Telecommunication Systems 6(1996)203-227 203 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 ana-lysed by numerical means. Furthermore, we demonstrate a Mean-Value Analysis (MVA) approach to calculate fficiently the results for the simple model. This MVA approach allows for the movement of groups of tokens (customers) rather than just in-dividual customers, as traditional MVA schemes for queueing network models do. Also, the MVA allows for non-disjoint place invariants, whereas previous MVA schemes ad-dressed isjoint 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 and reason-ably accurate means available to evaluate the performance ofslotted-ring systems, uch as our proposed MVA, eases this calibration task. The proposed MVA for the product-form SPN models hould therefore be regarded as a "quick engineering " tool. 1