Path delays in communication networks

A communication network is modelled by a weighted graph. The vertices of the graph represent stations with storage capabilities, while the edges of the graph represent communication channels (or other information processing media). Channel capacity weights are assigned to the edges of the network. The network is assumed to operate in a store-and-forward manner, so that when a channel is busy the messages directed into it are stored at the station, joining there a queue which is governed by a first-come first-served service discipline. Assuming messages, with fixed length, to arrive at random at the network, following the statistics of a Poisson point process, we calculate the statistical characteristics of the message time-delays along a path in a communication network. We solve for the steadystate distributions of the message waiting-times along the path, for the distribution of the overall message delay-time, for the average memory size requirements at the stations, as well as for other statistical characteristics of the message flow and the queueing processes along a communication path.