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A queueing model with two classes of retrial customers and paired services

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Abstract

We mathematically investigate a single server system accepting two types of retrial customers and paired service. If upon arrival a customer finds the server busy, it is routed to an infinite capacity orbit queue according to each type. Upon a service completion epoch, if at least one orbit queue is non-empty, the server seeks to find customers from the orbits. If both orbit queues are non-empty, the seeking process will bring to the service area a pair of customers, one from each orbit. If there is only one non-empty, then a single customer from this orbit queue will be brought to the service area. However, if a primary customer arrives during the seeking process it will occupy the server immediately. It is shown that the joint stationary orbit queue length distribution at service completion epochs is determined by solving a Riemann boundary value problem. Stability condition is investigated, while generalizations of the main model are also discussed. A simple numerical example is obtained and yields insight into the behavior of the system.

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Acknowledgments

The author is grateful to the editor and the anonymous referees for the valuable remarks and comments, from which the presentation of the paper has benefited. A part of this work was carried out at INRIA and the MAESTRO Project team, during the tenure of an ERCIM “Alain Bensoussan” Fellowship Program and had received funding by the EU 7th Framework Program (FP7/2007–2013) under Grant Agreement No. 246016.

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  1. Department of Mathematics, University of Patras, 26500, Patras, Greece

    Ioannis Dimitriou

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Dimitriou, I. A queueing model with two classes of retrial customers and paired services. Ann Oper Res 238, 123–143 (2016). https://doi.org/10.1007/s10479-015-2059-2

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