A characterization of independence for competing Markov chains with applications to stochastic Petri nets
IEEE Transactions on Software EngineeringPublished 1 July 1994
Richard J. Boucherie
Citations81
SJR quartileQ1
SJR score1.45
SNIP2.43
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
This paper shows that some of the recently obtained product form results for stochastic Petri nets can be obtained as a special case of a simple exclusion mechanism for the product process of a collection of Markov chains.>
Keywords
Computer ScienceBusiness, Management and Accounting
Proceedings of the IEEEPetri nets: Properties, analysis and applications
10,546 Citations1989T. Murata
The author proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis, and one section is devoted to marked graphs, the concurrent system model most amenable to analysis.
Journal of the ACMOpen, Closed, and Mixed Networks of Queues with Different Classes of Customers
2,436 Citations1975Forest Baskett, K. Mani Chandy +2 more
Many of the network results of Jackson on arrival and service rate dependencies, of Posner and Bernholtz on different classes of customers, and of Chandy on different types of service centers are combined and extended in this paper.
Operations ResearchNetworks of Waiting Lines
1,251 Citations1957James R. Jackson
What is perhaps the simplest theoretical question related to this class of problems, and derives expressions for certain steady-state parameters for discrete, statistically varying flows through complex networks.
IRE Transactions on Communications SystemsBlocking in a Shared Resource Environment
991 Citations1981J.S. Kaufman
It is shown that, for the important and commonly implemented policy of complete sharing, a simple one-dimensional recursion can be developed which eliminates all difficulty in computing quantities of interest-regardless of both the size and dimensionality of the underlying model.
Operations ResearchClosed Queuing Systems with Exponential Servers
687 Citations1967William J. Gordon, G. F. Newell
It is found that the distribution of customers in the closed queuing system is regulated by the stage or stages with the slowest effective service rate, which means that closed systems are shown to be stochastically equivalent to open systems in which the number of customers cannot exceed N.
Journal of the Royal Statistical Society Series B (Statistical Methodology)Stochastic Models of Computer Communication Systems
364 Citations1985F. P. Kelly
This paper describes some examples of the stochastic models found useful in the design and analysis of advanced computer and communication systems and discusses concurrency control procedures for databases, dynamic channel assignment for cellular radio, and random access schemes for the control of a broadcast channel.
Queueing SystemsProduct form in networks of queues with batch arrivals and batch services
112 Citations1990W. Henderson, Peter Taylor
A product form equilibrium distribution is derived for a class of queueing networks in either discrete or continuous time, in which multiple customers arrive simultaneously and batches of customers complete service simultaneously.
Journal of the ACMProbabilistic Models of Database Locking
107 Citations1984Debasis Mitra, P. Weinberger
Performance EvaluationMarkovian Petri Net protocols with product form solution
82 Citations1991Aurel A. Lazar, Thomas G. Robertazzi
A class of Markovian Petri Net models whose equilibrium state probabilities satisfy detailed (local) balance equations is presented, and examples of their applicability include a bus oriented multiprocessor model, a version of the classical dining philosophers problem and an alternating bit protocol model.
IEEE Transactions on ComputersModeling Bus Contention and Memory Interference in a Multiprocessor System
70 Citations1983Marsan, Balbo +2 more
Stochastic models of contention for shared resources in an experimental multiprocessor prototype are presented and are validated with simulation and measurement results that show that the accuracy of the analytical results is excellent.
IEEE Transactions on Software EngineeringEmbedded processes in stochastic Petri nets
68 Citations1991W. Henderson, Peter Taylor
Embedded discrete time processes are used to study a class of SPNs (stochastic Petri nets) which have a closed-form equilibrium distribution and an aggregation procedure is proposed which reduces a complex SPN to a much simpler skeleton SPN and obtains results which are exact marginal distributions for the original SPN.
Lecture notes in computer scienceOn the product form solution for Stochastic Petri Nets
51 Citations1992Susanna Donatelli, Matteo Sereno
The combinatorial explosion of the state space of Stochastic Petri Nets is a well known problem that inhibits the exact solution of large SPNs, and therefore a broad use of this kind of Petri nets as a modelling tool is recommended.
SIAM Journal on ComputingProbabilistic Models and Asymptotic Results for Concurrent Processing with Exclusive and Non-Exclusive Locks
31 Citations1985Debasis Mitra
A probabilistic model for conflicts among transactions in a database is given, allowing two kinds of locks for concurrency control, exclusive and non-exclusive, which yields exact formulas for performance measures, such as mean concurrency and throughput.
The Annals of Applied ProbabilityThe Philosophers' Process: An Ergodic Reversible Nearest Particle System
19 Citations1993Bernard Ycart
Performance EvaluationAggregation and disaggregation through insensitivity in stochastic Petri nets
16 Citations1993W. Henderson, D. Lucic
In doing so exact equilibrium distributions are derived for transition merging, marking amalgamation and aggregation and disaggregation for suitable classes of stochastic Petri nets.
IEEE Transactions on Software EngineeringGeneralization of queueing network product form solutions to stochastic Petri nets
15 Citations1991Gérard Florin, Stéphane Natkin
It is shown that the steady-state probability distribution can be expressed using matrix products and the results generalize the Gordon-Newell theorem.
IEEE Transactions on ComputersExact parametric analysis of stochastic Petri nets
7 Citations1992M. Li, N.D. Georganas
An algorithm for exact parametric analysis of stochastic Petri nets is presented, derived from the theory of decomposition and aggregation of Markov chains.
Queueing SystemsService stage Petri net models with product form solution
6 Citations1990I.Y. Wang, Thomas G. Robertazzi
A class of service stage Petri net models whose equilibrium probabilities satisfy local balance equations is presented, and the natural topological space for embedding the state transition lattice is shown to be a multidimensional toroidal manifold.