Response time for finite heterogeneous nonreliable queueing systems

This paper deals with nonhomogeneous queueing models to describe the performance of finite multiterminal systems subject to random breakdowns. The most important contribution of this paper is to give a closed formula for response time calculation. We use the model described earlier by Almási and Sztrik in [1]. The authors used there a closed formula—without proof—to calculate the response time of the terminals. Here we give a short proof of it. All random variables involved in this work are independent and exponentially distributed. Although the stochastic process describing the systemʹs behaviour is a Markov chain, the number of states becomes very large, and the response time calculation is not trivial in the heterogeneous model.