Delays in a series of queues: Independent versus identical service times

Series of queues are suitable performance models for a variety of communication network components and access technologies, but the usual assumption of independent service times at different nodes is critical. We consider delays in a series of queues with identical service times at each network node where for each customer the service time at the first node is a random variable and the successive service times are identical to the one at the first node. A recursive scheme for delays is provided and applied to efficient simulation. Average end-to-end delays are compared for independent service times at different nodes and identical service times, respectively. It turns out that in light traffic the delays in case of identical service times are larger than for independent service times by a factor that first increases with increasing traffic intensity up to a maximum value approached in medium traffic after which it decreases quickly and drops down to become significantly smaller than one in heavy traffic. This effect intensifies with increasing number of network nodes and depends, as well as the crossover point from which on identical service times yield smaller delays, on the distribution of the service times at the first node.