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    Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio

    Access Status
    Fulltext not available
    Authors
    Slamet, I.
    Gupta, Ritu
    Achuthan, N.
    Collinson, Roger
    Date
    2016
    Type
    Journal Article
    
    Metadata
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    Citation
    Slamet, I. and Gupta, R. and Achuthan, N. and Collinson, R. 2016. Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio. International Journal of Mathematical Models and Methods in Applied Sciences. 10: pp. 251-258.
    Source Title
    International Journal of Mathematical Models and Methods in Applied Sciences
    ISSN
    1998-0140
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/58292
    Collection
    • Curtin Research Publications
    Abstract

    The paper aims at deriving transient solutions of non- Markovian queuing system M/G/1 starting from (k,0) to (m,n),m > n remaining below the barrier Y = X and does not include any idle time of server through lattice path approach. The explicit form of the density and other measures of the system performance are not known. Our approach is to approximate general service time with Coxian 2-phase distribution, C2 and represent the queuing process as a lattice path by recording the state of the system at the point of transitions. We use the lattice path combinatorics to count the feasible number of paths and corresponding probabilities. The above leads to the required density that has simple probabilistic structure and can be computed using R .The investigation of the influence of taking different values of a parameter on the behavior of the graphs of the density is also presented.

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