Equilibrium in Queues Under Unknown Service Times and Service Value

Laurens Debo () and Senthil Veeraraghavan ()
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Laurens Debo: Chicago Booth School of Business, University of Chicago, Chicago, Illinois 60637
Senthil Veeraraghavan: The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104

Operations Research, 2014, vol. 62, issue 1, 38-57

Abstract: In the operations research literature, the queue joining probability is monotonic decreasing in the queue length; the longer the queue, the fewer consumers join. Recent academic and empirical evidence indicates that queue-joining probabilities may not always be decreasing in the queue length. We provide a simple explanation for these nonmonotonic queue-joining strategies by relaxing the informational assumptions in Naor's model. Instead of imposing that the expected service time and service value are common knowledge, we assume that they are unknown to consumers, but positively correlated. Under such informational assumptions, the posterior expected waiting cost and service value increase in the observed queue length. As a consequence, we show that queue-joining equilibria may emerge for which the joining probability increases locally in the queue length. We refer to these as “sputtering equilibria.” We discuss when and why such sputtering equilibria exist for discrete as well as continuously distributed priors on the expected service time (with positively correlated service value).

Keywords: queueing games; threshold policies; nonmonotone queue joining; randomization (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (24)

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