An analysis of queueing networks with unreliable servers and information delay
We consider the problem of determining the stationary distribution of state probabilities for an open queuing network containing two-device queuing systems, in which only one server is unreliable, and information about the failure of devices arrives with a delay. To route requests in an unreliable network, the problem of determining optimal routing matrices is solved in order to equalize the mathematical expectation of the duration of the stay of requests in the systems.
Keywords
открытая сеть массового обслуживания,
ненадежные приборы обслуживания,
задержка информации,
маршрутизация,
open queueing network,
unreliable servers,
information delay,
routingAuthors
Tananko Igor E. | Saratov National Research State University | tanankoie@info.sgu.ru |
Fokina Nadezhda P. | Saratov National Research State University | fokinanp.sgu@gmail.com |
Всего: 2
References
Economides A.A., Silvester J.A. Optimal routing in a network with unreliable links // IEEE INEOCOM88. 1988. P. 288-297.
Blake J.T., Reibman A.L., Trivedi K.S. Sensitivity analysis of reliability and performability measures for multiprocessor systems // Proc. SIGMETRICS '88 Proceed. of the 1988 ACM SIGMETRICS conference on Meas. and modeling of comp. systems. 1988. P. 177-186.
Vinod B., Solberg J.J. The optimal design of flexible manufacturing systems // International Journal of Production Research. 1985. V. 23, is. 6. P. 1141-1151.
Akyildiz I.F., Liu W. Performance optimization of distributed-system models with unreliable servers // IEEE Trans. on Reliability. 1990. V. 39, No. 2. P. 236-243.
Park K., Kim S. A capacity planning model of unreliable multimedia service systems // The Journal of Systems and Software. 2002. V. 63, is. 1. P. 69-76.
Sharony J. An architecture for mobile radio networks with dynamically changing topology using virtual subnets // Mobile Net works and applications. 1996. V. 1. P. 75-86.
Tassiulas L. Scheduling and performance limits of networks with constantly changing topology // IEEE Transactions on Infor mation Theory. 1997. V. 43, No. 3. P. 1067-1073.
Gottlich S., Kuhn S., Schwarz J.A., Stolletz R. Approximations of time-dependent unreliable flow lines with finite buffers // Mathematical Methods of Operations Research. 2016. V. 83, is. 3. P. 295-323.
Vinod B., Altiok T. Approximating unreliable queueing networks under the assumption of exponentiality // J. Opl. Res. Soc. 1986. V. 37, No. 3. P. 309-316.
Chao X. A queueing network model with catastrophes and product form solution // Operations Research Letters. 1995. V. 18. P. 75-79.
Thomas N., Thornley D., Zatschler H. Approximate solution of a class of queueing networks with breakdowns // Proceedings of 17th European Simulation Multiconference, SCS Publishers, Nottingham, UK. 2003. P. 251-256.
Sauer C., Daduna H. BCMP networks with unreliable servers // Preprint No. 2003-01, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, Universitat Hamburg. 2003.
Цициашвили Г.Ш., Осипова М.А. Вероятностное распределение в сетях массового обслуживания с переменной структурой // Проблемы передачи информации. 2006. Т. 42, № 2. C. 101-108.
Sommer J., Berkhout J., Daduna H., Heidergott B. Analysis of Jackson networks with infinite supply and unreliable nodes // Queueing Systems. 2017. V. 87, is. 1-2. P. 181-207.
Статкевич С.Э., Маталыцкий М.А. Исследование сети массового обслуживания с ненадежными системами в переходном режиме // Вестник Томского государственного университета. Управление, вычислительная техника и информатика. 2012. № 1 (18). С. 112-125.
Баччелли Ф., Рыбко А.Н., Шлосман С.Б. Сети массового обслуживания с подвижными приборами - предел среднего поля // Проблемы передачи информации. 2016. Т. 52, № 2. С. 85-110.
Тананко И.Е. Метод оптимизации маршрутных матриц открытых сетей массового обслуживания // Автоматика и вычислительная техника. 2002. № 4. C. 39-46.
Вишневский В.М. Теоретические основы проектирования компьютерных сетей. М. : Техносфера, 2003. 512 с.