The Impact of Ridesharing in Mobility-on-Demand Systems: SimulationCase Study in Prague

Davide Fiedler1, Michal Certicky1, Javier Alonso-Mora2, and Michal Cap1,2

Abstract— In densely populated-cities, the use of privatecars for personal transportation is unsustainable, due to highparking and road capacity requirements. The mobility-on-demand systems have been proposed as an alternative to aprivate car. Such systems consist of a fleet of vehicles thatthe user of the system can hail for one-way point-to-pointtrips. These systems employ large-scale vehicle sharing, i.e.,one vehicle can be used by several people during one day andconsequently the fleet size and the parking space requirementscan be reduced, but, at the cost of a non-negligible increasein vehicles miles driven in the system. The miles driven in thesystem can be reduced by ridesharing, where several peopletraveling in a similar direction are matched and travel inone vehicle. We quantify the potential of ridesharing in ahypothetical mobility-on-demand system designed to serve alltrips that are currently realized by private car in the cityof Prague. Our results show that by employing a ridesharingstrategy that guarantees travel time prolongation of no morethan 10 minutes, the average occupancy of a vehicle willincrease to 2.7 passengers. Consequently, the number of vehiclemiles traveled will decrease to 35 % of the amount in the MoDsystem without ridesharing and to 60% of the amount in thepresent state.

I. INTRODUCTION

In densely-populated cities, private cars are an unsustain-able mode of personal transportation. Parking capacity androad capacity in such environments are typically insufficientto accommodate the private car traffic. At the same time,roads and parking space are difficult to expand due to scarcityof free land. In result, many modern cities are plagued bycongested roads, unavailability of parking, and high levelsof air pollution.

Mobility-on-demand (MoD) systems represent an alter-native to transportation by private vehicles. In an MoDsystem, when a passenger requests a transportation service,a particular vehicle is assigned to pick up the passengerand carry him or her to the desired destination, where thepassenger is dropped off. Then, the vehicle is availableagain to serve other passengers. When an on-demand vehicletravels without a passenger, e.g., when it is moving from onedrop-off position to the next pick up position, we say that itdrives unallocated. Examples of on-demand systems includetaxi service, transportation network companies such as Uber,or future systems of self-driving taxis being developed bycompanies such as Waymo, Uber or nuTonomy. The MoDsystems employ massive vehicle sharing, and thus they canserve the existing transportation demand with smaller highly-utilized vehicle fleet and in turn, they promise to dramatically

1Department of Computer Science, Faculty of Electrical Engineering,CTU in Prague, Czech Republic david.fiedler@agents.fel.cvut.cz

2Department of Cognitive Robotics, 3ME, TU Delft, the Netherlands

reduce the need for urban parking capacity. The performanceof large-scale mobility-on-demand systems has been recentlystudied within newly developed mathematical models thatindeed confirm the ability to reduce the number of vehiclesin the system [1], [2]. However, they also show that the totalamount of vehicle miles driven in the system is bound toincrease due to unallocated vehicle trips [3]. For example,the case studies in Singapore [3] and Prague [4] indicate thatunallocated traffic in the MoD system would add more than30 % to total traffic in the system and subsequently wouldcontribute to the formation of congestion [4].

A possible solution to the above problem is to implementlarge-scale ridesharing, where multiple passengers that travelin the same direction are matched and transported in onevehicle. Efficient ridesharing can increase vehicle occupancyand consequently reduce the required fleet size and the totalamount of vehicle miles driven in the system.

The objective of this paper is to quantify the potential ofridesharing to reduce vehicular traffic in a large-scale MoDsystem. We use agent-based simulation to analyze hypothet-ical scenario of replacing all privately owned vehicles in thecity of Prague by a) a single-occupancy MoD system and byb) an MoD system with ridesharing.

Related work

The impact of potential large-scale MoD system deploy-ments have been studied extensively in recent years, bothusing simulation [1] and by means of formal mathematicalmodeling of such systems [3]. The impact on congestion aris-ing from unallocated vehicle trips in MoD system has beennumerically explored in [5] and [4]. One of the proposedmitigation is strategies is congestion-aware fleet routing [6].

Ridesharing was traditionally formalized in the frameworkof Vehicle Routing Problems (VRP) [7], typically as aspecific variant of VRP with Pickup and Delivery [8], [9],[10], [11] or a Dial a Ride Problem (DARP) [12], [9]. Yet,the existing VRP methods focus on instances with tens ofvehicles and requests [13], [14] and as such, they are notapplicable to management or analysis of large-scale fleetsthat often consist of thousands of vehicles and requests.

