Calculating light traffic limits for sojourn times in open markovian queueing systems
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Stochastic Models
- Vol. 9 (2) , 213-231
- https://doi.org/10.1080/15326349308807263
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 inversionKeywords
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