A Tandem Queueing System With Renewal Input

Abstract

We consider a tandem qucueing system consisting of two stations in serious. The first station is represented by a single-server queue with renewal input, PH (Phase-type) service time distribution and waiting room. After service at the first station a customer proceeds to the second station that is described by a single-server queue without a buffer. In case a customer completes the service at the first server and meets the second server being busy, it waits until the second server becomes free and then occupies this server immediately. The waiting period is accompanied by blocking the first stage server operation. The service time of a customer by the second server has the Ptf-type distribution. We derive the ergodicity condition and calculate the stationary distribution of the system states. The Laplace-Stielijes transforms of the distribution of the sojourn time at both the stations as well as the whole system are derived. The mean values of these sojourn times are calculated.