Proceeding from the 2006 workshop on Tools for solving sturctured Markov chains - SMCtools '06

Abstract

Performance evaluation methodologies based on structured Markov chains have taken a more prominent role over the last two decades. During this time, due to the strong exploitation of the involved structures, the techniques used to assess the performance measures of interest have advanced significantly in terms of their efficiency, while becoming more complex at the same time. This increased complexity often acts as an opposing force to a more wide spread use of these advanced methodologies.Making these novel techniques more accessible via a set of software tools is therefore essential to further promote their integration in the system design. SMCtools is the first workshop having as objective the development of software tools for solving structured Markov chains.The proceedings contain 12 papers selected after the reviewing process, and a paper authored by the keynote speaker, Prof. Peter Buchholz from the University of Dortmund.The contributions can be roughly classified into four themes. Some of the papers may be regarded as belonging to more than one theme. A first theme focuses on deriving steady state (or transient) performance measures of finite Markov chains with a very large state space. This is realized either by exploiting the hierarchical structure of the model or by relying on the strong stochastic ordering of Markov chains to derive lower and upper bounds. The keynote contribution given by Peter Buchholz follows the first approach.A second theme contains 6 contributions that are all situated in the matrix analytic paradigm. Four of these papers are very software oriented and describe tools in Java, FORTRAN and MATLAB for analyzing QBD, M/G/1, GI/M/1 and NSF type Markov chains. A Java tool for fitting and generating random numbers from Phase-type distributions is also discussed. The remaining two papers within this theme focus on algorithms and computational issues when analyzing the transient behavior of infinite QBDs and fluid flows.The development of queueing theory has heavily benefited from the advances made in Markov chain theory. Three papers are situated in this area. Two papers address a specific type of queueing problem, that is, a new generalized Schur decomposition method to analyze the GI/GI/1 queue and a novel technique to determine the consecutive loss probabilities in two types of queueing systems, are presented. A third enhances the InterVerdiKom tool with transient analysis features based on Wiener-Hopf and polynomial factorization.A last paper is concerned with the Reversed Compound Agent Theorem (RCAT), mainly useful in Markovian process algebra. It introduces MEERCAT, which implements the RCAT to generate product form solutions.