Paper Info
Title
Queue size distribution and capacity optimum design for N-policy Geo(λ1, λ2, λ3)/G/1 queue with setup time and variable input rate.
Abstract
In this paper we consider a discrete-time Geo/G/1 queue with N-policy and setup time, where the customers' input rate varies according to the server's status: idle, setup and busy states. By using the total probability decomposition technique, we study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursion expressions of the z-transformation of the transient queue length distribution and the recursion expressions of the steady state queue length distribution at arbitrary time epoch n+. The results obtained in this paper indicate that the queue length distribution in equilibrium no longer follows the stochastic decomposition discipline. The important relations between the steady state queue length distributions at different time epochs (n-, n, n+) are discovered. Finally, by numerical examples, we discuss the sensitivity of the steady state queue length distribution towards system parameters, and illustrate the application of the expressions for the steady state queue length distribution in the system capacity design. © 2012 Elsevier Ltd.
Year
DOI
Venue
2013
10.1016/j.mcm.2012.12.032
Mathematical and Computer Modelling: An International Journal
Keywords
Field
DocType
N-policy discrete time queue,Queue length distribution,Setup time,System capacity optimum design,Total probability decomposition technique,Variable input rate
M/M/1 queue,Mathematical optimization,Bulk queue,G/G/1 queue,M/M/c queue,Mathematical analysis,M/G/1 queue,M/G/k queue,Burke's theorem,M/D/c queue,Mathematics
Journal
Volume
Issue
ISSN
57
5-6
0895-7177
Citations 
PageRank 
References 
4
0.59
5
Authors
4
Name
Order
Citations
PageRank
Yingyuan Wei150.95
Miaomiao Yu2556.13
Yinghui Tang3425.95
Jianxiong Gu450.95