Sensitivity analysis of Markov regenerative stochastic Petri nets

Sensitivity analysis, i.e., the analysis of the eflect of small variations in system parameters on the output measures can be studied b y computing the derivatives of the output measures with respect t o the parameter. This paper presents an algorithm for parametric sensitivity analysis of Markov Regenerative Stochastic Petri Nets (MRSPN). MRSPNs are a true generalization of stochastic Petri nets, in that they allow for transitions to have generally distributed firing times (under certain conditions). The expressions for the steady state probabilities of MRSPNs were developed in [5, 71. We extend the steady state analysis and present equations for sensitiuily of the steady state probabilities with respect to an arbitrary system parameter. Sensitivity functions of the performance measures can accordingly be expressed in terms of the sensitivity functions of the steady state probabilities. We present an application of our algorithm b y finding an optimizing parameter for a vacation queue.