Homogeneous Approximations of General Queueing Networks

Product form queueing networks are of special interest because the algorithms for computing their performance statistics are fast. The concept of homogeneity, which arises in the operational analysis of queueing network models, asserts that the product form is exact if each device's on-line service function is the same as would be observed off-line under constant loads (A device's service function gives the mean time between departures conditioned on the queue length). We will show that, corresponding to any given general queueing network, there exist a product-form queueing network of the same topology whose queue length distributions are identical to those of the given network; this suggests that errors in approximations based on product-form models can be confined to parameters estimation. A numerical study compares several practical methods of approximating the service functions from on-line measurements.