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Transient analysis of general queueing systems via simulation-based transfer function modeling

This paper is concerned with characterizing the transient behavior of general queueing systems, which is widely known to be notoriously difficult. The objective is to develop a statistical methodology, integrated with extensive offline simulation and preliminary queueing analysis, for the estimation of a small number of transfer function models (TFMs) that quantify the input-output dynamics of a general queueing system. The input here is the time-varying release rate of entities to the system; the time-dependent output performances include the output rate of entities and the mean of the work in process (i.e., number of entities in the system). The resulting TFMs are difference equations, like the discrete approximations of the ordinary differential equations provided by an analytical approach, while possessing the high fidelity of simulation. The proposed method is expected to overcome the shortcomings of the existing transient analysis approaches, i.e., the computational burden of simulation and the lack of fidelity of analytical queueing models.