Sojourn time approximations in queueing networks with feedback

This paper is motivated by the response-time analysis of distributed information systems, where transactions are handled by a sequence of front-end server and back-end server actions. We study sojourn times in an open queueing network with a single Processor Sharing (PS) node and an arbitrary number of M multi-server First-Come-First-Served (FCFS) nodes. Customers arrive at the PS according to a Poisson process. After departing from the PS node a customer jumps to FCFS node k   with probability pkpk, and departs from the system with probability 1−p1−p, where p=∑k−1Mpk(0