A Mean-Value Analysis of Stochastic Petri Net Models of Slotted Rings

In this paper, we analyse Stochastic Petri Net (SPN) models of slotted-ring networks. We show that a simple SPN model of a slotted-ring network, which exhibits a product-form solution, yields similar results to a more detailed SPN model that has to be analysed by numerical means. Furthermore, we demonstrate a Mean-Value Analysis (MVA) approach to calculate efficiently the results for the simple model. This MVA approach allows for the movement of groups of tokens (customers) rather than just individual customers, as traditional MVA schemes for queueing network models do. Also, the MVA allows for non-disjoint place invariants, whereas previous MVA schemes addressed disjoint place invariants only. From the MVAs, it can be concluded that slotted-rings have very attractive performance characteristics, even under overload conditions (there is no ldquothrashingrdquo). Also, we found that the choice of the slot size is a key factor in calibrating slotted-ring systems for optimal performance. Having a fast and reasonably accurate means available to evaluate the performance of slotted-ring systems, such as our proposed MVA, eases this calibration task. The proposed MVA for the product-form SPN models should therefore be regarded as a ldquoquick engineeringrdquo tool.