Performance of a Single Server Batch Queueing Model with Second Optional Service under Transient and Steady State Domain.

Abstract

The aim of this paper is to investigate the performance of a single server batch queueing model with second optional service under transient and steady state domain. It is assumed that the customers arrive in groups as per compound Poisson process and the server gives two types of services, First Essential Service (FES), which is mandatory for all arriving customers and Second Optional Service (SOS), which is given to some customers those who request it. Both FES and SOS are provided in batches of maximum 𝑏 capacity. The transient and steady state probabilities of the model are obtained by using probability generating function and Laplace transform techniques. Finally, some numerical examples are presented to study the effect of the parameters on the system performance measures.