The potential for large-scale ridesharing within MoDsystems was studied using the shareability network modelin [15]. This analysis of taxi trips in Manhattan revealedthat up to 80% of the trips could be pairwise shared suchthat the travel time is increased be no more than a couple ofminutes. The analysis was later extended to other cities [16].The assumption of maximum two passengers in a vehiclewas later lifted in [17], where the authors proposed a

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technique for dynamic assignment of requests to vehiclesin the fleet and apply the technique to analyze the potentialof ridesharing within NYC taxi dataset. In contrast to theabove work, that analyzed the scenario of replacing all taxisin Manhattan by a fleet of 3 000 shared taxis, we analyzethe scenario of replacing all private vehicles with a fleetof 50 000 shared MoD vehicles and specifically study howwould large-scale ridesharing affect the utilization of roadinfrastructure.

The city of Prague was chosen for the case study partlybecause we have access to the demand model for the areaand partly because it is a ”regular” metropolis that sharesmany characteristics with other world cities and thus theresults are more likely to generalize. This is in contrast withthe previously considered urban areas such as Manhattanor Singapore that have an extremely high density of traveldemand which may lead to overly-optimistic estimates ofsystem performance.

Contribution

Our work extends the existing models of large-scale MoDsystems with consideration for the potential of ridesharing.More specifically, using agent-based simulation, we quantifythe potential of ridesharing to reduce traffic load and totalvehicle miles traveled. We compare how would be theexisting travel demand served a) in the current system withprivate vehicles, b) in the MoD system without ridesharingand c) in the MoD system with ridesharing. We run high-fidelity realistic-scale simulation of the three scenarios forthe city of Prague. In particular, we use a) real road networktopology, b) demand with realistic structure and realisticscale, and c) we simulate the whole lifetime of the vehicle,including empty trips.

Analyzing of the ridesharing in context of on-demandsystems is essential because it can answer the question ofwhether the MoD system can be, in fact, deployed withoutoverloading the capacity of existing road infrastructure.

II. BACKGROUND MATERIAL

When analyzing the traffic congestion on a road segment,the fundamental diagram of road traffic [18] is often used.This model relates traffic density to traffic flow. Traffic den-sity is the number of vehicles per unit of distance on the roadsegment, while traffic flow is the number of vehicles passinga reference point per unit of time. When traffic densitygrows, traffic flow also increases until it reaches a tippingpoint after which the flow starts dropping due to congestion.The tipping point is known as the critical density [19]. Theexact shape of the diagram is typically determined by fittingempirical data from real-world observations of vehiculartraffic. Subsequently, we will use the traffic density as ameasure of utilization of a particular road segment and thecritical density value yc = 0.08 vehiclem−1 from [20]. Theroad segments with traffic density above critical density ycwill be referred to as congested road segments.

III. METHODOLOGY

In this section, we describe the methodology that allowsus to quantify the potential of large-scale ridesharing in ahypothetical scenario of replacing all private cars in the cityof Prague by an MoD system.

First, we use a travel demand model to generate a represen-tative collection of trips that are currently realised by privatecars in Prague during the morning peak. Then, we designan MoD system that is capable of serving the existing tripswith required service quality. Further, we design a methodthat finds request-vehicle matching for ridesharing. Finally,we simulate the entire system in micro-simulation and gatherdata for subsequent analysis. We will now discuss each stepin detail.

A. Input data

The set of trips that represent the transportation demand isgenerated by the multi-agent activity-based model of Pragueand Central Bohemian Region [21]. In contrast to traditionalfour-step demand models [22], which use trips as the fun-damental modeling unit, activity-based models employ so-called activities (e.g. work, shop, sleep) and their sequencesto represent the transport-related behavior of the population.Travel demand then occurs due to the necessity of the agentsto satisfy their needs through activities performed at differentplaces at different times. These activities are arranged intime and space into sequential (daily) schedules. Trip origins,destinations and times are endogenous outcomes of activityscheduling. The activity-based approach considers individualtrips in context and therefore allows representing realistic tripchains.

