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    A finite capacity queue with Markovian arrivals and two servers with group services

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    IJSA.1994.434957.pdf (1.348Mb)
    Date
    1994-1-1
    Author
    Chakravarthy, S.
    Alfa, Attahiru Sule
    Metadata
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    Abstract
    In this paper we consider a finite capacity queuing system in which arrivals are governed by a Markovian arrival process. The system is attended by two exponential servers, who offer services in groups of varying sizes. The service rates may depend on the number of customers in service. Using Markov theory, we study this finite capacity queuing model in detail by obtaining numerically stable expressions for (a) the steady-state queue length densities at arrivals and at arbitrary time points; (b) the Laplace-Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. The stationary waiting time distribution is shown to be of phase type when the interarrival times are of phase type. Efficient algorithmic procedures for computing the steady-state queue length densities and other system performance measures are discussed. A conjecture on the nature of the mean waiting time is proposed. Some illustrative numerical examples are presented.
    URI
    http://hdl.handle.net/1993/23794
    DOI
    10.1155/S1048953394000171
    Collections
    • Price Faculty of Engineering Scholarly Works [48]
    • University of Manitoba Scholarship [1952]

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