Steady state analysis of system size-based balking in <i>M</i>/<i>M<SUP align="right">b</SUP></i>/1 queue

Abstract

In this paper we consider a single server Poisson queue where customers are served in batches of fixed size. The inter arrival time and the service time are considered to be exponentially distributed. The customers upon arrival may decide to join the system or not to join the system by observing the system length. They may join or balk the system with certain probability. Using probability generating function method we obtain the closed form expression for steady state queue length distribution, expected system (queue) length and expected waiting time of a customer in the system (queue). Finally, several numerical results are discussed in the form of table and graphs to explore the sensitivity of system parameters on key performance measures.