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

Authors:
G. Latouche;V. Ramaswami
Affiliations:
Département d’Informatique, Université Libre de Bruxelles, CP 212, Boulevard du Triomphe, 1050 Bruxelles, Belgium;Bellcore, 331 Newman Springs Road, Red Bank, NJ 07701-7030, USA
Venue:
Queueing Systems: Theory and Applications
Year:
1997

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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.