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  • 1
    Electronic Resource
    Electronic Resource
    The PH/PH/1 queue at epochs of queue size change (1997)
    Springer
    Queueing systems 25 (1997), S. 97-114 
    Details
    ISSN: 1572-9443
    Keywords: GI/G/1 queue ; quasi-birth-and-death processes ; embedded process
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The PH/PH/1 queue is considered at embedded epochs which form the union of arrival and departure instants. This provides us with a new, compact representation as a quasi-birth-and-death process, where the order of the blocks is the sum of the number of phases in the arrival and service time distributions. It is quite easy to recover, from this new embedded process, the usual distributions at epochs of arrival, or epochs of departure, or at arbitrary instants. The quasi-birth-and-death structure allows for efficient algorithmic procedures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019148217045
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    From the matrix-geometric to the matrix-exponential (1990)
    Springer
    Queueing systems 6 (1990), S. 229-260 
    Details
    ISSN: 1572-9443
    Keywords: Method of phases ; Neuts Process ; queues ; matrix-geometric method ; matrix-exponential solution ; duality of queues ; time reversal ; waiting times ; busy period
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider the single server queuesN/G/1 andGI/N/1 respectively in which the arrival process or the service process is a Neuts Process, and derive the matrix-exponential forms of the solution of relevant nonlinear matrix equations for such queues. We thereby generalize the matrix-exponential results of Sengupta forGI/PH/1 and of Neuts forMMPP/G/1 to substantially more general models. Our derivation of the results also establishes the equivalence of the methods of Neuts and those of Sengupta. A detailed analysis of the queueGI/N/1 is given, and it is noted that not only the stationary distribution at arrivals but also at an arbitrary time is matrix-geometric. Matrix-exponential steady state distributions are established for the waiting times in the queueGI/N/1. From this, by appealing to the duality theorem of Ramaswami, it is deduced that the stationary virtual and actual waiting times in aGI/PH/1 queue are of phase type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02411476
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    Paper (German National Licenses)
    Fulltext
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