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A survey of queueing systems with strategic timing of arrivals

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Abstract

Consider a population of customers, each of which needs to decide independently when to arrive to a facility that provides a service during a fixed period of time, say a day. This is a common scenario in many service systems such as a bank, lunch at a cafeteria, music concert, flight check-in and many others. High demand for service at a specific time leads to congestion that comes at a cost, for examlple, for waiting, earliness or tardiness. Queueing theory provides tools for the analysis of the waiting times and associated costs. If customers have the option of deciding when to join the queue, they will face a decision dilemma of when to arrive. The level of congestion one suffers from depends on others, behavior and not only that of the individual under consideration. This fact leads customers to make strategic decisions regarding their time of arrival. In addition, multiple decision makers that affect each other’s expected congestion call for noncooperative game-theoretical analysis of this strategic interaction. This common daily scenario has prompted a research stream pioneered by the ?/M/1 model of Glazer and Hassin (Eur J Oper Res 13(2):146–150, 1983) that first characterized an arrival process to a queue as a Nash equilibrium solution of a game. This survey provides an overview of the main results and developments in the literature on queueing systems with strategic timing of arrivals. Another issue is that of social optimality, namely the strategy profile used by customers that optimizes their aggregate utility. In particular, we review results concerning the price of anarchy (PoA), which is the ratio between the socially optimal and the equilibrium utilities.

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Acknowledgements

The authors wish to thank Refael Hassin, Yoni Nazarathy and an anonymous reviewer for their helpful comments. The first author acknowledges the financial support of the Israel Science Foundation, Grant No. 1512/19.

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Authors and Affiliations

  1. Department of Statistics and Data Science and the Center for Rationality, The Hebrew University of Jerusalem and School of Data Science, The Chinese University of Hong Kong, Shenzhen Campus, Hong Kong, China

    Moshe Haviv

  2. Department of Statistics, University of Haifa, Haifa, Israel

    Liron Ravner

  3. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands

    Liron Ravner

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  1. Moshe Haviv
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Correspondence to Liron Ravner.

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Haviv, M., Ravner, L. A survey of queueing systems with strategic timing of arrivals. Queueing Syst 99, 163–198 (2021). https://doi.org/10.1007/s11134-021-09717-8

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