Transient Queue Size Distribution Solution of Geom / G / 1 Queue with Feedback-A Recursive Method |
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Authors: | Chuanyi Luo Yinghui Tang Cailiang Li |
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Institution: | (1) Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 610074, China;(2) School of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China;(3) Department of Information and Computer Science, Chengdu Electron-Mechanical College, Chengdu, 610031, China |
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Abstract: | This paper considers the Geom / G / 1 queueing model with feedback according to a late arrival system with delayed access (LASDA). Using recursive method,
this paper studies the transient property of the queue size from the initial state N(0+) = i. Some new results about the recursive expression of the transient queue size distribution at any epoch n
+ and the recursive formulae of the equilibrium distribution are obtained. Furthermore, the recursive formulae of the equilibrium
queue size distribution at epoch n
−, and n are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered
(being different from the relations given in M / G / 1 queueing system). The model discussed in this paper can be widely applied in all kinds of communications and computer
network.
This research is supported by the National Natural Science Foundation of China under Grant No. 70871084, the Specialized Research
Fund for the Doctoral Program of Higher Education of China under Grant No. 200806360001, and the Scientific Research Fund
of Southwestern University of Finance and Economics. |
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Keywords: | Discrete time queue equilibrium distribution feedback recursive expression transient distribution |
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