{"title":"A general algorithm to compute the steady-state solution of product-form cooperating Markov chains","authors":"A. Marin, S. R. Bulò","doi":"10.1109/MASCOT.2009.5366744","DOIUrl":null,"url":null,"abstract":"In the last few years several new results about product-form solutions of stochastic models have been formulated. In particular, the Reversed Compound Agent Theorem (RCAT) and its extensions play a pivotal role in the characterization of cooperating stochastic models in product-form. Although these results have been used to prove several well-known theorems (e.g., Jackson queueing network and G-network solutions) as well as novel ones, to the best of our knowledge, an automatic tool to derive the product-form solution (if present) of a generic cooperation among a set of stochastic processes, is not yet developed. In this paper we address the problem of solving the non-linear system of equations that arises from the application of RCAT. We present an iterative algorithm that is the base of a software tool currently under development. We illustrate the algorithm, discuss the convergence and the complexity, compare it with previous algorithms defined for the analysis of the Jackson networks and the G-networks. Several tests have been conducted involving the solutions of a (arbitrary) large number of cooperating processes in product-form by RCAT.","PeriodicalId":275737,"journal":{"name":"2009 IEEE International Symposium on Modeling, Analysis & Simulation of Computer and Telecommunication Systems","volume":"32 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 IEEE International Symposium on Modeling, Analysis & Simulation of Computer and Telecommunication Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MASCOT.2009.5366744","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
In the last few years several new results about product-form solutions of stochastic models have been formulated. In particular, the Reversed Compound Agent Theorem (RCAT) and its extensions play a pivotal role in the characterization of cooperating stochastic models in product-form. Although these results have been used to prove several well-known theorems (e.g., Jackson queueing network and G-network solutions) as well as novel ones, to the best of our knowledge, an automatic tool to derive the product-form solution (if present) of a generic cooperation among a set of stochastic processes, is not yet developed. In this paper we address the problem of solving the non-linear system of equations that arises from the application of RCAT. We present an iterative algorithm that is the base of a software tool currently under development. We illustrate the algorithm, discuss the convergence and the complexity, compare it with previous algorithms defined for the analysis of the Jackson networks and the G-networks. Several tests have been conducted involving the solutions of a (arbitrary) large number of cooperating processes in product-form by RCAT.