New Trends in Solving Largeness Problem Arising in Petri Net Models

Abstract

This thesis deals with solution techniques for the largeness problem arising during solving Petri net models. Largeness problem is usually overcome using largeness tolerance or largeness avoidance techniques. Since largeness tolerance is performed coriventionally through efficient software tools, we first present a new modelling tool which has a high ability to tolerate largeness. The described tool uses stochastic reward nets (SRNs) as a high level formalism for system modeling. The proposed tool is the first tool that is capable of identifying transition rates of a SRN model to reach a desired performance response by making use of the well known identification techniques. Moreover, it works on PCs with a performance comparable to other tools working on other plateforms. We have shown how we can perform, using this tool, extensive performance analysis of a system modeled by SRNs. A novel tolerance technique, which we have called the Disk Based Segmentation technique (DBS), has also been proposed. This technique has the capability of solving the consequences of the fill-in problem that usually arises in Gauss elimination (GE) procedure. We show the merits of the DBS technique through extensive monitoring of its performance with respect to time and space. It has been shown, by varying the number of vertical segments, that we can reach a high percentage of reduction in required memory as compared to that needed by GE, with just only a small increase in solution time. A new approach has been presented for modeling DEDS. The proposed model consists of two main networks, which are coupled through logical interfaces. The first net represents the SRN for the part of the system that we are interested in evaluating its performance measures. The second net is needed to feed the first net by the required tokens. The two networks and the corresponding interfaces, represented by SRN's, can then be used for performance evaluation of the overall model. With this approach, the largeness problem can then be avoided. Additionally, the system designer can, by means c.;f this approach, avoid several problems that have been encountered in the literature such as: estimation of SRN parameters,