

Relative distance rate (RDR). Define the distance of a riderequest Q as the distance between its origin point Q : o andits destination point Q : d. Denote by DSR the sum of distan-ces of ride requests that get satisfied and by DV the totaldistance travelled by all taxis while being occupied in ataxi-sharing method. RDR is calculated by Eq. (16)

RDR ¼ DV =DSR: (16)

RDR evaluates the effectiveness of taxi-sharing by measur-ing howmuch distance is saved compared to the case whereno taxi-sharing is used. The value of RDR can be any posi-tive number. The smaller RDR is, the more vehice distancethe ridesharing system saves. When the value is greaterthan 1, it indicates that the ridesharing system does not savebut increases the total travel distance.

Satisfaction rate (SR). Is the ratio of the number of riderequests that get satisfied to the total number of ride request(exclude ride requests that are already served by taxis at theinitial state in the ride request counting). Thus, SR 2 ½0; 1�.The larger SR is, the more requests the ridesharing systemhas satisfied.

Seat occupancy rate (SOR). Measures the seat occupancyrate in all taxis during a given time period. Denote by C thenumber of passenger seats in a taxi, by N the number oftaxis, by T a period of time, and by Ts the sum of the traveltime of all requests that are satisfied during period T . SORis calculated by Eq. (17). SOR provides an inituitive percep-tion of how well the seats in the vehicles are utilized. SORranges from zero to one. When SOR equals to 1, it means afully utilizated outcome where each seat in every vehicle isoccupied all the time

SOR ¼ TS=ðN C T Þ: (17)

Taxi-sharing rate (TR). Is the percentage of ride requestsparticipating in taxi-sharing among all satisfied requests.The value of TR ranges from 0 to 1. A larger value indicatesmore ridesharing opportunities created.

Fare saving rate (FSR). Is the average saving percentage intaxi fare of riders who participate in taxi-sharing. The valuemay range from 0 to 1 with 1 meaning that all ridesharingriders save the whole fare and get free rides.

Now we introduce following efficiency measurements.Number of road nodes accessed per ride request (#RNAPR). Is

the number of accessed road network nodes per riderequest (due to the shortest path calculations).

Number of grid cells accessed per ride request (#GCAPR). Isthe number of accessed grid cells per ride request.

TABLE 1Parameter Setting for Ride Request Generation

Notation Definition Value

tststs The start time of simulation 09:00tetete The end time of simulation 09:30

#taxi#taxi#taxi The number of taxis 7088#taxio#taxio#taxio The number of taxis occupied initially 4722wswsws The window size 5 min

lenðfiÞlenðfiÞlenðfiÞ The length of a time frame 60 min


Num. of taxis accessed per ride request (#TAPR). Is the no. oftaxis accessed by the scheduling module per request.RNAPR, GCAPR, TAPR are machine-independent indica-tors for computation cost of the system.

Execution time per ride request. Is the CPU time spent forserving each ride request. It consists of taxi searching time(elapsed between step �2 and �4 in Fig. 1) and taxi schedul-ing time (elapsed between�5 and�7 in Fig. 1).

6.2 Experimental Results

Table 2 lists default values for experiment parameters.

6.2.1 Effectiveness

Fig. 16a shows SR, i.e., the satisfaction rate, of all methodsas D changes. All ridesharing methods first show a slightincrease and then keep declining in SR as D increases. Thisis because as the value of parameter D starts increasing, theridesharing opportunies increase as well. When D is small,the increase in ridesharing opportunies is larger than theincrease in the number of request, as a result, the satisfac-tion rate surges. When D gets larger, ridesharing opportu-nies do not emerge as fast as new requests arrive, therefore,the satisfiaction rate starts dropping. In contrast, the non-ridesharing method NR can only suffers from the increasein D, i.e., resulting in a decreasing SR. It is clear that all fla-vours of taxi-sharing methods have a considerably highersatisfaction rate (about 23 percent higher on average) thanthe NR method for all D values. The difference in the satis-faction rate among taxi-sharing methods is insignificant asno particular technique is proposed for minimizing the sat-isfaction rate.

Fig. 16b shows TR, the percentage of ride requests partic-ipating in taxi-sharing among all satisfied ride requests, forall taxi-sharing methods. Not surprisingly, TR surges as Dincreases. This is because taxi-sharing opportunities arelikely to rise as the number of taxi ride request increases.Consequently, more ride requests can be satisfied via taxi-sharing. But since the total number of ride requestsincreases even faster, the satisfaction rate still drops, asillustrated by Fig. 16a.