The model used in this work covers a typical work dayin Prague and the surrounding Central Bohemian Region.The population of over 1.3 million is modeled by thesame number of autonomous, self-interested agents, whosebehavior is influenced by their sociodemographic attributes,current needs, and situational context. Individual decisions ofthe agents are implemented using machine learning methods(neural networks, decision trees, random forests, etc.) andtrained using various real-world data sets, including censusdata, travel diaries, and other transportation-related surveys.Planned activity schedules are simulated and tuned, and,finally, their temporal, spatial, and structural properties arevalidated against additional historical real-world data (origin-destination matrices and surveys) using six-step validationframework VALFRAM [23], [24]. The model generates overthree million trips by all modes of transport in one 24-hourscenario, out of which there are roughly one million trips byprivate vehicles. For the analysis, we select only the personalcar trips during the morning peak, i.e, such that start between06:30 and 08:00, which yields a collection of about 130 000trips.

B. System model

We adopt a station-based design of the MoD system [3].That is, we partition the city into n = 40 regions using k-means clustering over the demand data, and we assume that

Fig. 1. MoD system stations in the city of Prague. Stations are shown ascircles. Spatial distribution of origins and destinations of travel demands isdepicted using brown dots.

there is a station at the center of each such region. The resultof this process is shown in Figure 1. The number of regionswas chosen such that the average travel time from station toa passenger is below 3 minutes. Stations serve as temporaryparking lots for idle vehicles, and they also contain facilitiessuch as refueling/charging and cleaning.

For simplicity, we assume that each station has suffi-cient stock of vehicles to cover the transportation demandoriginating in its region. Further, we assume that the stockof vehicles at each station is stabilized through a vehiclerebalancing process, that is, the stations with a surplus ofidle vehicles continuously send empty vehicles to stationsthat have a shortage of idle vehicles. In particular, we usethe rebalancing policy based on the solution of the optimaltransport problem [25] used, e.g., in the Singapore MoD casestudy [3].

We experimentally determined that in order to be ableto serve every request from the nearest station (withoutridesharing), the MoD system requires the total of 51 951vehicles.

The MoD system is modeled as follows. Let V = 1, . . . ,mbe the set of all vehicles in the system. The transportationrequests arriving to the system are represented by a sequence(t1, o1, d1), (t2, o2, d2), . . . , where ti, oi, and di are theannouncement time, origin point, and destination point ofrequest i respectively. The i-th transportation request isrevealed only at time ti.

The state of a vehicle v at a particular time point encodesits current position, the set of requests that are currently on-board of the vehicle and the current plan of the vehicle. Theplan of a vehicle is represented as a sequence of plan ordersπ = z1, z2, . . . , where each order zi is either to pick up arequest r, or to drop-off a request r. For a vehicle plan tobe valid, for each on-board passenger, the plan must containan order to drop-off this passenger and for every order topickup request r, the plan must contain an order to drop-off

the request r later in the sequence.The operational cost of vehicle v when following plan π is

denoted sv(π). For simplicity, we define sv(π) to be equal tothe distance driven by the vehicle when it follows plan π. Thetravel delay (or discomfort) of request r when the request isserved by vehicle v following plan πv is denoted qr(πv). Wedefine the travel delay as the difference between the traveltime in a shared vehicle and a travel time along the fastestroute:

qr(πv) := (tdropoffr − tr)− tbaseline

r ,

where tdropoffr is the time when the request was dropped

off under plan πv and tbaseliner is the duration of the fastest

route from pickup point of request r to the drop-off point ofrequest r.

We desire to minimize the total operational cost of thesystem, such that the discomfort of every passenger isbounded by qmax. That is, we will attempt to minimize∑

v

sv(πv)

subject toqr(πv(r)) ≤ qmax ∀r,

where πv(r) is the plan of the vehicle that serves therequest r.

C. Request-vehicle matching

To implement ridesharing in an MoD system, one has todetermine how should be the arriving travel requests assignedto individual vehicles in the system such that the overalldistance driven in the system is minimized. This problemcan be mathematically modeled as a dynamic dial-a-rideproblem (D-DARP), which is known to be NP-hard [26].Despite recent algorithmic advancements [27], [17], [28],the scalability of exact methods remains limited to prob-lem instances of moderate size. Therefore, in this work,we compute distance-minimizing request-vehicle ridesharingassignments using an Insertion Heuristic [29]. The request-vehicle matching is implemented as follows:

When a new request r = (t, o, d) arrives, the request-vehicle matching algorithm attempts to incorporate the re-quest into the current plan of every vehicle. For a particularvehicle v, we try all possible points to insert pickup and drop-off order into existing plan, such that the relative orderingof the previous orders in the plan remains unchanged.Further, we measure the increase of operational cost foreach plan generated by this process and select the plan (andthe corresponding vehicle) that minimizes the increase inoperational cost and at the same time satisfies the servicediscomfort constraints. The maximum discomfort thresholdqmax is chosen such that, if no other suitable ridesharingmatch is found, the request can always be served with delaysmaller than qmax using a vehicle dispatched from the nearestsystem station. For the pseudo-code of the request-vehiclematching method, see Algorithm 1.

