A recursive methodology for the derivation of the blocking probabilities of tandem queues with finite capacity

In this paper the authors deal with a two-station tandem queuing system incorporating a finite intermediate buffer between the stations. Blocking occurs when a customer is momentarily stopped at the first station owing to a capacity limitation of the second station having been reached. The authors assume general input and exponentially distributed service times. They observe that it is possible to calculate the conditional blocking probabilities (condition on the system state just before an arrival epoch) recursively and give closed-form expressions for them.