Asymptotic Expansions of the Sojourn Time Distribution Functions of Jobs in Closed, Product-Form Queuing Networks

Striking progress has been made recently in obtaining expressions for the Sojourn Time Distribution Function (STDF) of a job at a c-server, First Come First Serve (FCFS) center in a closed, product form queueing network. These results have more recently been extended, and expressions have been obtained for the joint Distribution Function (DF) of the sojourn times of a job at a sequence of single server, FCFS centers lying on an "overtake free" path. In this paper, asymptotic techniques developed by Mitra and McKenna for the calculation of the partition function of large, product form closed queueing networks, are applied to the sojourn time problem.