Collective Dynamics of Ride Sharing Systems with Pooled Stops: Sustainability and Reliability

Private cars are responsible for 15% of carbon emissions in the European Union. Ride hailing services like taxis could serve the door-to-door mobility demand of private car users with fewer overall vehicles. If the service combines multiple user trips, it might even reduce the distance driven compared to private cars which becomes ecologically sustainable. Such ride sharing services are particularly sustainable when many users share one vehicle. But connecting the trips of all users yields many small detours. These detours reduce if some users walk a short distance to a neighboring stop. When multiple stops are combined, vehicles drive to fewer stops. Such stop pooling promises to make ride sharing even more sustainable. Some ride sharing services already integrate short user walks into their system. But the effects of stop pooling on ride sharing systems are yet to be understood. Methods from theoretical physics like mean-field theory and agent-based modeling enable a systemic analysis of complex ride sharing systems. This thesis demonstrates that ride sharing may be more sustainable when users accept short walks. With stop pooling, users wait shorter for vehicles and drive shorter because of more direct vehicle routes. In consequence, the user travel time decreases on average despite additional walk time at constant fleet size. Put differently, stop pooling allows to reduce the fleet size at constant travel time. This also reduces the distance driven by all vehicles that is proportional to the fleet size when sufficient users share one vehicle. This result is robust in a data-driven model using taxi trip data from Manhattan (New York City, USA) with fluctuating demand over the day. At constant fleet size the travel time fluctuates with the demand and might deviate a lot from the expected average travel time. Such unreliable travel times might deter users from ride sharing. However, stop pooling reduces the travel time, the more the higher the travel time without walking. Consequently, stop pooling also reduces the fluctuations in the travel time. This effect is particularly large when adapting the maximum allowed walk distance to the current demand. In adaptive stop pooling users walk further at higher demand. Then, the travel time in ride sharing is more reliable when users accept short walks. All in all, this thesis contributes to the fundamental understanding of the collective dynamics of ride sharing and the effect of stop pooling at a systemic level while also explaining underlying mechanisms. The results suggest that ride sharing providers and users benefit from integrating adaptive stop pooling into the service. Based on the results, a framework can be established that roughly adjusts fleet size to demand to ensure that the ride sharing service operates sustainably. Even if this fleet size remains constant throughout the day, adaptive stop pooling keeps the travel time reliable.:1. Introduction 1 1.1. Private Cars are Unsustainable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Potentially More Sustainable Ride Sharing Faces Detours . . . . . . . . . . . . . 2 1.3. Less Detours in Ride Sharing with Walking to Pooled Stops . . . . . . . . . . . . 4 1.4. Physics Methods Help Understanding Ride Sharing . . . . . . . . . . . . . . . . . 5 1.5. Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Fundamentals - A Physics Perspective on Ride Sharing 7 2.1. State of Research on Ride Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1. Ride Sharing Systems are Complex . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2. Measuring Efficiency and Sustainability of Ride Sharing Services . . . . . 8 2.1.3. Ride Sharing might be More Sustainable when Users Accept Short Walks 10 2.1.4. Data-Driven Analysis Yields more Detailed Results . . . . . . . . . . . . . 11 2.1.5. Open Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2. Theoretical Physics Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1. What is a Complex System? . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2. Mean-Field Theory Simplifies Complex Systems . . . . . . . . . . . . . . 13 2.2.3. Model Complex Systems Based on Agents, not on Equations . . . . . . . 14 2.2.4. Methods from Statistical Physics to Evaluate Multi-Agent Simulations . . 14 2.2.5. Model Street Networks Using Graph Theory . . . . . . . . . . . . . . . . 20 3. Model for Ride Sharing with Walking to Pooled Stops 25 3.1. Ride Sharing Combines Trips with Similar Directions . . . . . . . . . . . . . . . . 25 3.2. Stop Pooling with Dynamic Stop Locations Maintains Flexibility . . . . . . . . . 26 3.3. Simple Algorithm Assigns Users by Reducing Bus Detour . . . . . . . . . . . . . 28 3.3.1. Standard Ride Sharing Algorithm . . . . . . . . . . . . . . . . . . . . . . 28 3.3.2. Stop Pooling Algorithm at Similar Speed . . . . . . . . . . . . . . . . . . 29 3.4. Basic Setting in Continuous Space . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4.1. Uniform Request Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4.2. Heterogeneous Request Distribution . . . . . . . . . . . . . . . . . . . . . 32 3.5. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5.1. Relative Distance Driven Measures Ecological Sustainability . . . . . . . . 