As we sketched out in Appendices A and B, by and large there are two approaches to the performance oriented study of DEDS, namely, the analytical or the simulation-based approaches. The former has as its centerpiece the product-form formula of Jackson-Newell-Gordon and their various extensions (see Appendix A); the latter, simulation languages such as SIMSCRIPT, GPSS, SLAM, SIMAN, and their mathematical formalization, GSMP (see Appendix B). Perturbation Analysis in some sense attempts to combine the advantages of both the theoretical and the simulation approaches. PA is time-domain based. It views a queueing network as a stochastic dynamical system evolving in time and analyzes the sample realization of its state process. To this extent, it is no different from the viewpoint (and, hence, enjoys the same advantages) of the simulation approach to DEDS. However, by observing a sample path (trajectory) of the network trajectory, we use analysis to derive answers to the question: “what” will happen “if’ we repeat the sample path exactly except for a small perturbation of the timing of some event at some time t? The efficiency of our approach lies in the fact that we can answer a multitude of such ”what if“ questions simultaneously, while a single sample path is being observed. Thus, compared with the brute-force simulation study, our approach has a computational advantage of N+1: 1, where N is the number of ”what if“ questions asked (the brute-force simulation method requires one additional simulation experiment for each question asked).
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- Informal Treatment of Infinitesimal Perturbation Analysis
- Springer US
- Chapter Three
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