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  1. Journal of Systems Science and Systems Engineering
  2. Journal of Systems Science and Systems Engineering : Volume 18
  3. Journal of Systems Science and Systems Engineering : Volume 18, Issue 3, September 2009
  4. The bulk input M$^{[X]}$ /M/1 queue with working vacations
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Journal of Systems Science and Systems Engineering : Volume 26
Journal of Systems Science and Systems Engineering : Volume 25
Journal of Systems Science and Systems Engineering : Volume 24
Journal of Systems Science and Systems Engineering : Volume 23
Journal of Systems Science and Systems Engineering : Volume 22
Journal of Systems Science and Systems Engineering : Volume 21
Journal of Systems Science and Systems Engineering : Volume 20
Journal of Systems Science and Systems Engineering : Volume 19
Journal of Systems Science and Systems Engineering : Volume 18
Journal of Systems Science and Systems Engineering : Volume 18, Issue 4, December 2009
Journal of Systems Science and Systems Engineering : Volume 18, Issue 3, September 2009
Healthcare: A complex service system
Optimum ordering policy for preventive age replacement
Combining classifiers for credit risk prediction
Dynamics of knowledge accumulation in technology follower countries: A system dynamics approach
A comparison of a simple procurement auction and generalized Nash bargaining
The bulk input M$^{[X]}$ /M/1 queue with working vacations
A new cascading failure model with delay time in congested complex networks
Journal of Systems Science and Systems Engineering : Volume 18, Issue 2, June 2009
Journal of Systems Science and Systems Engineering : Volume 18, Issue 1, March 2009
Journal of Systems Science and Systems Engineering : Volume 17
Journal of Systems Science and Systems Engineering : Volume 16
Journal of Systems Science and Systems Engineering : Volume 15
Journal of Systems Science and Systems Engineering : Volume 14
Journal of Systems Science and Systems Engineering : Volume 13
Journal of Systems Science and Systems Engineering : Volume 12

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The bulk input M$^{[X]}$ /M/1 queue with working vacations

Content Provider Springer Nature Link
Author Xu, Xiu li Liu, Ming xin Zhao, Xiao hua
Copyright Year 2009
Abstract In this paper, we analyze a bulk input M$^{[X]}$ /M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function(PGF) of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M$^{[X]}$ /M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.
Starting Page 358
Ending Page 368
Page Count 11
File Format PDF
ISSN 10043756
Journal Journal of Systems Science and Systems Engineering
Volume Number 18
Issue Number 3
e-ISSN 18619576
Language English
Publisher SP Systems Engineering Society of China
Publisher Date 2009-09-05
Publisher Place Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword M$^{[X]}$ /M/1 queue bulk input multiple working vacations stochastic decomposition the Laplace transform order Operations Research/Decision Theory Game Theory/Mathematical Methods Complexity
Content Type Text
Resource Type Article
Subject Control and Systems Engineering Information Systems
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