Optimal decisions in retrial queueing systems

Retrial queues are important stochastic models for many telecommunication systems. In order to construct competitive networks it is necessary to investigate problems related to optimal control of queueing systems. This paper considers K -server retrial systems with Markovian arrival process, heterogeneous service time distributions of general phase-type and exponentially distributed retrial times. It is shown that the optimal policy which minimizes the mean number of customers in the system is of a threshold type with threshold levels depending on the states of the arrival, retrial and service processes. Based on the Howard’s iteration algorithm a numerical procedure for an optimal control is proposed. Finally, some numerical results are given to illustrate the system’s dynamics.