Transient analysis of a finite-capacity queueing model with balking and repair periods

Abstract

A finite-capacity queueing system is considered in which the arrival stream is governed by a Poisson process and the service times are exponentially distributed. The service station is subject to breakdowns: exponential failure-free times are followed by a generally-distributed repair periods during which the processing is suspended. Moreover, the incoming job may resign (balk) from joining the buffer queue due to different reasons. In general we assume that the balking probability equals 0 ≤ d < 1. Applying the memoryless property of exponential distribution, a system of integral equations for the transient queue-size distribution is built, conditioned by the initial buffer state. The solution of the corresponding system written for Laplace transforms is found in the explicit form. The considered queueing model can be efficiently used in the performance evaluation of a telecommunication network node with the implementation of the Active Queue Management mechanism or in the analysis of an unreliable production line in which, to avoid job losses, some of the incoming items are being redirected to other lines.