Transient processing analysis in a finite-buffer queueing model with setup times

Abstract

A finite-buffer queueing model with Poisson arrivals and generally distributed processing times is investigated. Every time when the service station restarts the operation after the idle period, a random-length setup time is needed to achieve full readiness for the work, during which the service process is suspended. A system of integral equations for time-dependent departure process, conditioned by the initial buffer state, is built. The solution of the corresponding system written for double transforms is obtained in a compact form. Hence the mean number of packets completely processed up to fixed time epoch can be easily found. The analytical approach is based on the idea of embedded Markov chain, total probability law and integral equations. The considered queueing system can be successfully used in cellular networks or WSNs modelling, where the setup time corresponds to leaving the sleep mode in energy saving mechanism. Numerical utility of analytical formulae is shown in a network-motivated computational example.