Output analysis of a single-buffer multiclass queue: FCFS service

Abstract

We consider an infinite capacity buffer where the incoming fluid traffic belongs to K different types modulated by K independent Markovian on-off processes. The kth input process is described by three parameters: (λk, μk, rk), where 1/λk is the mean off time, 1/μk is the mean on time, and rk is the constant peak rate during the on time. The buffer empties the fluid at rate c according to a first come first served (FCFS) discipline. The output process of type k fluid is neither Markovian, nor on-off. We approximate it by an on-off process by defining the process to be off if no fluid of type k is leaving the buffer, and on otherwise. We compute the mean on time τkon and mean off time τkoff. We approximate the peak output rate by a constant rko so as to conserve the fluid. We approximate the output process by the three parameters (λko, μko, rko), where λko = 1/τkoff, and μko = 1/τkon. In this paper we derive methods of computing τkon, τkoff and rko for k = 1, 2,…, K. They are based on the results for the computation of expected reward in a fluid queueing system during a first passage time. We illustrate the methodology by a numerical example. In the last section we conduct a similar output analysis for a standard M/G/1 queue with K types of customers arriving according to independent Poisson processes and requiring independent generally distributed service times, and following a FCFS service discipline. For this case we are able to get analytical results.