A Mean-Value Analysis of Slotted-Ring Network Models

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 analyzed 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 nondisjoint 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 "thrashing"). 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 ..