A Tandem Network of Queues with Deterministic Service and Intermediate Arrivals

We present a complete analysis of delays for a tandem network of queues with deterministic service and multiple, interfering sources. The model is of a packet-based data collection system consisting of some finite, but arbitrary, number of stations connected in tandem by a unidirectional, asynchronous transmission network. Packets, or, more generally, tasks enter the system at every station, are handed from station to station in store-and-forward fashion, and exit at the downstream end; there are no intermediate departures. The stations are provided with infinite storage, and the lines between them operate concurrently and asynchronously. Intermediate sources are Poisson; the source at the head of the network can be somewhat more general than Poisson. Tasks from each source wait at each station downstream of their point of origin. We calculate the joint steady-state moment-generating functions for these waiting times, provided that the line capacities do not increase in the direction of flow; the solution contains as a special case the steady-state moment-generating function for end-to-end delay for each source.