Multiserver queueing networks and the tandem queue model

摘要

Using a tandem queue model we evaluate the local “endogenous” (= internal) queueing delay in single server and multiserver queueing networks. The new concept of theapparentoverall upstream queueing delay(as perceived by the downstream network) allows us to analyze the distribution of this local queue by interpolating between the distributions of thetandem queue(generated by aconcentration tree) and the isolatedG/G/squeue. The interpolation coefficients depend on the proportion of “premature departures”, typically interfering in the upstream stage and leaving the considered path without being offered to the considered local queue. On the other hand, local “exogenous” arrivals (from outside the network) require the introduction of the “interference delay” concept. Finally, in the case ofsingle serverqueueing networks, we stress the need toextend the capacities of the buffers, by considering the “worst case” scenario and by using an “equivalent tandem queue” model.