Sojourn Times in Queueing Networks

We consider a queueing network with types of customers. Poisson arrivals, type dependent routing and state dependent service. A number of stochastic aspects relating to sojourn times are investigated. Included are limiting state distributions imbedded at customer move times, mean sojourn times, and sojourn time distributions along overtake-free paths. It is shown that Reich's results extend to overtake-free paths yielding limiting sojourn time distributions which correspond to the sum of exponential independent stages of sojourn in individual nodes. The analysis is bused solely on considerations of population distributions through conditioning on customers' itineraries in the network.