Analysis of Non-Markovian Batch Service Queue with Second Optional Service Under Transient and Steady State Domain.

Abstract

This paper analyses the transient and steady state behaviour of a non-Markovian batch service queue with second optional service. The transient state probabilities are computed using the probability generating function, Rouche's theorem, and Laplace transform (L.T.) methods. The Tauberian property in the L.T. expressions is used to get steady state probabilities. Also, we obtain various performance measures along with cost optimisation and numerical results are presented by taking special cases of the service times. The results show the standard observation that the Erlang-k type distribution reduces to an exponential distribution when k = 1 and when k takes a large value, it becomes deterministic.