Time-dependent process of M/G/1 vacation models with exhaustive service

Time-dependent process of M/G/1 vacation models with exhaustive service

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Article ID: iaor19932438
Country: Israel
Volume: 29
Issue: 2
Start Page Number: 418
End Page Number: 429
Publication Date: Jun 1992
Journal: Journal of Applied Probability
Authors:
Keywords: vacations
Abstract:

Generalized M/G/1 vacation systems with exhaustive service include multiple and single vacation models and a setup time model possibly combined with an N-policy. In these models with given initial conditions, the time-dependent joint distribution of the server’s state, the queue size, and the remaining vacation or service time is known. In this paper, capitalizing on the above results, the Laplace transforms (with respect to time) are obtained for the distributions of the virtual waiting time, the unfinished work (backlog), and the depletion time. The steady-state limits of those transforms are also derived. An erroneous expression for the steady-state distribution of the depletion time in a multiple vacation model given by Keilson and Ramaswamy is corrected.

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