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International Conference on Web and Internet Economics

WINE 2019: Web and Internet Economics pp 129–141Cite as

Mix and Match: Markov Chains and Mixing Times for Matching in Rideshare

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11920))

Abstract

Rideshare platforms such as Uber and Lyft dynamically dispatch drivers to match riders’ requests. We model the dispatching process in rideshare as a Markov chain that takes into account the geographic mobility of both drivers and riders over time. Prior work explores dispatch policies in the limit of such Markov chains; we characterize when this limit assumption is valid, under a variety of natural dispatch policies. We give explicit bounds on convergence in general, and exact (including constants) convergence rates for special cases. Then, on simulated and real transit data, we show that our bounds characterize convergence rates—even when the necessary theoretical assumptions are relaxed. Additionally these policies compare well against a standard reinforcement learning algorithm which optimizes for profit without any convergence properties.

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Notes

  1. 1.

    We have \(\sum _{r \in \mathcal {R}} p_r \le 1\). Thus, with probability \(1-\sum _{r \in \mathcal {R}} p_r\), there is no request in any given time.

  2. 2.

    The choice of \(u_\sigma \) can be random since \(\sigma \) can be a randomized policy.

  3. 3.

    It is not critical for our purposes, but the experiments use New York city and road-distance is measured in Manhattan distance.

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Acknowledgements

John Dickerson and Michael Curry were supported in part by NSF CAREER Award IIS-1846237 and DARPA SI3-CMD Award S4761. Aravind Srinivasan, Karthik Abinav Sankararaman and Pan Xu were supported in part by NSF CNS-1010789, CCF-1422569 and CCF-1749864, and by research awards from Adobe, Amazon and Google. Yuhao Wan was supported via an REU grant, NSF CCF-1852352, and was advised by John Dickerson. John Dickerson and Aravind Srinivasan were both supported by a gift from Google and a seed grant from the Maryland Transportation Institute (MTI). Work done when Karthik was at the University of Maryland, College Park.

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Authors and Affiliations

  1. University of Maryland, College Park, MD, USA

    Michael Curry, John P. Dickerson, Karthik Abinav Sankararaman, Aravind Srinivasan, Yuhao Wan & Pan Xu

  2. Facebook, Inc., Menlo Park, CA, USA

    Karthik Abinav Sankararaman

  3. University of Washington, Seattle, WA, USA

    Yuhao Wan

  4. New Jersey Institute of Technology, Newark, NJ, USA

    Pan Xu

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  1. Michael Curry
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  3. Karthik Abinav Sankararaman
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  4. Aravind Srinivasan
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  5. Yuhao Wan
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  6. Pan Xu
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Corresponding author

Correspondence to Pan Xu .

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Editors and Affiliations

  1. University of Patras, Rio, Greece

    Ioannis Caragiannis

  2. Google Research New York, New York, NY, USA

    Vahab Mirrokni

  3. The University of Texas System, Austin, TX, USA

    Evdokia Nikolova

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Curry, M., Dickerson, J.P., Sankararaman, K.A., Srinivasan, A., Wan, Y., Xu, P. (2019). Mix and Match: Markov Chains and Mixing Times for Matching in Rideshare. In: Caragiannis, I., Mirrokni, V., Nikolova, E. (eds) Web and Internet Economics. WINE 2019. Lecture Notes in Computer Science(), vol 11920. Springer, Cham. https://doi.org/10.1007/978-3-030-35389-6_10

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  • DOI: https://doi.org/10.1007/978-3-030-35389-6_10

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  • Online ISBN: 978-3-030-35389-6

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