M/G/\(\infty\) tandem queues (Q799040)

Another contribution to the currently fashionable topic of networks of service systems. The subsystems are in this case in series and each node is endowed with an infinite number of parallel service channels. The input to the total system is Poisson and the service times at each node have a common distribution which may be different from node to node. A neat analysis yields the joint stationary distribution of the numbers of customers at the various nodes when a particular customer arrives there on his way through the system. It is interesting to speculate how far the analysis might go with finite (greater than one) numbers of channels at the nodes.