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Stochastic decomposition in discrete-time queues with generalized vacations and applications
M/M/c multiple synchronous vacation model with gated discipline
1. | Department of Telecommunications, Budapest University of Technology and Economics, Budapest |
2. | Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501 |
  This vacation queue is suitable to model a single operator controlled system consisting of more machines. Hence the provided analysis can be applied to study and optimize such systems.
References:
[1] |
A. Begum and M. Nadarajan, Multiserver markovian queueing system with vacation,, Optimization, 41 (1997), 71.
doi: 10.1080/02331939708844326. |
[2] |
S. C. Borst and O. J. Boxma, Polling models with and without switch over times,, Operations Research, 45 (1997), 536.
doi: 10.1287/opre.45.4.536. |
[3] |
X. Chao and Y. Zhao, Analysis of multi-server queues with station and server vacations,, European Journal of Operational Research, 110 (1998), 392.
doi: 10.1016/S0377-2217(97)00253-1. |
[4] |
B. T. Doshi, Queueing systems with vacations-a survey,, Queueing Systems, 1 (1986), 29.
doi: 10.1007/BF01149327. |
[5] |
M. Kuczma, "Functional Equations in a Single Variable,", PWN-Polish Scientific Publishers, (1968).
|
[6] |
Y. Levy and U. Yechiali, An M/M/s queue with server's vacations,, In INFOR 14, (1976), 153.
|
[7] |
Z. Saffer, An introduction to classical cyclic polling model,, In Proc. of the 14th Int. Conf. on Analytical and Stochastic Modelling Techniques and Applications (ASMTA'07), (2007), 59. Google Scholar |
[8] |
H. Takagi, "Analysis of Polling Systems,", MIT Press, (1986). Google Scholar |
[9] |
H. Takagi, "Queueing Analysis - A Foundation of Performance Evaluation, Vacation and Prority Systems,", North-Holland, (1991).
|
[10] |
N. Tian and G. Zhang, "Vacation Queueing Models: Theory and Applications. Series: International Series in Operations Research & Management Science,", Springer-Verlag, (2006).
|
[11] |
N. Tian and L. Li, The M/M/c queue with PH synchronous vacations,, Journal of Systems Science and Complexity, 13 (2000), 007.
|
[12] |
N. Tian and G. Zhang, Stationary distributions of GI/M/c queue with PH type vacations,, Queueing Systems, 44 (2003).
doi: 10.1023/A:1024424606007. |
[13] |
R. W. Wolff, Poisson arrivals see times averages,, Operations Research, 30 (1982), 223.
doi: 10.1287/opre.30.2.223. |
[14] |
W. Yue, Y. Takahashi and H. Takagi, "Advances in Queueing Theory and Network Applications,", Springer Science + Business Media, (2010).
|
[15] |
G. Zhang and N. Tian, Analysis of queueing systems with synchronous single vacation for some servers,, Queueing System, 45 (2003), 161.
doi: 10.1023/A:1026097723093. |
[16] |
G. Zhang and N. Tian, An analysis of queueing systems with multi-task servers,, European Journal of Operational Research, 156 (2004), 375.
doi: 10.1016/S0377-2217(03)00015-8. |
[17] |
R. W. Wolff, "Stochastic Modeling and the Theory of Queues,", Prentice-Hall, (1989).
|
show all references
References:
[1] |
A. Begum and M. Nadarajan, Multiserver markovian queueing system with vacation,, Optimization, 41 (1997), 71.
doi: 10.1080/02331939708844326. |
[2] |
S. C. Borst and O. J. Boxma, Polling models with and without switch over times,, Operations Research, 45 (1997), 536.
doi: 10.1287/opre.45.4.536. |
[3] |
X. Chao and Y. Zhao, Analysis of multi-server queues with station and server vacations,, European Journal of Operational Research, 110 (1998), 392.
doi: 10.1016/S0377-2217(97)00253-1. |
[4] |
B. T. Doshi, Queueing systems with vacations-a survey,, Queueing Systems, 1 (1986), 29.
doi: 10.1007/BF01149327. |
[5] |
M. Kuczma, "Functional Equations in a Single Variable,", PWN-Polish Scientific Publishers, (1968).
|
[6] |
Y. Levy and U. Yechiali, An M/M/s queue with server's vacations,, In INFOR 14, (1976), 153.
|
[7] |
Z. Saffer, An introduction to classical cyclic polling model,, In Proc. of the 14th Int. Conf. on Analytical and Stochastic Modelling Techniques and Applications (ASMTA'07), (2007), 59. Google Scholar |
[8] |
H. Takagi, "Analysis of Polling Systems,", MIT Press, (1986). Google Scholar |
[9] |
H. Takagi, "Queueing Analysis - A Foundation of Performance Evaluation, Vacation and Prority Systems,", North-Holland, (1991).
|
[10] |
N. Tian and G. Zhang, "Vacation Queueing Models: Theory and Applications. Series: International Series in Operations Research & Management Science,", Springer-Verlag, (2006).
|
[11] |
N. Tian and L. Li, The M/M/c queue with PH synchronous vacations,, Journal of Systems Science and Complexity, 13 (2000), 007.
|
[12] |
N. Tian and G. Zhang, Stationary distributions of GI/M/c queue with PH type vacations,, Queueing Systems, 44 (2003).
doi: 10.1023/A:1024424606007. |
[13] |
R. W. Wolff, Poisson arrivals see times averages,, Operations Research, 30 (1982), 223.
doi: 10.1287/opre.30.2.223. |
[14] |
W. Yue, Y. Takahashi and H. Takagi, "Advances in Queueing Theory and Network Applications,", Springer Science + Business Media, (2010).
|
[15] |
G. Zhang and N. Tian, Analysis of queueing systems with synchronous single vacation for some servers,, Queueing System, 45 (2003), 161.
doi: 10.1023/A:1026097723093. |
[16] |
G. Zhang and N. Tian, An analysis of queueing systems with multi-task servers,, European Journal of Operational Research, 156 (2004), 375.
doi: 10.1016/S0377-2217(03)00015-8. |
[17] |
R. W. Wolff, "Stochastic Modeling and the Theory of Queues,", Prentice-Hall, (1989).
|
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