Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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Dolgov V. I., Mitrophanov Y. I., Rogachko E. S. Method for Analysis of Queueing Networks with Dynamic Control of Service Rates. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 3, pp. 22-27. DOI: 10.18500/1816-9791-2009-9-3-22-27

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Method for Analysis of Queueing Networks with Dynamic Control of Service Rates

Dolgov Vitalii Igorevich, Saratov State University
Mitrophanov Yurii Ivanovich, Saratov State University
Rogachko Ekaterina Sergeevna, Saratov State University

Model of evolution and a method for analysis of closed exponential queueing networks with dynamic control of service rates are proposed. A method of computing of the stationary distribution and formulas for calculating of stationary characteristics of the networks are presented. An example of analysis of considered type queueing network is given. According to the results of analysis and simulation of this network the accuracy of this method is sufficient for practical application.

  1. Alidrisi M. Linear programming model for the optimal control of a queueing network // Intern. J. Syst. Sci. 1987. V. 18. P. 1079–1089.
  2. Azaron A., Ghomi S.M. Optimal control of the service rates and arrivals in Jackson networks // Eur. J. Oper. Res. 2003. V. 147, № 1. P. 17–31.
  3. Weber R.R., Stidham S. Optimal control of service rates in networks of queues // Advances in Applied Probability. 1987. V. 19. P. 202–218.
  4. Jo K.Y. Decomposition approximation of queueingnetwork control models with tree structures // Annals of Operations Research. 1987. V. 8. P. 117–132.
  5. Alidrisi M. Optimal control of the service rate of an exponential queueing network using Markov decision theory // Intern. J. Syst. Sci. 1990. V. 21. P. 2553–2563.
  6. Bruell S.C., Balbo G., Afshari P.V. Mean value analysis of mixed, multiple class BCMP networks with load dependent service stations // Performance Evaluation. 1984. V. 4. P. 241–260.
  7. Mitra D., McKenna J. Asymptotic expansions for closed Markovian networks with state-dependent service rates // J. of the Association for Computing Machinery. 1986. V. 33, № 3. P. 568–592.
  8. Ляхов А.И. Асимптотический анализ замкнутых сетей очередей, включающих устройства с переменной интенсивностью обслуживания // Автоматика и телемеханика. 1997. № 3. С. 131–143.
  9. Mandelbaum A., Massey W.A., Reiman M.I. Strong approximations for Markovian service networks // Queueing Systems. 1998. V. 30. P. 149–201.
  10. Митрофанов Ю.И., Долгов В.И. Динамическое управление интенсивностями обслуживания в сетях массового обслуживания // АВТ. 2008. № 6. С. 44–56.
  11. Баруча-Рид А.Т. Элементы теории марковских процессов и их приложения. М.: Наука, ГРФМЛ, 1969. 512 с.
  12. Митрофанов Ю.И. Анализ сетей массового обслуживания. Саратов: Науч. книга, 2005. 175 с.