Performance of Batch Service Queue Model with Second Optional Service, Repairable Breakdown and Standby Server.

Abstract

In this paper, we investigate the performance of batch service queue model with second optional service, repairable breakdown and warm standby server. Both primary operating and warm standby servers provide First Essential Service (FES) and Second Optional Service (SOS) to customers, wherein FES is all arriving customers and only some of them may further request the SOS. The service times, failure times and repair times of both primary operating and warm standby server are assumed to follow exponential distributions. We use Runge-Kutta method to obtain the transient state probabilities and matrix-decomposition method to obtain the steady-state probabilities of the model. Also, a cost model is presented to determine the optimal service rates so that the expected cost is minimized. Finally, the effect of the model parameters on the system behaviour is demonstrated through numerical results and discussions.