On Total Sojourn Time in Acyclic Jackson Networks

Abstract
In this paper, we compute the mean of the equilibrium (steady-state) total sojourn time distribution for the important class of infinite capacity acyclic Jackson networks with a single server at each node. In addition, for those acyclic Jackson networks with a 'tree-like' structure, we derive the Laplace transform of the equilibrium total sojourn time distribution and then give a simple recursive procedure for computing the higher moments of the distribution. Such basic results should prove helpful in testing procedures for simulation output analysis of infinite capacity open networks of queues.

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