کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
463684 697205 2013 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Numerical analysis of rational processes beyond Markov chains
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر شبکه های کامپیوتری و ارتباطات
پیش نمایش صفحه اول مقاله
Numerical analysis of rational processes beyond Markov chains
چکیده انگلیسی

Matrix exponential distributions and rational arrival processes have been proposed as an extension to pure Markov models. The paper presents an approach where these process types are used to describe the timing behavior in quantitative models like queueing networks, stochastic Petri nets or stochastic automata networks. The resulting stochastic process, which is called a rational process, is defined and it is shown that the matrix governing the behavior of the process has a structured representation which allows one to represent the matrix in a very compact form.The main emphasis of the paper is on numerical techniques to compute the stationary distribution. It is shown which techniques from Markov chain analysis may also be applied for rational processes. Aggregation steps can be used to build an aggregated process which is a Markov chain and allows one to compute certain marginal probabilities for the detailed rational process. Furthermore, a block iteration method is presented which exploits the matrix structure and is an extension of previously published techniques for Markov chains.Finally, we present some examples showing that the extension of Markov models results in models which may have a significantly smaller state space than equivalently or similar behaving Markov chains.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Performance Evaluation - Volume 70, Issue 9, September 2013, Pages 646–662
نویسندگان
,