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Analytic solution of stochastic activity networks with exponential and deterministic activities
 The University of Arizona
, 1993
"... This dissertation has been submitted in partial ful llment of requirements for an ..."
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Cited by 15 (0 self)
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This dissertation has been submitted in partial ful llment of requirements for an
SPN2MGM: Tool Support for MatrixGeometric Stochastic Petri Nets
 in Proceedings of the 2nd International Computer Performance and Dependability Symposium
, 1996
"... In this paper we present the tool spn2mgm that can be used to construct and solve stochastic Petri nets using matrixgeometric techniques. The tool automatically recognizes the "matrixgeometric structure" of the Markov chain underlying the stochastic Petri net, and solves the Markov chain ..."
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In this paper we present the tool spn2mgm that can be used to construct and solve stochastic Petri nets using matrixgeometric techniques. The tool automatically recognizes the "matrixgeometric structure" of the Markov chain underlying the stochastic Petri net, and solves the Markov chain with these wellknown and efficient techniques. We informally characterize the class of stochastic Petri nets of interest (a formal definition has been given in an earlier paper) after which we briefly touch upon the matrixgeometric solution approach. We then present an overview of spn2mgm by discussing the model class supported and the internal methods used. We finish the paper with a case study in the area of queues with breakdowns. In particular, we present a model of a queueing system in which checkpointing can be used to shorten the recovery process after serverbreakdowns have occurred. 1 Introduction Stochastic Petri nets (SPNs) have been used extensively for the performance evaluation of com...
NonExponential Stochastic Petri Nets: an Overview of Methods and Techniques
 In To be published in: Computer Systems Science & Engineering
, 1997
"... The analysis of stochastic systems with nonexponential timing requires the development of suitable modeling tools. Recently, some eort has been devoted to generalize the concept of Stochastic Petri nets, by allowing the ring times to be generally distributed. The evolution of the PN in time beco ..."
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Cited by 8 (4 self)
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The analysis of stochastic systems with nonexponential timing requires the development of suitable modeling tools. Recently, some eort has been devoted to generalize the concept of Stochastic Petri nets, by allowing the ring times to be generally distributed. The evolution of the PN in time becomes a stochastic process, for which in general, no analytical solution is available. The paper surveys suitable restrictions of the PN model with generally distributed transition times, that have appeared in the literature, and compares these models from the point of view of the modeling power and the numerical complexity. Key words: Stochastic Petri Nets, Nonexponential Distributions, Phasetype Distributions, Markov and Semimarkov Reward Models, Markov Regenerative Processes, Queueing Systems with Preemption. 1 Introduction The usual denition of Stochastic Petri Net (SPN) implies that all the timed activities associated to the transitions are represented by exponential random ...
Efficient Handling of Phasetype Distributions in Generalized Stochastic Petri Nets
, 1997
"... We study the introduction of transitions with Phasetype distribution ring time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose ..."
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Cited by 5 (0 self)
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We study the introduction of transitions with Phasetype distribution ring time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works. The method is based on a structural decomposition of the net. We establish conditions under which this decomposition leads to a tensor expression of the generator of the chain. The tensor expression is used to solve the chain with an iterative method.
Reliability Analysis Techniques Explored Through a Communication Network Example
"... This paper reviews general methods used to perform dependability analysis on a given system. A communication network example is used in relation to a client/server type of application to illustrate the reliability and availability modeling techniques. We review both nonstate space as well as state ..."
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This paper reviews general methods used to perform dependability analysis on a given system. A communication network example is used in relation to a client/server type of application to illustrate the reliability and availability modeling techniques. We review both nonstate space as well as state space based methods and discuss the bene ts and limitations of each. The paper assumes a general understanding of probability theory.
Structural Decomposition and Serial Solution of SPN Models of the ATM GAUSS Switch
 PNPM 95
, 1999
"... We address the performance, in particular, the cell loss ratio, of the ATM GAUSS switch under a variety of realistic video and constant bit rate traffic patterns. ..."
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Cited by 3 (0 self)
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We address the performance, in particular, the cell loss ratio, of the ATM GAUSS switch under a variety of realistic video and constant bit rate traffic patterns.
Approximation Technique of Finite Capacity Queuing Networks Exploiting Petri Net Analysis
"... In this paper we present a technique for deriving approximate measures for finite capacity queuing networks. The fact that buffers have finite capacity makes the analysis of such networks very difficult. Indeed, FCQNs do not have a product form solution, except for a limited number of special cases ..."
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In this paper we present a technique for deriving approximate measures for finite capacity queuing networks. The fact that buffers have finite capacity makes the analysis of such networks very difficult. Indeed, FCQNs do not have a product form solution, except for a limited number of special cases. In general exact solution for such models can only be obtained using numerical methods. However these techniques can only handle networks of very small size. For this reason analyses based on approximate techniques represent an interesting possibility to compute measures for queuing network models with finite capacity. In this paper we present an approximation technique that is inspired to the method called Response Time Preservation. The developing of the proposed technique is based on a representation of FCQNs by means of Generalized Stochastic Petri Nets. 1