Calculating light traffic limits for sojourn times in open markovian queueing systems
Communications in Statistics Stochastic Models1993Vol. 9(2), pp. 213–231
Abstract
Let be the m thmoment of the sojourn time distribution for some particular customer class in an open queueing system, where λ is the overall arrival rate. We derive closed form expressions, in terms of the basic system data, for the first order light traffic limit, , in the cases where the total arrival process is Poisson, a phase-type renewal process, and a superposition of independent phase-type renewal processes. For certain phase-type renewal processes, the k th order light traffic limit is zero for n≷k. In these cases we derive the kth order limit. The expressions are numerically tractable. The most difficult operation is a matrix inversion
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