33 3.5.2. Measure Service Quality by Average User Travel Time . . . . . . . . . . . 34 3.5.3. Further Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5.4. Bisection Method to Find Minimal Travel Time with Small Effort . . . . 36 3.6. Model Extensions Yield More Detailed Results . . . . . . . . . . . . . . . . . . . 37 3.6.1. Fine-Grained Street Network Enables Short Walk Distances . . . . . . . . 38 iii Contents 3.6.2. Data-Driven Demand is Heterogeneous . . . . . . . . . . . . . . . . . . . . 39 3.6.3. Explicit Stop Times Ensure Penalty For Each Stop . . . . . . . . . . . . . 41 3.6.4. Imbalanced Demand Requires Rebalancing of Buses . . . . . . . . . . . . 42 3.6.5. More Detailed Assignment Algorithm Uses Constraints . . . . . . . . . . 43 4. Quantifying Sustainability of Ride Sharing 45 4.1. Two Mechanisms Influence Ride Sharing Sustainability . . . . . . . . . . . . . . . 46 4.1.1. Pickup Detours Increase Distance Driven . . . . . . . . . . . . . . . . . . 46 4.1.2. Trip Overlap Reduces Distance Driven . . . . . . . . . . . . . . . . . . . . 47 4.2. Distance Driven Reduces with Bus Occupancy . . . . . . . . . . . . . . . . . . . 48 4.3. Ride Sharing is more Sustainable than Private Cars for Sufficient Load . . . . . . 50 4.4. Result is Robust for more Complex Models . . . . . . . . . . . . . . . . . . . . . 52 4.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5. Ride Sharing Sustainability with Stop Pooling 55 5.1. Ride Sharing Trades Sustainability for Travel Time . . . . . . . . . . . . . . . . . 57 5.2. Stop Pooling is more Sustainable at Same Travel Time . . . . . . . . . . . . . . . 58 5.2.1. Roughly Constant Distance Driven Despite Saved Stops . . . . . . . . . . 58 5.2.2. Stop Pooling Reduces Travel Time . . . . . . . . . . . . . . . . . . . . . . 59 5.2.3. Stop Pooling Breaks The Trade-off Between Sustainability And Travel Time 60 5.3. Higher Stop Pooling Effect for High Loads . . . . . . . . . . . . . . . . . . . . . . 61 5.3.1. Stop Pooling Limits Growth of Best Travel Time . . . . . . . . . . . . . . 62 5.3.2. Stop Pooling Breaks Trade-off for Sufficient Load . . . . . . . . . . . . . . 63 5.4. Robust Effect for Simple Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.5. Robust Effect with More Detailed Model . . . . . . . . . . . . . . . . . . . . . . . 66 5.5.1. Load Quantifies Stop Pooling Sustainability . . . . . . . . . . . . . . . . . 67 5.5.2. Already 1.2 Minutes Walk Time might Save 1 Minute Travel Time . . . . 68 5.5.3. Robust Result for Different Parameters . . . . . . . . . . . . . . . . . . . 69 5.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6. Ride Sharing Reliability with Stop Pooling 71 6.1. Unreliable Standard Ride Sharing with Fluctuating Demand . . . . . . . . . . . . 72 6.2. More Reliable Stop Pooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.3. Robust Effect of Stop Pooling with Limited User Delay . . . . . . . . . . . . . . 77 6.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.5. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7. Discussion 81 7.1. Results and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.1.1. When is Ride Sharing More Sustainable than Private Cars? . . . . . . . . 81 7.1.2. How Does Stop Pooling Influence Sustainability of Ride Sharing? . . . . . 82 7.1.3. How Does Stop Pooling Influence Reliability of Ride Sharing? . . . . . . . 82 7.2. Limitations of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 7.2.1. Simple Algorithms for Ride Sharing and Stop Pooling . . . . . . . . . . . 82 7.2.2. Integrate Adaptive Stop Pooling into Virtual Bus Stops . . . . . . . . . . 83 7.2.3. Distance Driven as Estimator for Ecological Sustainability . . . . . . . . . 83 7.2.4. Deviations from Load Prediction . . . . . . . . . . . . . . . . . . . . . . . 84 7.2.5. Mean-Field Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.2.6. Further Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 A. Appendix 87 A.1. Manhattan Street Network Resembles Grid . . . . . . . . . . . . . . . . . . . . . 87 A.2. Computation Details of Bisection Method . . . . . . . . . . . . . . . . . . . . . . 88 A.3. Average Pickup Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 A.4. Robustness of Ride Sharing Sustainability . . . . . . . . . . . . . . . . . . . . . . 90 A.5. Stop Pooling Saves Stops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 A.6. Stop Pooling Effectively Reduces Load . . . . . . . . . . . . . . . . . . . . . . . . 92 A.7. Example Breaking of Trade-off in Simple Model . . . . . . . . . . . . . . . . . . . 93 A.8. Transition in Best Walk Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 A.9. Maximal Trade-off Shift Increases with Load . . . . . . . . . . . . . . . . . . . . 95 A.10.Rebalancing Buses is more Important with Constraint . . . . . . . . . . . . . . . 97 A.11.Breaking of Trade-off in Complex Model . . . . . . . . . . . . . . . . . . . . . . . 98 A.12.More Stop Pooling at Destinations and High Demand . . . . . . . . . . . . . . . 99 A.13.Roughly Constant Wait and Drive Time in Adaptive Stop Pooling . . . . . . . . 100 A.14.Influence of Capacity Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A.15.Walk Time of Rejected Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Bibliography 101 Acknowledgment 116 Statement of Contributions 11

