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Real-time Approximate Routing for Smart Transit Systems

Published:04 June 2021Publication History
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Abstract

We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its fleet of cars as a feeder to connect passengers to its high-capacity fleet, which operates on fixed routes. Our goal is to find the optimal set of (bus) routes and corresponding frequencies to maximize the social welfare of the system in a given time window. This generalizes the Line Planning Problem, a widely studied topic in the transportation literature, for which existing solutions are either heuristic (with no performance guarantees), or require extensive computation time (and hence are impractical for real-time use). To this end, we develop a 1-1/e-ε approximation algorithm for the Real-Time Line Planning Problem, using ideas from randomized rounding and the Generalized Assignment Problem. Our guarantee holds under two assumptions: (i) no inter-bus transfers and (ii) access to a pre-specified set of feasible bus lines. We moreover show that these two assumptions are crucial by proving that, if either assumption is relaxed, the łineplanningproblem does not admit any constant-factor approximation. Finally, we demonstrate the practicality of our algorithm via numerical experiments on real-world and synthetic datasets, in which we show that, given a fixed time budget, our algorithm outperforms Integer Linear Programming-based exact methods.

References

  1. Javier Alonso-Mora, Samitha Samaranayake, Alex Wallar, Emilio Frazzoli, and Daniela Rus. 2017. On-demand highcapacity ride-sharing via dynamic trip-vehicle assignment. Proceedings of the National Academy of Sciences 114, 3 (2017), 462--467.Google ScholarGoogle ScholarCross RefCross Ref
  2. Siddhartha Banerjee, Daniel Freund, and Thodoris Lykouris. 2016. Pricing and optimization in shared vehicle systems: An approximation framework. arXiv preprint arXiv:1608.06819 (2016).Google ScholarGoogle Scholar
  3. Siddhartha Banerjee, Yash Kanoria, and Pengyu Qian. 2018. State dependent control of closed queueing networks. In ACM SIGMETRICS '18.Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Alexandre Barra, Luis Carvalho, Nicolas Teypaz, Van-Dat Cung, and Ronaldo Balassiano. 2007. Solving the transit network design problem with constraint programming.Google ScholarGoogle Scholar
  5. Dimitri P Bertsekas. 1991. Linear network optimization: algorithms and codes. MIT press.Google ScholarGoogle Scholar
  6. Robert G Bland, Donald Goldfarb, and Michael J Todd. 1981. The ellipsoid method: A survey. Operations research 29, 6 (1981), 1039--1091.Google ScholarGoogle Scholar
  7. Geoff Boeing. 2017. OSMnx: A Python package to work with graph-theoretic OpenStreetMap street networks. Journal of Open Source Software 2, 12 (2017).Google ScholarGoogle ScholarCross RefCross Ref
  8. Ralf Borndörfer and Marika Karbstein. 2012. A direct connection approach to integrated line planning and passenger routing. In 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.Google ScholarGoogle Scholar
  9. Ralf Borndörfer, Martin Grötschel, and Marc E. Pfetsch. 2007. A Column-Generation Approach to Line Planning in Public Transport. Transportation Science 41, 1 (2007), 123--132.Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Anton Braverman, Jim G Dai, Xin Liu, and Lei Ying. 2019. Empty-car routing in ridesharing systems. Operations Research 67, 5 (2019), 1437--1452.Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Robert Carr and Santosh Vempala. 2000. Randomized metarounding. In Proceedings of the thirty-second annual ACM symposium on Theory of computing. 58--62.Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Avishai Ceder and Nigel H.M. Wilson. 1986. Bus network design. Transportation Research Part B: Methodological 20, 4 (1986), 331 -- 344.Google ScholarGoogle ScholarCross RefCross Ref
