Equilibrium joining probabilities in observable queues with general service and setup times

Feng Zhang; Jinting Wang; Bin Liu

doi:10.3934/jimo.2013.9.901

Article Contents

2013, Volume 9, Issue 4: 901-917. Doi: 10.3934/jimo.2013.9.901

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Equilibrium joining probabilities in observable queues with general service and setup times

1.
Department of Mathematics, Beijing Jiaotong University, 100044 Beijing
2.
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506

Received: September 30, 2012

Revised: February 28, 2013

Published: September 2013

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Abstract

This paper analyzes an M/G/1 queue with general setup times from an economical point of view. In such a queue whenever the system becomes empty, the server is turned off. A new customer's arrival will turn the server on after a setup period. Upon arrival, the customers decide whether to join or balk the queue based on observation of the queue length and the status of the server, along with the reward-cost structure of the system. For the observable and almost observable cases, the equilibrium joining strategies of customers who wish to maximize their expected net benefit are obtained. Two numerical examples are presented to illustrate the equilibrium joining probabilities for these cases under some specific distribution functions of service times and setup times.

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Mathematics Subject Classification: Primary: 60K25; Secondary: 90B22.

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