To calculate the fare of riders in the experiments, weinstantiate the fare calculation function as follows: the farecharged by a taxi driver is linear to the distance travelled bythe taxi, i.e., the product of the distance travelled and fareper unit distance. Fig. 16c shows that FSR, the average faresaving of riders who participate in taxi-sharing, drops as Dincreases. The larger D is, the more passengers participatein ridesharing. However this does not necessarily guaranteethat the average saving of the participants increases. Theaverage cost of this amount saving is about 5.08 minutedelay in travel time. We believe that most riders are willingto tolerate this amount of delay, especially under the highrequest demand scenarios in which this taxi-sharing systemis most likely to be useful.

Fig. 16d shows RDR steadily drops as parameter Dincreases. Again, this is likely because as the number ofride requests increases, more ride requests can share partialtrips with each other and thus more distance the taxi-sharing methods save. The SB taxi-sharing method outper-forms other methods, since SB reduces the increase in traveldistance most. The DB taxi-sharing method slightly trails SBmethod as the taxi searching step of it explores fewer gridcells. Two first-fit based taxi-sharing methods show clearlyhigher relative distance rate. From the picture, we can seethat taxi-sharing methods save up to 12 percent in traveldistance, depending on delta. Given the fact that there are67,000 taxis in Beijing (not in the data set) and each taxiruns 480 km per day (learned from the data set), the savingachieved by taxi-sharing here means over 1.5 billion kilo-metres in distance per year, which equals to 120 million literof gas per year (supposing a taxi consumes 8 liter of gaso-line per 100 km) and 2.2 million of carbon dioxide emissionper year (supposing each liter of gas consumption generates2.3 kg of carbon dioxide).

Fig. 16e shows SOR increase as parameter increases. Thisis easy to understand since as the number of requestsincreases, more ridesharing opportunies appear. As a result,SOR increases as well. The differences between ridesharingmethods in SOR are not significant since these methods arenot designed for optimizing SOR.

Figs. 17a, 17b, 17c, 17d and 17e shows SR, TR, FSR, RDRand SOR of taxi-sharing methods for different mean valuesof the money-to-time rate of ride requests, respectively,when D ¼ 1. All measurements except FSR show a decreasetendency as the mean money-to-time rate increases. Whenthe mean money-to-time rate increases from ¥0.25/min to¥0.5/min, the decrease is the largest.

6.2.2 Efficiency

Tested on a single server with 2.67 GHz CPU and 16 GBRAM (using a single thread), the average taxi searching

TABLE 2Default Values of Parameters Used in Experiments

Definition Value

Beijing Map Size 32 40 km2

The size of grid (i.e., number of grid cells) 3030Schedule reordering before insertion nop, taxi fare per kilometer ¥2C, no. of passenger seats in a taxi 3m, mean of the money-to-time rate distribution ¥0/min

Fig. 16. Performance in effectiveness measurements of different methods.


time and scheduling time for the DB method is 0.15 and10.33 ms, respectively.

We also test the efficiency of the system using machine-independent measurements. The three sub-graphs of Fig. 18show the number of taxis accessed per ride request, the num-ber of road nodes accessed per ride request, and the numberof grid cells accessed per ride request, respectively, for differ-ent taxi-sharing methods under different D. It is clear fromthe pictures that all taxi-sharing methods do not show sharpincrease in computation cost as D increases. It is also obviousthat the computation cost of the DB taxi-sharing method issignificantly smaller than that of SB taxi-sharing method.Especially when D � 4, the computation cost of the DBmethod is even smaller than that of the SF method. Theresult of Figs. 16 and 18 together validate our motivation forthe dual-side taxi searching algorithm. That is, the dual-sidesearching indeed incurs small increase in travel distance inexchange for the significant decrease in computation cost.

6.2.3 Necessity of the Schedule Reordering

Fig. 19 shows the average execution time per ride requestunder different values of D when using the DB taxi-sharingmethod with and without the schedule reordering beforeinsertion. The execution time per ride request is about20 percent longer on average when the schedule reorderingis performed.

Meanwhile there is almost no change in all effectivenessmeasurements. From the results, we also learned that inpractice it is extremely rare that the optimal insertionrequires the schedule reordering. Although the executiontime per ride request remains a reasonable small valuewith the schedule reordering step, there is still no incentiveto do so in practice.

7 RELATED WORK

We study three categories of related works, positioning ourwork in the research community.

