Performance analysis of the 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. In this paper we analyse a controlled retrial queue with two exponential heterogeneous servers in which the time between two successive repeated attempts is independent of the number of customers applying for the service. The customers upon arrival are queued in the orbit or enters service area according to the control policy. This system is analyzed as controlled quasibirth- and-death (QBD) process. It is showed that the optimal control policy is of threshold and monotone type. We propose the value iteration algorithm for the calculation of optimal threshold levels and perform the steady-state analysis using matrix-geometric approach. The main performance characteristics are calculated for the system under optimal threshold policy (OTP) and compared with the same characteristics for the model under scheduling threshold policy (STP) and other heuristic policies, e.g. the usage of the Fastest Free Server (FFS) or Random Server Selection (RSS).