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Structured Solution of Asynchronously Communicating Stochastic Modules
, 1997
"... Asynchronously Communicating Stochastic Modules (SAM) are Petri nets that can be seen as a set of modules that communicate through buffers, so they are not (yet another) Petri net subclass, but they complement a net with a structured view. This paper considers the problem of exploiting the compositi ..."
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Asynchronously Communicating Stochastic Modules (SAM) are Petri nets that can be seen as a set of modules that communicate through buffers, so they are not (yet another) Petri net subclass, but they complement a net with a structured view. This paper considers the problem of exploiting the compositionality of the view to generate the state space and to find the steadystate probabilities of a stochastic extension of SAM in a netdriven, efficient way. Essentially, we give an expression of an auxiliary matrix, G, which is a supermatrix of the infinitesimal generator of a SAM. G is a tensor algebra expression of matrices of the size of the components for which it is possible to numerically solve the characteristic steadystate solution equation \Delta G = 0, without the need to explicitly compute G. Therefore, we obtain a method that computes the steadystate solution of a SAM without ever explicitly computing and storing its infinitesimal generator, and therefore without computing and ...
Design And Implementation Of A Reduced Base Model Construction Technique For Stochastic Activity Networks
, 1990
"... This thesis has been submitted in partial ful lment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the library. Brief quotations from this thesis are allowable without special permission, ..."
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This thesis has been submitted in partial ful lment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the library. Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of the source is made. Requests for permission for extended quotation from or reproduction of thesis manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED:
Performance Evaluation of Repetitive Automated Manufacturing Systems
 in: Proc. of the Rensselaer's Second Int. Conf. on CIM
, 1990
"... Steadystate performance evaluation of some repetitive automated manufacturing systems modelled by means of stochastic or deterministic timed Petri nets is considered. Basically, concepts and techniques developed by the authors in other works are applied to repetitive manufacturing systems in this p ..."
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Steadystate performance evaluation of some repetitive automated manufacturing systems modelled by means of stochastic or deterministic timed Petri nets is considered. Basically, concepts and techniques developed by the authors in other works are applied to repetitive manufacturing systems in this paper. Linear programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight upper and lower bounds for the performance measures of jobshop systems and decisionfree kanban systems in polynomial time on the net structure. The results can be extended to other models in which some decisions are allowed, such as producerconsumer systems with mutual exclusion. Exact performance measures for a class of systems containing sequential processes can be computed in polynomial time. 1 Introduction Modelling tools for designing complex manufacturing systems must be selected such that qualitative and quantitative analysis can be achieved in an efficient way....
Structural characterization and qualitative properties of Product Form Stochastic Petri Nets
"... The model of Stochastic Petri nets (SPN) with a product form solution (#net) is a class of nets for which there is an analytic expression of the steady state probabilities w.r.t. markings, as for product form queueing networks w.r.t. queue lengths. In this paper, we prove new important properties o ..."
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The model of Stochastic Petri nets (SPN) with a product form solution (#net) is a class of nets for which there is an analytic expression of the steady state probabilities w.r.t. markings, as for product form queueing networks w.r.t. queue lengths. In this paper, we prove new important properties of this kind of nets. First we provide a polynomial time (w.r.t. the size of the net structure) algorithm to check whether a SPN is a #net.
construction technique for stochastic activity networks Item type text; ThesisReproduction (electronic)
"... Design and implementation of a reduced base model ..."
A P and Tinvariant Characterization of Product Form and Decomposition in Stochastic Petri Nets
"... Structural product form and decomposition results for stochastic Petri nets are surveyed, unified and extended. The contribution is threefold. First, the literature on structural results for product form over the number of tokens at the places is surveyed and rephrased completely in terms of Tinvar ..."
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Structural product form and decomposition results for stochastic Petri nets are surveyed, unified and extended. The contribution is threefold. First, the literature on structural results for product form over the number of tokens at the places is surveyed and rephrased completely in terms of Tinvariants. Second, based on the underlying concept of grouplocalbalance, the product form results for stochastic Petri nets are demarcated and an intuitive explanation is provided of these results based on Tinvariants, only. Third, a decomposition result is provided that is completely formulated in terms of both Tinvariants and Pinvariants.