Equilibrium customer strategies and social–profit maximization in the single-server constant retrial queue

Equilibrium customer strategies and social–profit maximization in the single-server constant retrial queue

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Article ID: iaor201112739
Volume: 58
Issue: 2
Start Page Number: 107
End Page Number: 122
Publication Date: Mar 2011
Journal: Naval Research Logistics (NRL)
Authors: ,
Keywords: service, simulation: applications, game theory
Abstract:

We consider the single-server constant retrial queue with a Poisson arrival process and exponential service and retrial times. This system has not waiting space, so the customers that find the server busy are forced to abandon the system, but they can leave their contact details. Hence, after a service completion, the server seeks for a customer among those that have unsuccessfully applied for service but left their contact details, at a constant retrial rate. We assume that the arriving customers that find the server busy decide whether to leave their contact details or to balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait. We examine the customers' behavior, and we identify the Nash equilibrium joining strategies. We also study the corresponding social and profit maximization problems. We consider separately the observable case where the customers get informed about the number of customers waiting for service and the unobservable case where they do not receive this information. Several extensions of the model are also discussed.

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