Controlled stochastic Petri nets

A new framework for the extension of stochastic Petri nets (SPNs) is introduced. SPNs are extended by elements providing means for a dynamic optimization of performability measures. A new type of transition is defined, offering a feature for specification of controlled switching, called reconfiguration, from one marking of a SPN to another marking. Optional reconfiguration transitions are evaluated in order to optimize a specified reward or cost function. The result of an analysis is provided in the output of a numerical computation, in the form of a graphical presentation of an optimal, marking dependent control strategy and the resulting performability measure when applying the optimal strategy. The extended SPNs are called COSTPNs (Controlled Stochastic Petri Nets). COSTPNs are mapped on EMRMs (Extended Markov Reward Models) for a numerical analysis. Computational analysis is possible with algorithms adopted from Markov decision theory, including transient and stationary optimization. The scope of the paper is to introduce the new control structure for SPNs and to present an algorithm for the mapping of COSTPNs on EMRMs