Stochastic analysis of a controlled queue with heterogeneous servers and constant retrial rate

In this paper we analyze a controlled retrial queue with several 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 quasi-birth-and-death (QBD) process. It is showed that the optimal control policy is of threshold and monotone type. We give the explicit formula for the approximation to the optimal threshold levels and propose value iteration algorithm for the exact calculation of the levels. The steady-state analysis is performed 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).