Образец для цитирования:
Тананко И. Е., Фокина Н. П. Анализ замкнутых ненадежных сетей массового обслуживания с групповыми переходами требований // Изв. Сарат. ун-та. Нов. сер. Сер. Математика. Механика. Информатика. 2013. Т. 13, вып. 2. С. 111-117. DOI: https://doi.org/10.18500/1816-9791-2013-13-2-1-111-117
Анализ замкнутых ненадежных сетей массового обслуживания с групповыми переходами требований
Рассматривается замкнутая ненадежная сеть массового обслуживания с групповыми переходами. Основным результатом статьи является стационарное распределение вероятностей состояний сетей обслуживания данного типа.
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.
9. Woodward M. E. Towards the accurate modelling of high-speed communication networks with productform
discrete-time networks of queues // Computer
Communications. 1998. Vol. 21. P. 1530–1543.
10. Митрофанов Ю. И., Рогачко Е. С., Станке-
вич Е. П. Анализ неоднородных сетей массового об-
служивания с групповыми переходами требований //
Известия Сарат. ун-та. Нов. сер. Сер. Математика. Ме-
ханика. Информатика. 2011. Т. 11, вып. 3, ч. 1. С. 41–46.
11. Bakeva V., Kolev N. Minimization of the blocking
time of the unreliable Geo/Gd/1 queueing system //
Math. Commun. 1999. Vol. 4. P. 1–10.
12. Liu Z., Gao S. Reliability indices of a Geo/G/1/1
Erlang loss system with active breakdowns under
Bernoulli schedule // Intern. J. of Manag. Sci. and Eng.
Manag. 2010. Vol. 5(6). P. 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, № 4. P. 385–421.
14. Vinod B., Altiok T. Approximating unreliable
queueing networks under the assumption of
exponentiality // J. Opl. Res. Soc. 1986. Vol. 37, № 3.
P. 309–316.
15. Митрофанов Ю. И., Рогачко Е. С., Станке-
вич Е. П. Метод анализа сетей массового обслужива-
ния с групповыми переходами требований // Компью-
терные науки и информационные технологии : матери-
алы Междунар. науч. конф. Саратов : Изд-во Сарат.
ун-та, 2009. С. 143–145.
16. Boucherie R. J., Dijk N. M. van Product forms
for queueing networks with state-dependent multiple job
transitions // Adv. Appl. Probab. 1991. Vol. 23, № 1.
P. 152–187.
