Relations between the prearrival and postdeparture state probabilities and the fcfs waiting time distribution in theEk/G/s queue

We generalize a theorem by Burke concerning the relations between the prearrival and the postdeparture state probabilities and we establish the relation of the postdeparture probabilities and the FCFS waiting time distribution in the Ek/G/s queue. Based on these results, an exact probabilistic method for the explicit evaluation of the stationary FCFS waiting time distribution of the Ek/G/s queue is offered. By exploiting previous analytic results of the authors, this method is applied to the general Coxian class of service time distributions with rational Laplace transform and leads to closed form expressions involving linear combinations of a finite number of exponential terms. Finally some computational results are presented.