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    A discrete single server queue with Markovian arrivals and phase type group services

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    IJSA.1995.614742.pdf (1.505Mb)
    Date
    1995-1-1
    Author
    Alfa, Attahiru Sule
    Dolhun, K. Laurie
    Chakravarthy, S.
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    Abstract
    We consider a single-server discrete queueing system in which arrivals occur according to a Markovian arrival process. Service is provided in groups of size no more than M customers. The service times are assumed to follow a discrete phase type distribution, whose representation may depend on the group size. Under a probabilistic service rule, which depends on the number of customers waiting in the queue, this system is studied as a Markov process. This type of queueing system is encountered in the operations of an automatic storage retrieval system. The steady-state probability vector is shown to be of (modified) matrix-geometric type. Efficient algorithmic procedures for the computation of the rate matrix, steady-state probability vector, and some important system performance measures are developed. The steady-state waiting time distribution is derived explicitly. Some numerical examples are presented.
    URI
    http://hdl.handle.net/1993/23793
    DOI
    10.1155/S1048953395000153
    Collections
    • Price Faculty of Engineering Scholarly Works [48]
    • University of Manitoba Scholarship [1952]

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