ON SOJOURN TIME IN JACKSON NETWORKS OF QUEUES

This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let h, be the Laplace transform of the residual system sojourn time for a customer 'arriving' to node i, 'arrival' meaning external input or internal transfer. The transforms {hi: i = 1,. * , N) are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables { Ti: i = 1, * * , N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.