The PH/PH/1 queue at epochs of queue size change

The PH/PH/1 queue at epochs of queue size change

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Article ID: iaor20002493
Country: United States
Volume: 25
Issue: 1/4
Start Page Number: 97
End Page Number: 114
Publication Date: Jun 1997
Journal: Queueing Systems
Authors: ,
Keywords: GI/G/1 queues
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 arbitary instants. The quasi-birth-and-death structure allows for efficient algorithmic procedures.

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