Multiserver queueing networks and the tandem queue model

Pierre Le Gall
1998 Journal of Applied Mathematics and Stochastic Analysis  
Using a tandem queue model we evaluate the local "endogenous" (internal) queueing delay in single server and multiserver queueing networks. The new concept of the apparent overall 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 the tandem queue (generated by a concentration tree) and the isolated G/G/s queue. The interpolation coefficients depend on the proportion of
more » ... 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 of single server queueing networks, we stress the need to extend the capacities o_._f the buffers, by considering the "worst case" scenario and by using an "equivalent tandem queue" model.
doi:10.1155/s1048953398000318 fatcat:ldclnpgczvfhbozxplo4qd7gxu