-
Previous Article
Stochastic method for power-aware checkpoint intervals in wireless environments: Theory and application
- JIMO Home
- This Issue
-
Next Article
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), 71-78.
doi: 10.1080/02331939708844326. |
[2] |
S. C. Borst and O. J. Boxma, Polling models with and without switch over times, Operations Research, 45 (1997), 536-543.
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), 392-406.
doi: 10.1016/S0377-2217(97)00253-1. |
[4] |
B. T. Doshi, Queueing systems with vacations-a survey, Queueing Systems, 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[5] |
M. Kuczma, "Functional Equations in a Single Variable," PWN-Polish Scientific Publishers, Warsaw, 1968. |
[6] |
Y. Levy and U. Yechiali, An M/M/s queue with server's vacations, In INFOR 14, (1976), 153-163. |
[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), 59-64. |
[8] | |
[9] |
H. Takagi, "Queueing Analysis - A Foundation of Performance Evaluation, Vacation and Prority Systems," North-Holland, New York, 1991. |
[10] |
N. Tian and G. Zhang, "Vacation Queueing Models: Theory and Applications. Series: International Series in Operations Research & Management Science," Springer-Verlag, New York, 2006. |
[11] |
N. Tian and L. Li, The M/M/c queue with PH synchronous vacations, Journal of Systems Science and Complexity, 13 (2000), 007-016. |
[12] |
N. Tian and G. Zhang, Stationary distributions of GI/M/c queue with PH type vacations, Queueing Systems, 44 (2003), 183–-202.
doi: 10.1023/A:1024424606007. |
[13] |
R. W. Wolff, Poisson arrivals see times averages, Operations Research, 30 (1982), 223-231.
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, New York, 2010. |
[15] |
G. Zhang and N. Tian, Analysis of queueing systems with synchronous single vacation for some servers, Queueing System, 45 (2003), 161-175.
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), 375-389.
doi: 10.1016/S0377-2217(03)00015-8. |
[17] |
R. W. Wolff, "Stochastic Modeling and the Theory of Queues," Prentice-Hall, Englewood Cliffs, NJ, 1989. |
show all references
References:
[1] |
A. Begum and M. Nadarajan, Multiserver markovian queueing system with vacation, Optimization, 41 (1997), 71-78.
doi: 10.1080/02331939708844326. |
[2] |
S. C. Borst and O. J. Boxma, Polling models with and without switch over times, Operations Research, 45 (1997), 536-543.
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), 392-406.
doi: 10.1016/S0377-2217(97)00253-1. |
[4] |
B. T. Doshi, Queueing systems with vacations-a survey, Queueing Systems, 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[5] |
M. Kuczma, "Functional Equations in a Single Variable," PWN-Polish Scientific Publishers, Warsaw, 1968. |
[6] |
Y. Levy and U. Yechiali, An M/M/s queue with server's vacations, In INFOR 14, (1976), 153-163. |
[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), 59-64. |
[8] | |
[9] |
H. Takagi, "Queueing Analysis - A Foundation of Performance Evaluation, Vacation and Prority Systems," North-Holland, New York, 1991. |
[10] |
N. Tian and G. Zhang, "Vacation Queueing Models: Theory and Applications. Series: International Series in Operations Research & Management Science," Springer-Verlag, New York, 2006. |
[11] |
N. Tian and L. Li, The M/M/c queue with PH synchronous vacations, Journal of Systems Science and Complexity, 13 (2000), 007-016. |
[12] |
N. Tian and G. Zhang, Stationary distributions of GI/M/c queue with PH type vacations, Queueing Systems, 44 (2003), 183–-202.
doi: 10.1023/A:1024424606007. |
[13] |
R. W. Wolff, Poisson arrivals see times averages, Operations Research, 30 (1982), 223-231.
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, New York, 2010. |
[15] |
G. Zhang and N. Tian, Analysis of queueing systems with synchronous single vacation for some servers, Queueing System, 45 (2003), 161-175.
