Use of Flow Equivalent Servers in the Transient Analysis of Product Form Queuing Networks

In this paper we deal with approximate transient analysis of Product Form Queuing Networks. In particular, we exploit the idea of flow equivalence to reduce the size of the model. It is well-known that flow equivalent servers lead to exact steady state solution in many cases. Our goal is to investigate the applicability of flow equivalence to transient analysis. We show that exact results can be obtained even in the transient phase, but the definition of the equivalent server requires the analysis of the whole original network. We propose thus to use approximate aggregate servers whose characterization demands much less computation. Specifically, the characterization corresponds to the steady state equivalent server of the stations that we aim to aggregate and thus can be achieved by analyzing the involved stations in isolation. This way, approximations can be derived for any queuing network, but the precision of the results depends heavily on the topology and on the parameters of the model. We illustrate the approach on numerical examples and briefly discuss a set of criteria to identify the cases when it leads to satisfactory approximation.