Performance Characterization of Two-Server Batch Service Queue With Second Optional Service.

Abstract

In this paper, we analyze the performance of a finite capacity two-server Markovian batch service queueing model with second optional service. The servers provide two kinds of services, the first essential service (FES), which is provided to all incoming customers and the second optional service (SOS) to those who demand it after completing FES. The service times of the two servers are identical and are exponentially distributed. Matrix-decomposition method is used to obtain the steady-state probabilities of the model. Numerical results and discussion are presented to demonstrate the impact of the model parameters on the system behavior. Furthermore, the cost model optimization is developed to determine the optimal service rates using the Quasi-Newton method to minimize the expected cost. Finally, the findings of this work show that the blocking probability is monotonically decreases as finite buffer size increases and approaches its minimum value of zero when finite buffer is sufficiently large.