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A Model of Rational Retrials in Queues

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  • Shiliang Cui

    (McDonough School of Business, Georgetown University, Washington, District of Columbia 20057)

  • Xuanming Su

    (The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Senthil Veeraraghavan

    (The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

Abstract

Customers often wait in queues before being served. Because waiting is undesirable, customers may come back later (i.e., retry) when the queue is too long. However, retrial attempts can be costly as a result of transportation fees and service delays. This paper introduces a framework for rational retrial decisions in stationary queues. Our approach accommodates retrials in queues by replicating the Naor's model [ Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24.] repeatedly over time periods. Within each period, we study an observable queue in which customers make rational state-dependent decisions to join, balk, or retry in a future period. We focus on a stationary environment where all arrivals, including new and retrying customers, will face the steady-state distribution of the system in equilibrium. Equilibrium analysis on customers’ decision making is necessary, as they choose optimal strategies corresponding to the stationary queueing dynamics that are in turn determined by their decisions. We characterize the equilibria in both stable and overloaded systems. We find the following: (1) Compared with a system without retrials, the additional option to retry can hurt consumer welfare. (2) Compared with the socially optimal decisions, surprisingly, self-interested customers retry insufficiently (they join overly long queues) when the retrial cost is low and retry too often when the retrial cost is high. (3) Self-interested (retrial) customers can generate positive externalities by smoothing workload over time.

Suggested Citation

  • Shiliang Cui & Xuanming Su & Senthil Veeraraghavan, 2019. "A Model of Rational Retrials in Queues," Operations Research, INFORMS, vol. 67(6), pages 1699-1718, November.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:6:p:1699-1718
    DOI: 10.1287/opre.2018.1833
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    1. Erica L. Plambeck & Qiong Wang, 2013. "Implications of Hyperbolic Discounting for Optimal Pricing and Scheduling of Unpleasant Services That Generate Future Benefits," Management Science, INFORMS, vol. 59(8), pages 1927-1946, August.
    2. Baric{s} Ata & Shiri Shneorson, 2006. "Dynamic Control of an M/M/1 Service System with Adjustable Arrival and Service Rates," Management Science, INFORMS, vol. 52(11), pages 1778-1791, November.
    3. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    4. Uri Yechiali, 1971. "On Optimal Balking Rules and Toll Charges in the GI / M /1 Queuing Process," Operations Research, INFORMS, vol. 19(2), pages 349-370, April.
    5. Zeynep Akşin & Barış Ata & Seyed Morteza Emadi & Che-Lin Su, 2013. "Structural Estimation of Callers' Delay Sensitivity in Call Centers," Management Science, INFORMS, vol. 59(12), pages 2727-2746, December.
    6. Bruce L. Miller & A. G. Buckman, 1987. "Cost Allocation and Opportunity Costs," Management Science, INFORMS, vol. 33(5), pages 626-639, May.
    7. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    8. Haim Mendelson & Seungjin Whang, 1990. "Optimal Incentive-Compatible Priority Pricing for the M/M/1 Queue," Operations Research, INFORMS, vol. 38(5), pages 870-883, October.
    9. Francis de Véricourt & Yong-Pin Zhou, 2005. "Managing Response Time in a Call-Routing Problem with Service Failure," Operations Research, INFORMS, vol. 53(6), pages 968-981, December.
    10. Philip M. Morse, 1955. "Stochastic Properties of Waiting Lines," Operations Research, INFORMS, vol. 3(3), pages 255-261, August.
    11. Avishai Mandelbaum & Uri Yechiali, 1983. "Optimal Entering Rules for a Customer with Wait Option at an M/G/1 Queue," Management Science, INFORMS, vol. 29(2), pages 174-187, February.
    12. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    13. Hoffman, Karla L. & Harris, Carl M., 1986. "Estimation of a caller retrial rate for a telephone information system," European Journal of Operational Research, Elsevier, vol. 27(2), pages 207-214, October.
    14. Ali K. Parlaktürk & Sunil Kumar, 2004. "Self-Interested Routing in Queueing Networks," Management Science, INFORMS, vol. 50(7), pages 949-966, July.
    15. Amedeo R. Odoni & Emily Roth, 1983. "An Empirical Investigation of the Transient Behavior of Stationary Queueing Systems," Operations Research, INFORMS, vol. 31(3), pages 432-455, June.
    16. Aguir, M. Salah & Aksin, O. Zeynep & Karaesmen, Fikri & Dallery, Yves, 2008. "On the interaction between retrials and sizing of call centers," European Journal of Operational Research, Elsevier, vol. 191(2), pages 398-408, December.
    17. Gérard P. Cachon & Pnina Feldman, 2011. "Pricing Services Subject to Congestion: Charge Per-Use Fees or Sell Subscriptions?," Manufacturing & Service Operations Management, INFORMS, vol. 13(2), pages 244-260, June.
    18. Mor Armony & Constantinos Maglaras, 2004. "On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design," Operations Research, INFORMS, vol. 52(2), pages 271-292, April.
    19. Luyi Yang & Laurens G. Debo & Varun Gupta, 2019. "Search Among Queues Under Quality Differentiation," Management Science, INFORMS, vol. 65(8), pages 3605-3623, August.
    20. Uri Yechiali, 1972. "Customers' Optimal Joining Rules for the GI/M/s Queue," Management Science, INFORMS, vol. 18(7), pages 434-443, March.
    21. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    22. Parlakturk, Ali & Kumar, Sunil, 2004. "Self-Interested Routing in Queueing Networks," Research Papers 1782r, Stanford University, Graduate School of Business.
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