Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Mitrophanov Y. I., Dolgov V. I., Rogachko E. S., Stankevich E. P. Queueing networks with batch movements of customers, blocking and clusters. Izv. Sarat. Univ. Math. Mech. Inform., 2013, vol. 13, iss. 2, pp. 20-31. DOI: 10.18500/1816-9791-2013-13-2-2-20-31

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.05.2013
Full text:
(downloads: 52)
Language: 
Russian
Heading: 
UDC: 
519.872

Queueing networks with batch movements of customers, blocking and clusters

Autors: 
Mitrophanov Yurii Ivanovich, Saratov State University
Dolgov Vitalii Igorevich, Saratov State University
Rogachko Ekaterina Sergeevna, Saratov State University
Stankevich Elena Petrovna, Saratov State University
Abstract: 

 Two types queueing networks with batch movements of customers – networks with blocking and networks with clusters are investigated. Product form stationary distribution for networks with blocking of transitions in states, in which the number of customers in queueing systems exceeds given values, is derived. For queueing networks with disjoint clusters of systems the problem of analyzing is solved and the product form stationary distribution is found. Examples of analysis of the network with blocking and the network with clusters are presented. 

References: 
  1. Balsamo S., Nitto Persone V. A survey of product form queueing networks with blocking and their equivalences. Ann. Oper. Res., 1994, vol. 48, pp. 31–61.
  2. Boxma O. J., Konheim A. G. Approximate analysis of exponential queueing systems with blocking. Acta Informatica, 1981, vol. 15, pp. 19–66.
  3. Clo M. C. MVA for product-form cyclic queueing networks with blocking. Ann. Oper. Res., 1998, vol. 79, pp. 83–96.
  4. Balsamo S., Clo M. C. A convolution algorithm for product-form queueing networks with blocking. Ann. Oper. Res., 1998, vol. 79, pp. 97–117.
  5. Liu X., Buzacott J. A. A decomposition-related throughput property of tandem queueing networks with blocking. Queueing Systems, 1993, vol. 13, pp. 361–383.
  6. Strelen J. C., Bark B., Becker J., Jonas V. Analysis of queueing networks with blocking using a new aggregation technique. Ann. Oper. Res., 1998, vol. 79, pp. 121–142.
  7. Boucherie R. J., Dijk N. M. A generalization of Norton’s theorem for queueing networks. Queueing Systems, 1993, vol. 13, pp. 251–289.
  8. Dijk N. M., Sluis E. Simple product-form bounds for queueing networks with finite clusters. Ann. Oper. Res., 2002, vol. 113, pp. 175–195.
  9. Boucherie R. J., Dijk N. M. Queueing networks: a fundamental approach. New York, Heidelberg, London, Springer Science+Business Media, LLC, 2011, 823 p.
  10. Henderson W., Taylor P. G. Product form in networks of queues with batch arrivals and batch services. Queueing Systems, 1990, vol. 6, pp. 71–88.
  11. Henderson W., Pearce C. E. M., Taylor P. G., Dijk N. M. Closed queueing networks with batch services. Queueing Systems, 1990, vol. 6, pp. 59–70.
  12. Boucherie R. J., Dijk N. M. Spatial birth-dearth processes with multiple changes and applications to batch service networks and clustering processes. Adv. Appl. Prob., 1991, vol. 22, pp. 433–455.
  13. Boucherie R. J., Dijk N. M. Product forms for queueing networks with state-dependent multiple job transitions. Adv. Appl. Prob., 1991, vol. 23, no. 1, pp. 152– 187.
  14. Boucherie R. J. Batch routing queueing networks with jump-over blocking. Probability in the Engineering and Informational Sciences, 1996, vol. 10, pp. 287–297.
  15. Miyazawa M. Structure-reversibility and departure functions of queueing networks with batch movements and state dependent routing. Queueing Systems, 1997, vol. 25, pp. 45–75.
  16. Bause F., Boucherie R. J., Buchholz P. Norton’s theorem for batch routing queueing networks. Stochastic Models, 2001, vol. 17, pp. 39–60.
  17. Mitrophanov Yu. I., Rogachko E. S., Stankevich E. P. Analysis of heterogeneous queueing networks with batch movements of customers. Izv. Sarat. Univ. N. S. Ser. Math. Mech. Inform., 2011, vol. 11, iss. 3, pt. 1, pp. 41–46 (in Russian).
Short text (in English):
(downloads: 75)