In order to evaluate the operational cost and servicediscomfort associated with a particular plan, one needs to

Algorithm 1: Finding a vehicle and a plan to serverequest r using insertion heuristic.

1 On arrival of new request r2 for v ∈ V do3 let πv be the current plan of vehicle v;4 let l be the length of plan pv;5 for i ∈ 1, . . . , l + 1 do6 for j ∈ i+ 1, . . . , l + 2 do7 π′ ← insert pick-up(r) order before

position i in plan πv;8 πij

v ← insert drop-off(r) orderbefore position j in plan π′;

9 v∗, i∗, j∗ ← argminv,i,j

sv(πi,jv )− sv(πv) subj. to

πi,jv is valid andqr(π

ijv ) ≤ qmax ∀ req. r served by plan πij

v ;

10 request r is assigned to vehicle v∗;11 vehicle v∗ follows plan pi

∗j∗

v∗ ;

estimate the travel time of the vehicle from one order inthe plan (e.g., from pickup position of one request) to thesubsequent order in the plan (e.g., the drop-off position ofsome other request). Notice that the number of evaluationof travel time estimate can be up to the order of O(m · l3).The fleet size in our case study will be m ≈ 50 000 andthe average length of the plan will be l ≈ 4 resultinghundreds of thousands of evaluations of the travel timeestimate within single request assignment procedure. In orderto maintain computational tractability, instead of planing thefastest route on the road network, we approximate the traveltime between two locations on the map with a linear modelbased on the Euclidean distance between the two points. Themodel is calibrated to minimize the difference between theestimate and the duration of the fastest route in the roadnetwork. Since the road network travel time may be longerthan the estimate, a plan that satisfies discomfort constraintscomputed using estimate may violate the constraint whenevaluated using road network travel time. Nevertheless, inour experiments, we observed that the average road networktravel delay is significantly lower than the maximum delayconstraint.

D. Simulation

The scenarios were simulated in multi-agent transportationsimulation framework AgentPolis1. AgentPolis is a large-scale multi-agent discrete-event simulation written in Java.The simulation environment consists of a) road networkthat is in turn composed of nodes (crossroads) connectedby edges (road segments), b) stations in which on-demandvehicles park, c) on-demand vehicle agents, and d) passengeragents. In Figure 2, we show the city of Prague simulated inAgentPolis.

1https://github.com/aicenter/agentpolis

Video: https://sum.fel.cvut.cz/itsc2018/

Fig. 2. AgentPolis visualization of the traffic in Prague at 07:00.

The topology of the road network is obtained from Open-StreetMap (OSM), resulting in a road network consisting of158 674 edges and 63 995 nodes. The speed limit for eachroad segment was also taken from OpenStreetMap data andmissing entries were generated according to following rulesbased on the local legislation: highway: 130 km/h, livingstreet: 20 km/h, otherwise: 50 km/h.

During simulation initialization, we create the vehiclesrepresenting the on-demand fleet and assign them to sta-tions. For each travel request, at the request announcementtime, we create a passenger agent. The passenger is thenpicked up by the assigned on-demand vehicle, driven to thedesired location, dropped off and finally released from thesimulation. The vehicle to serve the passenger is selectedusing the request-vehicle matching procedure described inSection III-C. Note that each passenger can be either matchedto one of the empty vehicles parked in a station or to a non-idle vehicle that is already on its way to serve previouslyassigned requests. After the passenger has been dropped off,the vehicle continues executing its plan. In the case the planof the vehicle becomes empty, the vehicle returns to thenearest system station.

In this paper, we analyze the system during the morningpeak, i.e., during the period between 7:00 and 8:00. To avoidthe “cold start” artifacts, the simulation begins at 6:30, but forsubsequent analysis, we only use the data generated between7:00 and 8:00.

IV. RESULTS

In this section, we report on the results of our simulationanalysis. We run the following three scenarios:

1) Present situation scenario: Each travel request is real-ized by a private vehicle.

2) MoD scenario: Travel demands is served by the MoDsystem.

3) MoD with ridesharing scenario: Travel demand isserved by the MoD system with ridesharing. Request-vehicle matching uses maximum travel delay qmax =10min.

