3rd International ICST Workshop on Tools for solving Structured Markov Chains

Research Article

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

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  • @INPROCEEDINGS{10.4108/ICST.VALUETOOLS2008.4368,
        author={Juan F.  P\^{e}rez and Jeroen Van Velthoven and Benny Van Houdt},
        title={Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods},
        proceedings={3rd International ICST Workshop on Tools for solving Structured Markov Chains},
        publisher={ACM},
        proceedings_a={SMCTOOLS},
        year={2010},
        month={5},
        keywords={Matrix-analytic methods, queueing systems, software tool, MATLAB, structured Markov chains},
        doi={10.4108/ICST.VALUETOOLS2008.4368}
    }
    
  • Juan F. Pérez
    Jeroen Van Velthoven
    Benny Van Houdt
    Year: 2010
    Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods
    SMCTOOLS
    ICST
    DOI: 10.4108/ICST.VALUETOOLS2008.4368
Juan F. Pérez1,*, Jeroen Van Velthoven1,*, Benny Van Houdt1,*
  • 1: Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerpen, Belgium
*Contact email: juanfernando.perez@ua.ac.be, jeroen.vanvelthoven@ua.ac.be, benny.vanhoudt@ua.ac.be

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-birth-death and non-skip-free Markov chains (implemented by the SMCSolver tool), as well as Markov processes with a matrix exponential distribution. We consider various single server queueing systems with phase-type, matrix exponential, Markovian, rational and semi-Markovian arrival and service processes; queues with multiple customer types, where the service depends on the customer type and where consecutive customer types may be correlated; and queues with multiple servers for which the typical dimensionality problem can be avoided. Apart from implementing various classical and more advanced solution techniques, the tool also extends and improves some of the existing solution techniques in a number of cases.