Finite Queueing Model with Multitask Servers and Blocking

Abstract

This paper deals with a Markovian queueing system having a multi-task service counters and finite queue in front of each counter. The total service of a customer is completed in three stages provided by two servers at three counters. The first server (S1) can serve the counter I and III alternatively, whereas second server (S2) provides the service at counter II. The server (S1) gives the priority to the customers waiting for stage third for the service at counter III since they are in last phase of service completion. The steady state queue size distribution has been obtained. The expressions for mean number of customers in the system, average queue length and blocking probability have been obtained. Sensitivity analysis has been carried out to study the effect of variation of different parameters.