Cite this article as:

Mitrophanov Y. I., Rogachko E. S., Stankevich E. P. Dynamic load allocation in closed queueing networks with batch movements . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2012, vol. 12, iss. 1, pp. 22-28. DOI: https://doi.org/10.18500/1816-9791-2012-12-1-22-28

Language: 
Russian
Heading: 
Mathematics
UDC: 
519.872

Dynamic load allocation in closed queueing networks with batch movements

Authors: 
Mitrophanov Yurii Ivanovich, Saratov State University 1, Saratov State University, Russia, 410012, Saratov, Astrahanskaya st., 83 , MitrophanovYuI@info.sgu.ru
Rogachko Ekaterina Sergeevna, Saratov State University 1, Saratov State University, Russia, 410012, Saratov, Astrahanskaya st., 83 , RogachkoES@info.sgu.ru
Stankevich Elena Petrovna, Saratov State University 1, Saratov State University, Russia, 410012, Saratov, Astrahanskaya st., 83 , StankevichElena@mail.ru
Abstract: 

A method of load allocation control in closed queueing networks with batch movements is proposed. When this method is used in queueing networks of considered type, close to given customer allocation among queueing systems is provided. The control is realized by use of different routing matrices during fixed time intervals in process of network operation. Models of evolution and an approximate method of computing a stationary distribution and other stationary characteristics of considered type queueing networks are presented.

 

Key words: 
queueing networks, batch movements, load allocation, routing control, stationary distribution.
DOI: 
https://doi.org/10.18500/1816-9791-2012-12-1-22-28
References

1. Bovopoulos A. D., Lazar A. A. Optimal load balancing

for Markovian queueing networks // Proc. 30th Midwest

Symp. Circ. and Syst. Syracuse; N.Y., 1987. P. 1428–1432.

2. Alanyali M., Hajek B. Analysis of simple algorithms

for dynamic load balancing // Math. Oper. Res. 1997.

Vol. 22, № 4. P. 840–871.

3. Bonald T., Jonckheere M., Proutiere A. Insensitive

load balancing // Proc. of ACM Sigmetrics/Performance.

N.Y., 2004. P. 6367–6378.

4. Down D. G., Lewis M. E. Dynamic load balancing in

parallel queueing systems: stability and optimal control //

Eur. J. Oper. Res. 2006. Vol. 168, № 2. P. 509–519.

5. Henderson W., Pearce C. E. M., Taylor P. G.,

Dijk N. M. Closed queueing networks with batch

services // Queueing Systems. 1990. Vol. 6. P. 59–70.

6. Henderson W., Taylor P. G. Product form in networks

of queues with batch arrivals and batch services //

Queueing Systems. 1990. Vol. 6. P. 71–88.

7. Boucherie R. J., Dijk N. M. Product forms for queueing

networks with state-dependent multiple job transitions //

Adv. Appl. Prob. 1991. Vol. 23, № 1. P. 152–187.

8. Serfozo R. F. Queueing networks with dependent nodes

and concurrent movements // Queueing Systems. 1993.

Vol. 13. P. 143–182.

9. Miyazawa M. Structure-reversibility and departure

functions of queueing networks with batch movements

and state dependent routing // Queueing Systems. 1997.

Vol. 25. P. 45–75.

10. Coyle A. J., Henderson W., Pearce C. E. M.,

Taylor P. G. A general formulation for mean-value

analysis in product-form batch-movement queueing

networks // Queueing Systems. 1994. Vol. 16. P. 363–

372.

11. Bause F., Boucherie R. J., Buchholz P. Norton’s

theorem for batch routing queueing networks //

Stochastic Models. 2001. Vol. 17. P. 39–60.

12. Митрофанов Ю. И., Рогачко Е. С. Модели и анализ

сетей массового обслуживания с динамическим управ-

лением распределением нагрузки // Автоматика и вы-

числительная техника. 2006. № 5. С. 69–77.

13. Митрофанов Ю. И., Фокина Н. П. Анализ сетей

массового обслуживания с динамическим управлени-

ем маршрутизацией // Изв. Сарат. ун-та. Нов. сер.

2007. Т. 7. Сер. Математика. Механика. Информати-

ка, вып. 1. С. 27–33.

14. Митрофанов Ю. И., Рогачко Е. С. Управление рас-

пределением нагрузки в сетях массового обслуживания

// Автоматика и телемеханика. 2008. № 9. С. 94–102.

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