Abstract
In this paper, we consider a queue with multiple K job classes, Poisson arrivals, exponentially distributed required service times in which a single processor serves according to the DPS discipline. More precisely, if there are n i class i jobs in the system, i=1,…, K, each class j job receives a fraction α j /∑ i=1 K α i n i of the processor capacity. For this queue, we obtain a system of equations for joint transforms of the sojourn time and the number of jobs. Using this system of equations we find the moments of the sojourn time as a solution of linear simultaneous equations, which solves an open problem.
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