Approximate analysis of queues in series with phase-type service times and blocking

Queues in series with phase-type service times and finite queue capacities are considered. Servers may get blocked due to the limited space in queues. An approximation method is developed to compute the steady state probability distributions of the number of units in each queue. Three cases are considered: the first queue has an infinite capacity; the first queue has a finite capacity; and the first server is always busy. The method decomposes the system of tandem queues into individual queues with revised arrival and service processes and with queue capacities. Then, each queue is analyzed in isolation within an iterative scheme which relates these queues to each other. The approximation method is computationally efficient and it appears to have an acceptable error level.