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Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods

Juan Fernando Perez · Jeroen Van Velthoven · Benny Van Houdt B

16 citations0/0 files storedInternational ICST Conference on Performance Evaluation Methodologies and Tools (VALUETOOLS)

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Advanced Queuing Theory Analysis Probability and Statistical Research Petri Nets in System Modeling

Abstract

In this paper we propose a novel MATLAB tool, called Q-MAM, to compute queue length, waiting time and so-journ time distributions of various discrete and continuous time queuing systems with an underlying structured Markov chain/process. The underlying paradigms include M/G/1-and GI/M/1-type, quasi-

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1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.2012Queueing Theory: A Linear Algebraic Approach 2005Matching Three Moments with Minimal Acyclic Phase Type Distributions 2007A minimal representation of Markov arrival processes and a moments matching method 1989Markov processes whose steady state distribution is matrix-exponential with an application to theGI/PH/1 queue 2006Structured Markov chains solver 1997Non-Skip-Free M/G/ 1 and G/M/ 1 Type Markov Chains

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