Present MoD MoD with ridesharingTotal veh. dist. traveled (km) 940 645 1 586 495 560 875

Avg. dist. traveled/vehicle (km) 18.1 30.5 10.8Avg. density (veh/km) 0.0080 0.0101 0.0052Congested segments 14 55 4

Heavily loaded segments 208 551 35

TABLE ICOMPARISON BETWEEN THE THREE CONSIDERED SCENARIOS.

CONGESTED SEGMENTS ARE SEGMENTS ON WHICH TRAFFIC DENSITY IS

ABOVE CRITICAL DENSITY, HEAVILY LOADED SEGMENTS ARE

SEGMENTS WITH DENSITY ABOVE 50% OF THE CRITICAL DENSITY.

Figure 3 shows the distribution of the traffic density overthe road network for the three compared scenarios. We cansee that when the transportation demand is served by an MoDsystem without ridesharing, the traffic density at most parts ofthe road network increases compared to the present situation.When the MoD system employs ridesharing, however, thetraffic density at most road segments decreases relative toboth the present situation and to the MoD system withoutridesharing.

Figure 4 shows the histogram of travel densities in thethree scenarios. The first row shows the traffic densityhistograms for all edges with non-zero density (used at leastonce in the analyzed time window) while the second rowshows histograms that are “zoomed-in” to the values aroundthe critical density. Again, we can see that MoD system withridesharing is able to serve the current transportation demandusing less road capacity than the private vehicles use todayand than the on-demand vehicles would use if they do notemploy ridesharing.

Table I summarizes the performance of the three evaluatedsystems. It is remarkable that ridesharing can reduce the totalamount of vehicle miles traveled in an MoD system (and thusalso its energy consumption) almost three-fold.

To understand the effectiveness of ridesharing, the vehicleoccupancy is one of the most important indicators. Theoccupancy of each non-idle vehicle (i.e., a vehicle thatis not in a station) was measured during the simulationin one-minute intervals. Figure 5 shows a histogram ofvehicle occupancies measured in time period 7:00 - 8:00.The MoD system with ridesharing has average occupancyof 2.74 passengers per vehicle. This represents a significantimprovement over the MoD system without ridesharing thathas the average occupancy of 0.7 passengers per vehicle.

In order to get better insights into the relationship betweenthe travel discomfort and vehicle occupancy, we simulatedMoD system with ridesharing and travel delay constraintsqmax = 7, 10, 12 and 15 minutes. Figure 6 shows therelation between the maximum delay and the average vehicleoccupation. As expected, the vehicle occupancy can beincreased, and in turn operation cost reduced, if we sacrificethe comfort of passengers.

V. CONCLUSION

In cities, the private vehicle is becoming an unsustainablemode of personal transportation due to its significant parking

and road capacity requirements. Mobility-on-Demand (MoD)systems represent an alternative to transportation by privatevehicles. These systems employ massive vehicle sharing, andthus they can serve existing transportation demand with asmaller highly-utilized fleet and in turn drastically reducethe need for parking capacity. However, studies show thatunallocated trips in such systems would significantly increasevehicular traffic compared to the present state.

A proposed solution to this problem is to employ large-scale ridesharing. The potential of this solution strategyhowever remained unclear.

In this paper, we quantified the potential of ridesharingto reduce vehicular traffic in an MoD system. We analyzedhypothetical scenario of MoD deployment in the city ofPrague and compared performance of three scenarios: a)the current state, where the demand is served by privatevehicles, b) an MoD system without ridesharing and c) anMoD system with ridesharing.

The simulation results demonstrate that the MoD systemswith ridesharing can not only compensate for the trafficgenerated by the unallocated trips within on-demand sys-tems, but that ridesharing can significantly improve the roadnetwork utilization even with respect to the present state.In particular, by employing ridesharing, the average totaltraveled distance was reduced to 35% of the distance traveledin MoD system without ridesharing and to 60% of thedistance traveled by private vehicles in the present state.

In future, we plan to study the applicability of more so-phisticated request-vehicle matching methods to such large-scale scenarios and conduct test with more complex conges-tion models.

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Fig. 3. Comparison of traffic densities over the road network in the three compared scenarios. The darker colors indicates higher traffic density, blackcolor is reserved for the roads that are congested, i.e., the traffic density exceeds the critical density.

Fig. 4. Histogram of traffic densities in the three different scenarios. In the second row, only the bins with traffic density above 50% of critical density(0.04 vehiclem−1) are shown to improve readability. Edges with zero traffic density were discarded from all histograms.

Fig. 5. Vehicle occupancy histogram

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