On a Two-Stage Birth and Death Queueing Process

A sequential two-stage service system with a single server at each stage and finite waiting space in both stages is considered. If the second stage is full, upon a service completion in stage 1, then the customer is unable to emerge from the first stage channel and this channel is blocked. An additional feature of the model is the provision of state-dependent arrival and service rates. The state probabilities p_ij and all moments of the waiting time of a customer in stage 1 and in the whole system are obtained. Finally, various characteristics of state-dependent tandem systems are evaluated and conclusions are drawn from numerical calculations.