Flow time distributions in aK classM/G/1 priority feedback queue

In this paper, aK classM/G/1 queueing system with feedback is examined. Each arrival requires at least one, and possibly up toK service phases. A customer is said to be in classk if it is waiting for or receiving itskth phase of service. When a customer finishes its phasek ≤K service, it either leaves the system with probabilityp _k, or it instantaneously reenters the system as a classk + 1 customer with probability (1 −p _k). It is assumed thatp _k = 1. Service is non-preemptive and FCFS within a specified priority ordering of the customer classes. Level crossing analysis of queues and delay cycle results are used to derive the Laplace-Stieltjes Transform (LST) for the PDF of the sojourn time in classes 1,…,k;k ≤K.