Threshold policies for controlled retrial queues with heterogeneous servers

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 Neut's 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 Howard's iteration algorithm. Finally, some numerical results will be given in order to illustrate the system dynamics.