Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Mitrophanov Y. I., Rogachko E. S., Stankevich E. P. Dynamic load allocation in closed queueing networks with batch movements. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2012, vol. 12, iss. 1, pp. 22-28. DOI: 10.18500/1816-9791-2012-12-1-22-28

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
24.02.2012
Full text:
download
(downloads: 211)
Language: 
Russian
Heading: 
Mathematics
UDC: 
519.872
DOI: 
10.18500/1816-9791-2012-12-1-22-28

Dynamic load allocation in closed queueing networks with batch movements

Autors: 
Mitrophanov Yurii Ivanovich, Saratov State University
Rogachko Ekaterina Sergeevna, Saratov State University
Stankevich Elena Petrovna, Saratov State University
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
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.
  • 1141 reads