Tandem Queues with Correlated Service Times and Finite Capacity

This paper studies tandem queues where the ith customer has the same service time, X_i, at each queue and capacity at each queue is finite. The behaviour of the tandem queue is examined in the presence and absence of blocking. For bounded service time distributions, it is already known that provided there is sufficient capacity available to prevent blocking, it is optimal to allocate the capacity uniformly. We show that for some simple service time distributions with support on two points, the throughput can be calculated exactly and that it is always optimal to allocate the capacity as uniformly as possible, even when blocking occurs. These results contrast with those of previous authors that suggest that a ‘reversed-bowl’ allocation of capacity may be optimal when service times are independent from queue to queue.