Embedded Product-Form Queueing Networks and the Improvement of Performance Bounds for Petri Net Systems

This paper addresses the computation of upper bounds for the steady-state throughput of stochastic Petri net systems with immediate and generally distributed timed transitions. It is achieved through the use of a kind of decomposition of the whole net system. Results are obtained deeply bridging stochastic Petri net theory to untimed Petri net and queueing network theories. Previous results are improved by considering some embedded product-form queueing networks (generated by the support of some left annullers of the incidence matrix of the net). The obtained results for the case of live and bounded free choice systems are of special interest. In this case, the subnets generated by the minimal left annullers of the incidence matrix always have a topology of product-form closed monoclass queueing networks.