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. Analysis of Heterogeneous Queueing Networks with Batch Movements of Customers. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 3, pp. 41-46. DOI: 10.18500/1816-9791-2011-11-3-1-41-46

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 135)

Analysis of Heterogeneous Queueing Networks with Batch Movements of Customers

Mitrophanov Yurii Ivanovich, Saratov State University
Rogachko Ekaterina Sergeevna, Saratov State University
Stankevich Elena Petrovna, Saratov State University

Closed exponential queueing network with different classes of customers and batch movements is considered. To model evolution of given network Markov chains are used. Two approaches to stationary distribution calculation for given type queueing networks are presented. Formulas for basic stationary characteristics are given.

  1. Kelly F. P. Reversibility and stochastic networks. London: Wiley, 1979. 230 p.
  2. Уолренд Дж. Введение в теорию сетей массового обслуживания. М.: Мир, 1993. 335 с.
  3. Митрофанов Ю. И. Анализ сетей массового обслуживания. Саратов: Научная книга, 2005. 177 с.
  4. 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.
  5. 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.
  6. Boucherie R. J., Dijk N. M. Product forms for queueing networks with state-dependent multiple job transitions // Advances in Applied Probability. 1991. Vol. 23, No 1. P. 152–187.
  7. Serfozo R. F. Queueing networks with dependent nodes and concurrent movements // Queueing Systems. 1993. Vol. 13. P. 143–182.
  8. 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.
  9. Woodward M. E. Towards the accurate modelling of high-speed communication networks with product- form discrete-time networks of queues // Computer Communications. 1998. Vol. 21. P. 1530–1543.
  10. Гурьянов А. И., Митрофанов Ю. И. Определение параметров замкнутых линейных сетей систем массового обслуживания // Системное моделирование. Новосибирск, 1970. Вып. 1. C. 39–49.