Abstract
In this paper we investigate the applicability of flow equivalence to transient analysis with the specific aim of reducing the computational complexity of the solution of complex queuing networks. It is well-known that flow equivalent servers lead to exact steady state solution in many cases, and specifically when applied for the steady-state analysis of Product Form Queuing Networks (PFQN). We show that exact results can be obtained even in the transient phase of the study of PFQNs, 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. To identify the cases in which the approach is likely to provide acceptable results, structural and behavioral criteria are proposed that are computationally inexpensive and that can be preliminarily applied to a queuing network before starting its analysis. We motivate our findings with the study of several small models, but we subsequently show the relevance of our methodology by applying it to a web service case study derived from the literature. Results are computed to assess the effectiveness of possible design choices and the impact of certain reconfiguration strategies on the possibility of satisfying possible Service Level Agreements.