  13. Partha Chakroborty and Tathagat Wivedi. 2002. Optimal Route Network Design for Transit Systems Using Genetic Algorithms. Engineering Optimization 34, 1 (2002), 83--100.Google ScholarGoogle ScholarCross RefCross Ref
  14. Chandra Chekuri and Martin Pal. 2005. A recursive greedy algorithm for walks in directed graphs. In 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05). IEEE, 245--253.Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Guy Desaulniers, Jacques Desrosiers, and Marius M Solomon. 2006. Column generation. Vol. 5. Springer Science & Business Media.Google ScholarGoogle Scholar
  16. D. Dubois, G. Bel, and M. Llibre. 1979. A Set of Methods in Transportation Network Synthesis and Analysis. The Journal of the Operational Research Society 30, 9 (1979), 797--808.Google ScholarGoogle ScholarCross RefCross Ref
  17. T. Erlebach and F.C.R. Spieksma. 2003. Interval selection: applications, algorithms, and lower bounds. Journal of Algorithms 46, 1 (Jan. 2003), 27--53. https://doi.org/10.1016/S0196--6774(02)00291--2Google ScholarGoogle ScholarCross RefCross Ref
  18. Wei Fan and Randy B. Machemehl. 2006. Using a Simulated Annealing Algorithm to Solve the Transit Route Network Design Problem. Journal of Transportation Engineering 132, 2 (2006), 122--132.Google ScholarGoogle ScholarCross RefCross Ref
  19. Reza Zanjirani Farahani, Elnaz Miandoabchi, Wai Yuen Szeto, and Hannaneh Rashidi. 2013. A review of urban transportation network design problems. European Journal of Operational Research 229, 2 (2013), 281--302.Google ScholarGoogle ScholarCross RefCross Ref
  20. Emma G. Fitzsimmons. 2016. Surge in Ridership Pushes New York Subway to Limit. The New York Times (2016).Google ScholarGoogle Scholar
  21. Lisa Fleischer, Michel X Goemans, Vahab S Mirrokni, and Maxim Sviridenko. 2011. Tight approximation algorithms for maximum separable assignment problems. Mathematics of Operations Research 36, 3 (2011), 416--431.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Philine Gattermann, Jonas Harbering, and Anita Schöbel. 2017. Line pool generation. Public Transport 9, 1--2 (2017), 7--32.Google ScholarGoogle ScholarCross RefCross Ref
  23. Valérie Guihaire and Jin-Kao Hao. 2008. Transit network design and scheduling: A global review. Transportation Research Part A: Policy and Practice 42, 10 (2008), 1251--1273.Google ScholarGoogle ScholarCross RefCross Ref
  24. LLC Gurobi Optimization. 2021. Gurobi Optimizer Reference Manual. http://www.gurobi.comGoogle ScholarGoogle Scholar
  25. AJ Hawkins. 2017. Lyft Shuttle mimics mass transit with fixed routes and fares. The Verge (2017). https://www.theverge.com/2017/3/29/15111492/lyft-shuttle-fixed-route-fare-sf-chicagoGoogle ScholarGoogle Scholar
  26. Doug Johnson. 2020. Microtransit Gives City Agencies a Lift During the Pandemic. Wired (2020). https://www.wired.com/story/microtransit-gives-city-agencies-a-lift-during-the-pandemic/Google ScholarGoogle Scholar
  27. Christos Kalaitzis, Aleksander Madry, Alantha Newman, Luká? Polácek, and Ola Svensson. 2015. On the configuration LP for maximum budgeted allocation. Mathematical Programming 154, 1--2, 427--462.Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Yash Kanoria and Pengyu Qian. 2019. Near optimal control of a ride-hailing platform via mirror backpressure. arXiv preprint arXiv:1903.02764 (2019).Google ScholarGoogle Scholar
  29. Tai-Yu Ma. 2017. On-demand dynamic Bi-multi-modal ride-sharing using optimal passenger-vehicle assignments. In 2017 IEEE International Conference on Environment and Electrical Engineering and 2017 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I & CPS Europe). IEEE, 1--5.Google ScholarGoogle ScholarCross RefCross Ref
