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Journal Article
Decomposition of the Queue Length Distribution in the MAP/G/1 Queue under Multiple and Single Vacation with N-policy
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- Authors
- Ho Woo Lee, Boo Yong Ahn, No Ik Park
- Issue Date
- 2001-04
- Citation
- Stochastic Models, v.17, no.2, pp.157-190
- ISSN
- 0882-0287
- Publisher
- Taylor & Francis
- Language
- English
- Type
- Journal Article
- Abstract
- In this paper, we establish an explicit form of matrix decompositions for the queue length distributions of the MAP/G/1 queues under multiple and single vacations with N-policy. We show that the vector generating function Y(z) of the queue length at an arbitrary time and X(z) at departures are decomposed into Y(z) = pidle(z)瓘Y(z) and X(z) = pidle(z)瓘X(z) where pidle(z) is the vector generating function of the queue length at an arbitrary epoch at which the server is not in service, and 瓘Y(z) and 瓘X(z) are unidentified matrix generating functions. Copyright © 2001 by Marcel Dekker, Inc.
- KSP Keywords
- Generating function, Matrix decomposition, N-policy, Queue length distribution, single vacation