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

Part of: Special processes Operations research and management science Computer system organization

Published online by Cambridge University Press:  14 July 2016

Hideaki Takagi
Hideaki Takagi*
Affiliation:
IBM Research, Tokyo Research Laboratory
*
∗Postal address: IBM Japan, Ltd., No. 36 Kowa Building, 5–19 Sanban-cho, Chiyoda-ku, Tokyo 102, Japan.
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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 (Takagi (1990)). In this paper, capitalizing on the above results, we obtain the Laplace transforms (with respect to time) 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 (1988) is corrected.

Keywords

SERVER VACATIONSN-POLICYTIME-DEPENDENT QUEUESUNFINISHED WORKDEPLETION TIME

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 418 - 429
Copyright
Copyright © Applied Probability Trust 1992 

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