  30. Tai-Yu Ma, Saeid Rasulkhani, Joseph YJ Chow, and Sylvain Klein. 2019. A dynamic ridesharing dispatch and idle vehicle repositioning strategy with integrated transit transfers. Transportation Research Part E: Logistics and Transportation Review 128 (2019), 417--442.Google ScholarGoogle ScholarCross RefCross Ref
  31. Thomas L Magnanti and Richard T Wong. 1984. Network design and transportation planning: Models and algorithms. Transportation science 18, 1 (1984), 1--55.Google ScholarGoogle Scholar
  32. Pasin Manurangsi. 2017. Almost-polynomial ratio ETH-hardness of approximating densest k-subgraph. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing. 954--961.Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Ángel G Marín and Patricia Jaramillo. 2009. Urban rapid transit network design: accelerated Benders decomposition. Annals of Operations Research 169, 1 (2009), 35--53.Google ScholarGoogle ScholarCross RefCross Ref
  34. Karl Nachtigall and Karl Jerosch. 2008. Simultaneous network line planning and traffic assignment. In 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08). Schloss Dagstuhl-Leibniz-Zentrum für Informatik.Google ScholarGoogle Scholar
  35. Jake Offenhartz. 2020. MTA Will End Free Cab Rides For EssentialWorkers, As Overnight Subway Shutdown Continues. Gothamist (2020). https://gothamist.com/news/mta-will-end-free-cab-rides-essential-workers-overnight-subwayshutdown-continuesGoogle ScholarGoogle Scholar
  36. Uwe Pape, Yean-Suk Reinecke, and Erwin Reinecke. 1995. Line network planning. In Computer-Aided Transit Scheduling. Springer, 1--7.Google ScholarGoogle Scholar
  37. Paolo Santi, Giovanni Resta, Michael Szell, Stanislav Sobolevsky, Steven H. Strogatz, and Carlo Ratti. 2014. Quantifying the benefits of vehicle pooling with shareability networks. Proceedings of the National Academy of Sciences 111, 37 (2014), 13290--13294.Google ScholarGoogle ScholarCross RefCross Ref
  38. Thibault Séjourné, Samitha Samaranayake, and Siddhartha Banerjee. 2018. The price of fragmentation in mobility-ondemand services. Proceedings of the ACM on Measurement and Analysis of Computing Systems 2, 2 (2018), 1--26.Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. Lionel Adrian Silman, Zeev Barzily, and Ury Passy. 1974. Planning the route system for urban buses. Computers & operations research 1, 2 (1974), 201--211.Google ScholarGoogle Scholar
  40. Mitja Stiglic, Niels Agatz, Martin Savelsbergh, and Mirko Gradisar. 2018. Enhancing urban mobility: Integrating ride-sharing and public transit. Computers & Operations Research 90 (2018), 12--21.Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Pranshu Verma. 2020. 'We're Desperate': Transit Cuts Felt Deepest in Low-Income Areas . The New York Times (2020).Google ScholarGoogle Scholar
  42. José Verschae and Andreas Wiese. 2014. On the configuration-LP for scheduling on unrelated machines. Journal of Scheduling 17, 4 (2014), 371--383.Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. Quentin K Wan and Hong K Lo. 2003. A mixed integer formulation for multiple-route transit network design. Journal of Mathematical Modelling and Algorithms 2, 4 (2003), 299--308.Google ScholarGoogle ScholarCross RefCross Ref
  44. Laurence A. Wolsey. 1982. Maximising Real-Valued Submodular Functions: Primal and Dual Heuristics for Location Problems. Mathematics of Operations Research 7, 3 (1982), 410--425.Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. Fang Zhao and Ike Ubaka. 2004. Transit network optimization-minimizing transfers and optimizing route directness. Journal of Public Transportation 7, 1 (2004), 4.Google ScholarGoogle ScholarCross RefCross Ref
  46. Fang Zhao and Xiaogang Zeng. 2006. Simulated annealing--genetic algorithm for transit network optimization. Journal of Computing in Civil Engineering 20, 1 (2006), 57--68.Google ScholarGoogle ScholarCross RefCross Ref

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