Equilibrium and optimal arrival patterns to a server with opening and closing times

Refael Hassin and Yana Kleiner

IISE Transactions, 2011, vol. 43, issue 3, 164-175

Abstract: This article considers a first-come first-served single-server system with opening and closing times. Service durations are exponentially distributed, and the total number of arrivals is a Poisson random variable. Naturally each customer wishes to minimize his/her waiting time. The process of choosing an arrival time is presented as a (non-cooperative) multi-player game. The overall goal of this work is to find a Nash equilibrium game strategy. It is assumed in the literature that arrivals before the opening time of the system are allowed. In this work the case where early arrivals are forbidden is studied. It turns out that unless the system is very heavily loaded, the equilibrium solution with such a restriction does not reduce the expected waiting time in a significant way. The equilibrium solution is compared with the solution which maximizes social welfare. Finally, it is show that social welfare can be increased in equilibrium by restricting arrivals to certain points of time.

Date: 2011
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DOI: 10.1080/07408171003792449

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