Expected number analysis of a two-server queueing network subject to inter-stage inspection and rework

In this paper, an attempt has been made to incorporate the concept of rework in the probabilistic analysis of queueing systems. The paper provides an integrated framework to consider servicing, inspection and rework activities simultaneously in two-stage queueing systems. The purpose of this paper is to analyse some of the transient-state characteristics of a two-server queueing system subject to an initial buffer of finite capacity, inter-stage inspection and rework. A stochastic model is developed to analyze the system and explicit analytical expressions for some of the system characteristics have been obtained using the state-space method and regeneration point technique. All the random variables involved in the analysis are assumed to be arbitrary except for the arrival time distribution to the initial buffer which is assumed to follow exponential distribution.