A model for queues in series

This paper studies the stationary behaviour of a finite space queueing model consisting of r queues in series with multi-server service facilities at each queue. Poisson input and exponential service times have been assumed. The model is suitable for phase-type service as well as service with waiting allowed before the different phases. In the case of single-server queues explicit expressions for certain probability distributions, parameters and a steady-state solution for infinite queueing space have been obtained.