7.1 Taxi Recommendation and Dispatching

Quite a few recommender systems have been proposedfor improving an individual taxi driver’s income andreducing unnecessary cruising. Based on historical taxitrajectories, Yuan et al. [11] proposed a system that sug-gests some parking places for an individual taxi drivertowards which they can find passengers quickly and max-imize the profit of the next trip. Similarly, Ge et al. [12]suggests a sequence of pickup points for a taxi driver.While these systems are only designed from the perspec-tive of taxi drivers, our system considers the needs ofboth taxi drivers and riders.

Taxi dispatching services [13], [14], [15], [16], [17] usu-ally send a taxi close to a passenger as per the passenger’scall without considering taxi-sharing. Consequently, onlyvacant taxis need to be examined for each dispatch, whichcan be easily retrieved by answering a range query. In ourcase, each taxi that is occupied under full capacity needsto be considered. This complication introduces newchallenges.

7.2 Carpool and Dial-A-Ride

Carpool often refers to ridesharing which deals with routinecommutes. There are already websites and mobile Apps forthis purpose, such as Avego. Given the usual small size of

Fig. 17. Performance in effective measurements versus money-to-time rate.

Fig. 18. Computation cost in terms of node access per ride request.

Fig. 19. Time cost of schedule reordering.


the problem, researchers are able to solve it optimally byusing linear programming techniques [1], [2]. Unlike in car-pool where ride requests are known in advance, the real-time taxi-sharing system here is more challenging as riderequests are generated on-the-fly and the routes of taxischange continuously.

The taxi-sharing problem can be viewed as a specialmember of the general class of the dial-a-ride problem(DARP). The DARP is originated from and has been studiedin various transport scenarios, notably goods transport [18],paratransit for handicapped and elderly personnel [19], etc.Existing works on the DARP have primarily focused on thestatic DARP, where all customer ride requests are known inpriori. Since the general DARP is NP-hard, only smallinstances (involving only a few cars and dozens of riderequests) can be solved optimally (often by resorting to inte-ger programming techniques, see [20], [21]). Large staticDARP instances are usually solved by using the two-phasescheduling strategy [6], [22], [23], [24] with heuristics. Spe-cifically, the phase I partitions ride requests into somegroup and computes an initial schedule for delivering theriders in each group. In phase II, ride requests are swappedbetween different groups, aiming to find new schedulesoptimizing a predefined objective function.

Little research has been carried out on the dynamicDARP, where requests are generated on the fly. Previousworks on the dynamic DARP problem [25] continues toadapt the two-phase scheduling strategy. However, thetwo-phase strategy is not feasible for the real-time taxi-sharing. As if the strategy is applied, the cloud will notserve a new request immediately. Instead it needs to waitfor more requests in order to make the phase II possible,which prolongs the response time of a request. In addi-tion, the heavy computation load of the phase II will fur-ther increase the response time, resulting in manyrequests unsatisfied.

7.3 Real-Time Taxi-Sharing

Though real-time taxi-sharing has been studied in severalprevious works [4], [26], [27], [28], [29], our work demon-strates three major advantages. First, our problem defini-tion is more realistic by considering three different typesof constraints. Some existing works (e.g., [28]) did not con-sider time window constraints and none of these previousworks explicitly modelled monetary constraints. (though[30] implicitly considers monetary constraint by convert-ing it to distance constraint.) Second, we analysed thecomputational cost of each component of the system, pro-posing a spatio-temporal index and a taxi searching algo-rithm, which significantly improve the system efficiency.Third, simulation results presented here is more convinc-ing as we evaluated our system based on the real dataand at a much larger scale than most previous works did.This is also one of main concepts of urban computing[31], which tackles the big challenges in cities by using bigdata. The size of the ride request stream in our experi-ment is as large as 20K and these ride requests are learnedfrom the historical trajectory data set. Detail comparisonsbetween this work and our previous paper [3] are statedin the end of Section 1.

8 CONCLUSIONS

This paper proposed and developed a mobile-cloud basedreal-time taxi-sharing system. We presented detail interac-tions between end users (i.e. taxi riders and drivers) andthe Cloud. We validated our system based on a GPS trajec-tory data set generated by 33,000 taxis over three months,in which over 10 million ride requests were extracted. Theexperimental results demonstrated the effectiveness andefficiency of our system in serving real-time ride requests.Firstly, our system can enhance the delivery capability oftaxis in a city so as to satisfy the commute of more people.For instance, when the ratio between the number of taxiride requests and the number of taxis is 6, our proposedsystem served three times as many ride requests as thatwith no taxi-sharing. Secondly, the system saves the totaltravel distance of taxis when delivering passengers, e.g., itsaved 11 percent travel distance with the same ratio men-tioned above. Supposing a taxi consumes 8 liters of gaso-line per 100 km and given the fact learned from the realtrajectory data set that the average travel distance of a taxiin a day in Beijing is about 480 km, the system can saveover one third million liter of gasoline per day, which isover 120 million liter of gasoline per year (worth about 150million dollar). Thirdly, the system can also save the taxifare for each individual rider while the profit of taxi driv-ers does not decrease compared with the case where notaxi-sharing is conducted. Using the proposed monetaryconstraints, the system guarantees that any rider that par-ticipates in taxi-sharing saves 7 percent fare on average. Inaddition, the experimental results justified the importanceof the dual-side searching algorithm. Compared to the sin-gle-side taxi searching algorithm, the dual-side taxi search-ing algorithm reduced the computation cost by over 50percent, while the travel distance was only about 1 percenthigher on average. The experimental results also suggestthat reordering the points of a schedule before the insertionof the new ride request is not necessary in practice for thepurpose of travel distance minimization.

