In: Billington, J.; Diaz, M.; Rozenberg, G.: Lecture Notes in Computer Science, Vol. 1605: Application of Petri Nets to Communication Networks, pages 232-272. Springer-Verlag, 1999.
Abstract: The design of modern telecommunication systems is a complex task since many parameters, mostly of stochastic nature, have to be taken into account in order to achieve desired performance values. Stochastic Petri nets (SPNs) are a well-known modeling and analysis tool for such systems. In addition, the ability to adapt system operations to quickly changing environment or system conditions is of great importance. Therefore, a new framework for the extension of SPNs is presented in this paper which introduces elements providing means for s dynamic optimization of performability measures. A new type of transitions is defined offering a feature for specification of controlled switching, called reconfiguration, from one set of markings of an SPN to another set of markings. In numerical analysis, these optional reconfiguration transitions are evaluated in order to optimize a specified reward or cost function. The result of the analysis is a set of strategies which tell the controller of the system when to fire enabled reconfiguration transitions and when to remain in the current state. The extended SPNs are called SOTPNs (controlled stochastic Petri nets). For the numerical analysis, COSTPNs are mapped on EMRMs (extended Markov reward models). Computational analysis is possible with algorithms adopted fro Markov decision theory, including transient and stationary optimization. This paper introduces the new COSTPN model, discusses the algorithms necessary for the mapping of COSTPNs on EMRMs and shows how COSTPNs can be applied to the modeling and control of a typical telecommunications system, namely a multimedia server. Major emphasis is put on the introduction of new enabling and firing rules for reconfiguring transitions and on illustration of the new modeling approach by means of the multimedia server example.
Keywords: Markov decision theory, dynamic optimization, extended Markov reward model, stochastic Petri nets, telecommunication systems.