Calculating light traffic limits for sojourn times in open markovian queueing systems

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