In the future, we consider incorporating the creditabil-ity of taxi drivers and riders into the taxi searching andscheduling algorithms. Additionally, we will furtherreduce the travel distance of taxis via ridesharing. Wealso consider refining the ridesharing model by introduc-ing social constraints, such as gender preference, habitspreference (e.g., some people may prefer co-passengerswho do not smoke).

ACKNOWLEDGMENTS

This research was partially supported by US Department ofTransportation National University Rail Center (NURAIL);Illinois Department of Transportation (METSI); and USNational Science Foundation grants IIS-1213013, CCF-1216096, DGE-0549489, IIP-1315169. The work was done inMicrosoft Research when the first author was an internunder the supervision of the second author.

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Shuo Ma received the BS degree in computerscience in 2008 from Beijing University of Postsand Telecommunications, Beijing, China. He iscurrently working toward the PhD degree with theDepartment of Computer Science, University ofIllinois at Chicago. His research interests includemobile computing, computational transportationscience, and spatial databases.

Yu Zheng is a lead researcher at MicrosoftResearch and a Chair Professor at ShanghaiJiao Tong University. He leads the research onurban computing at Microsoft Research, and ispassionate about using big data to tackle urbanchallenges. He has published over 50 referredpapers at prestigious conferences and journals,such as KDD, VLDB, UbiComp and TKDE, wherehe received five best paper awards, e.g. atICDE’13. Dr. Zheng is a member of the EditorialAdvisory Board of IEEE Spectrum and an Associ-

ate Editor of the IEEE Transactions on Big Data. He has served as chairon over 10 prestigious international conferences, e.g., the program co-chair of ICDE 2014 (Industrial Track). He has been invited to give over10 keynote speeches at international conferences (e.g., IE 2014 andAPEC 2014 Smart City Forum). In 2013, he was named one of the TopInnovators under 35 by MIT Technology Review (TR35) and featured byTime Magazine for his research on urban computing. In 2014, he wasnamed one of the top 40 Business Elites under 40 in China by Fortune,for the business impact of urban computing he has been advocatingsince 2008. Dr. Zheng is also an Adjunct Professor at Hong Kong Poly-technic University and Southwest Jiaotong University. He is a seniormember of the IEEE and ACM.

Ouri Wolfson (F’ 12) received the BA degree inmathematics and the PhD degree in computerscience from the Courant Institute of Mathemati-cal Sciences, New York University, New York,NY. He was a consultant with Argonne NationalLaboratory, Argonne, IL; the U.S. Army ResearchLaboratory, Adelphi, MD; the Defense AdvancedResearch Projects Agency, Arlington, VA; andthe Center of Excellence in Space Data and Infor-mation Sciences, Goddard Space Flight Center,National Aeronautics and Space Administration,

Greenbelt, MD. He was also with the computer science faculty of theTechnion—Israel Institute of Technology, Haifa, Israel, and ColumbiaUniversity, New York. He has been a member of Technical Staff withBell Laboratories. He is currently the Richard and Loan Hill professor ofcomputer science with the University of Illinois at Chicago and an affiliateprofessor with the Department of Computer Science, University of Illinoisat Urbana-Champaign. His research interests include database systems,distributed systems, and mobile/pervasive computing. He founded Mobi-trac, which is a high-tech startup that was acquired by Fluensee Co. in2006. He is a fellow of the Association for Computing Machinery, theAmerican Association for the Advancement of Science, and the IEEE.


Documents

1782 IEEE TRANSACTIONS ON KNOWLEDGE AND …sma/Papers/taxisharing_TKDE...Real-Time City-Scale Taxi Ridesharing Shuo Ma, Yu Zheng, Senior Member, IEEE, and Ouri Wolfson, Fellow, IEEE