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), 375-389.
doi: 10.1016/S0377-2217(03)00015-8. |
[17] |
R. W. Wolff, "Stochastic Modeling and the Theory of Queues," Prentice-Hall, Englewood Cliffs, NJ, 1989. |
[1] |
Tzu-Hsin Liu, Jau-Chuan Ke. On the multi-server machine interference with modified Bernoulli vacation. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1191-1208. doi: 10.3934/jimo.2014.10.1191 |
[2] |
Tao Jiang, Liwei Liu. Analysis of a batch service multi-server polling system with dynamic service control. Journal of Industrial and Management Optimization, 2018, 14 (2) : 743-757. doi: 10.3934/jimo.2017073 |
[3] |
Willem Mélange, Herwig Bruneel, Bart Steyaert, Dieter Claeys, Joris Walraevens. A continuous-time queueing model with class clustering and global FCFS service discipline. Journal of Industrial and Management Optimization, 2014, 10 (1) : 193-206. doi: 10.3934/jimo.2014.10.193 |
[4] |
Wai-Ki Ching, Sin-Man Choi, Min Huang. Optimal service capacity in a multiple-server queueing system: A game theory approach. Journal of Industrial and Management Optimization, 2010, 6 (1) : 73-102. doi: 10.3934/jimo.2010.6.73 |
[5] |
Jeongsim Kim, Bara Kim. Stability of a queue with discriminatory random order service discipline and heterogeneous servers. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1237-1254. doi: 10.3934/jimo.2016070 |
[6] |
Gábor Horváth, Zsolt Saffer, Miklós Telek. Queue length analysis of a Markov-modulated vacation queue with dependent arrival and service processes and exhaustive service policy. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1365-1381. doi: 10.3934/jimo.2016077 |
[7] |
Ke Sun, Jinting Wang, Zhe George Zhang. Strategic joining in a single-server retrial queue with batch service. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3309-3332. doi: 10.3934/jimo.2020120 |
[8] |
Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial and Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167 |
[9] |
Jian Zhang, Tony T. Lee, Tong Ye, Liang Huang. An approximate mean queue length formula for queueing systems with varying service rate. Journal of Industrial and Management Optimization, 2021, 17 (1) : 185-204. doi: 10.3934/jimo.2019106 |
[10] |
Pikkala Vijaya Laxmi, Singuluri Indira, Kanithi Jyothsna. Ant colony optimization for optimum service times in a Bernoulli schedule vacation interruption queue with balking and reneging. Journal of Industrial and Management Optimization, 2016, 12 (4) : 1199-1214. doi: 10.3934/jimo.2016.12.1199 |
[11] |
Shaojun Lan, Yinghui Tang, Miaomiao Yu. System capacity optimization design and optimal threshold $N^{*}$ for a $GEO/G/1$ discrete-time queue with single server vacation and under the control of Min($N, V$)-policy. Journal of Industrial and Management Optimization, 2016, 12 (4) : 1435-1464. doi: 10.3934/jimo.2016.12.1435 |
[12] |
Ali Delavarkhalafi. On optimal stochastic jumps in multi server queue with impatient customers via stochastic control. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021030 |
[13] |
Wenjuan Zhao, Shunfu Jin, Wuyi Yue. A stochastic model and social optimization of a blockchain system based on a general limited batch service queue. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1845-1861. doi: 10.3934/jimo.2020049 |
[14] |
Dequan Yue, Wuyi Yue. A heterogeneous two-server network system with balking and a Bernoulli vacation schedule. Journal of Industrial and Management Optimization, 2010, 6 (3) : 501-516. doi: 10.3934/jimo.2010.6.501 |
[15] |
Gopinath Panda, Veena Goswami, Abhijit Datta Banik, Dibyajyoti Guha. Equilibrium balking strategies in renewal input queue with Bernoulli-schedule controlled vacation and vacation interruption. Journal of Industrial and Management Optimization, 2016, 12 (3) : 851-878. doi: 10.3934/jimo.2016.12.851 |
[16] |
Yoshiaki Inoue, Tetsuya Takine. The FIFO single-server queue with disasters and multiple Markovian arrival streams. Journal of Industrial and Management Optimization, 2014, 10 (1) : 57-87. doi: 10.3934/jimo.2014.10.57 |
[17] |
Dhanya Shajin, A. N. Dudin, Olga Dudina, A. Krishnamoorthy. A two-priority single server retrial queue with additional items. Journal of Industrial and Management Optimization, 2020, 16 (6) : 2891-2912. doi: 10.3934/jimo.2019085 |
[18] |
Yi Peng, Jinbiao Wu. Analysis of a batch arrival retrial queue with impatient customers subject to the server disasters. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2243-2264. doi: 10.3934/jimo.2020067 |
[19] |
Lingjiao Zhang, Jinting Wang. Strategic shield against external shocks in a Markovian queue with vulnerable server. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022095 |
[20] |
Dequan Yue, Wuyi Yue, Zsolt Saffer, Xiaohong Chen. Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy. Journal of Industrial and Management Optimization, 2014, 10 (1) : 89-112. doi: 10.3934/jimo.2014.10.89 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]