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Threshold policies for controlled retrial queues with heterogeneous servers. (English) Zbl 1114.90020

Summary: Retrial queues are an important stochastic model for many telecommunication systems. In order to construct competitive networks it is necessary to investigate ways for optimal control. This paper considers \(K\)-server retrial systems with arrivals governed by Neuts’ Markovian arrival process, and heterogeneous service time distributions of general phase-type. We show that the optimal policy which minimizes the number of customers in the system is of a threshold type with threshold levels depending on the states of the arrival and service processes. An algorithm for the numerical evaluation of an optimal control is proposed on the basis of Howar’s iteration algorithm. Finally, some numerical results will be given in order to illustrate the system dynamics.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
93E20 Optimal stochastic control

Software:

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