Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


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Tananko I. E., Fokina N. P. Analysis of closed unreliable queueing networks with batch movements of customers. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 2, pp. 111-117. DOI: 10.18500/1816-9791-2013-13-2-1-111-117, EDN: SJJBBB

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
27.02.2013
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Russian
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SJJBBB

Analysis of closed unreliable queueing networks with batch movements of customers

Autors: 
Tananko Igor' Evstaf'evich, Saratov State University
Fokina Nadezhda Petrovna, Saratov State University
Abstract: 

 Closed unreliable queueing network with batch movements is considered. The main result of the paper is the steady state distribution for given type queueing networks. 

References: 
  1. Morrison J. A. Two discrete-time queues in tandem. IEEE Trans. Commun., 1979, vol. 27, no. 3, pp. 563–573.
  2. Boxma O., Kelly F., Konheim A. The product form for sojourn time distributions in cyclic exponential queues. J. of ACM., 1984, vol. 31, pp. 128–133.
  3. Neely M. J. Exact queueing analysis of discrete time tandems with arbitrary arrival processes. IEEE Proc. of the Intern. Conf. of Commun., Paris, 20-24 June 2004, pp. 1–5.
  4. Pestien V., Ramakrishnan S. Monotonicity and asymptotic queue-length distribution in discrete-time networks. Queueing Systems., 2002, vol. 40, pp. 313– 331.
  5. 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.
  6. Henderson W., Taylor P. G. Some new results on queueing networks with batch movement. J. Appl. Prob., 1991, vol. 28, pp. 409–421.
  7. Henderson W., Pearce C. E. M., Taylor P. G., van Djik N. M. Closed queueing networks with batch services. Queueing Systems, 1990, vol. 6, pp. 59–70.
  8. Henderson W., Northcote B. S., Taylor P. G. Triggered batch movement in queueing networks. Queueing Systems, 1995, vol. 21, pp. 125–141.
  9. Woodward M. E. Towards the accurate modelling of high-speed communication networks with product-form discrete-time networks of queues. Computer Communi- cations, 1998, vol. 21, pp. 1530–1543.
  10. 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).
  11. Bakeva V., Kolev N. Minimization of the blocking time of the unreliable Geo/Gd/1 queueing system. Math. Commun., 1999, vol. 4, pp. 1–10. 
  12. Liu Z., Gao S. Reliability indices of a Geo/G/1/1 Erlang loss system with active breakdowns under Bernoulli schedule. Int. J. of Manag. Sci. and Eng. Manag., 2010, vol. 5(6), pp. 433–438.
  13. Malchin C., Daduna H. Discrete time queueing networks with product form steady state. Availability and performance analysis in an integrated model. Queueing Systems, 2010, vol. 65, no. 4, pp. 385–421.
  14. Vinod B., Altiok T. Approximating unreliable queueing networks under the assumption of exponentiality. J. Opl. Res. Soc., 1986, vol. 37, no. 3, pp. 309–316.
  15. Mitrophanov Yu. I., Rogachko E. S., Stankevich E. P. A method for analysis of queueing networks with batch movements of customers. Comp. Nauki i Inf. Tech. : Mater. Mejdun. Nauch. Conf. Saratov, 2009, pp. 142–145 (in Russian).
  16. Boucherie R. J., van Dijk N. M. Product forms for queueing networks with state-dependent multiple job transitions. Adv. Appl. Probab., 1991, vol. 23, no. 1, pp. 152–187.
Received: 
10.08.2012
Accepted: 
11.01.2013
Published: 
27.02.2013
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