The max-plus algebra approach in modelling of queueing networks

A class of queueing networks which consist of single-server fork-join nodes with infinite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. We show how the matrix may be calculated from the service time of customers in the general case, and give examples of matrices inherent in particular networks.