Analysis of Markovian Batch Service Queue with Feedback and Second Optional Service.

Abstract

The aim of this paper is to analyze a single server batch service queue model with feedback and second optional service under a transient and steady state environment. The server provides the first essential service (FES) to all customers who arrive at the system and the second optional service (SOS) to those who need it. After completion of FES, if the customer is not satisfied with the service, he may rejoin the queue or may opt for SOS or exit the system with a particular probability. The service times of both FES and SOS follow exponential distribution. We use the probability generating function and the Laplace transform expression to obtain probabilities in the transient state after inverting Laplace transforms into the time domain. Also, we apply the Tauberian property in the Laplace transform expression to get the steady state probabilities. Finally, some performance measures and numerical results are provided.