Abstract
We consider a time-sharing model with a single server, multiple queues, priorities, and feedback to lower priority queues, which, disregarding the service discipline, is of type M/G/l. In the model, there is a finite or countably infinite number K of queues. Jobs arrive at queue 1 according to a Poisson process. A fraction qk+1 of jobs is appended to queue k + 1 after having received service in queue k; the remainder leaves the system. Feedback may or may not depend on service time. Jobs in queue k have priority over jobs in queue /, when k < I. In [7], Schrage introduces a method to derive the Laplace-Stieltjes transform of the total residence time in queues 1,2,..., j of jobs that ever reach queue j, and Wolff [9] uses the same method to derive the total delay in queues 1,2,..., j in the special case of one overall service time and quantum allocation, both in the nonpreemptive case. In this paper, this method is extended to the preemptive discipline, and analogous results are obtained.
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