An Analysis of issues against the adoption of Dynamic Carpooling

Using a private car is a transportation system very common in industrialized countries. However, it causes different problems such as overuse of oil, traffic jams causing earth pollution, health problems and an inefficient use of personal time. One possible solution to these problems is carpooling, i.e. sharing a trip on a private car of a driver with one or more passengers. Carpooling would reduce the number of cars on streets hence providing worldwide environmental, economical and social benefits. The matching of drivers and passengers can be facilitated by information and communication technologies. Typically, a driver inserts on a web-site the availability of empty seats on his/her car for a planned trip and potential passengers can search for trips and contact the drivers. This process is slow and can be appropriate for long trips planned days in advance. We call this static carpooling and we note it is not used frequently by people even if there are already many web-sites offering this service and in fact the only real open challenge is widespread adoption. Dynamic carpooling, on the other hand, takes advantage of the recent and increasing adoption of Internet-connected geo-aware mobile devices for enabling impromptu trip opportunities. Passengers request trips directly on the street and can find a suitable ride in just few minutes. Currently there are no dynamic carpooling systems widely used. Every attempt to create and organize such systems failed. This paper reviews the state of the art of dynamic carpooling. It identifies the most important issues against the adoption of dynamic carpooling systems and the proposed solutions for such issues. It proposes a first input on solving the problem of mass-adopting dynamic carpooling systems.Comment: 10 pages, whitepaper, extracted from B.Sc. thesis "Dycapo: On the creation of an open-source Server and a Protocol for Dynamic Carpooling" (Daniel Graziotin, 2010

Synergistic Interactions of Dynamic Ridesharing and Battery Electric Vehicles Land Use, Transit, and Auto Pricing Policies

It is widely recognized that new vehicle and fuel technology is necessary, but not sufficient, to meet deep greenhouse gas (GHG) reductions goals for both the U.S. and the state of California. Demand management strategies (such as land use, transit, and auto pricing) are also needed to reduce passenger vehicle miles traveled (VMT) and related GHG emissions. In this study, the authors explore how demand management strategies may be combined with new vehicle technology (battery electric vehicles or BEVs) and services (dynamic ridesharing) to enhance VMT and GHG reductions. Owning a BEV or using a dynamic ridesharing service may be more feasible when distances to destinations are made shorter and alternative modes of travel are provided by demand management strategies. To examine potential markets, we use the San Francisco Bay Area activity based travel demand model to simulate business-as-usual, transit oriented development, and auto pricing policies with and without high, medium, and low dynamic ridesharing participation rates and BEV daily driving distance ranges. The results of this study suggest that dynamic ridesharing has the potential to significantly reduce VMT and related GHG emissions, which may be greater than land use and transit policies typically included in Sustainable Community Strategies (under California Senate Bill 375), if travelers are willing pay with both time and money to use the dynamic ridesharing system. However, in general, large synergistic effects between ridesharing and transit oriented development or auto pricing policies were not found in this study. The results of the BEV simulations suggest that TODs may increase the market for BEVs by less than 1% in the Bay Area and that auto pricing policies may increase the market by as much as 7%. However, it is possible that larger changes are possible over time in faster growing regions where development is currently at low density levels (for example, the Central Valley in California). The VMT Fee scenarios show larger increases in the potential market for BEV (as much as 7%). Future research should explore the factors associated with higher dynamic ridesharing and BEV use including individual attributes, characteristics of tours and trips, and time and cost benefits. In addition, the travel effects of dynamic ridesharing systems should be simulated explicitly, including auto ownership, mode choice, destination, and extra VMT to pick up a passenger