Simplified Analysis of Queueing Systems with Random Requirements
In this work, a simplification approach for analysis of queueing systems with random requirements is proposed. The main point of the approach is to keep track of only total amount of occupied system resources. Therefore, we cannot know the exact amount of resources released by the departure of a customer, so we assume it a random variable with conditional cumulative distribution function depending on only number of customers in the system and total occupied resources at the moment just before the departure. In the chapter, we briefly describe the queuing system with random requirements, the simplification method and show that in case of Poisson arrival process simplified system has exactly the same stationary probability distribution as the original one.
KeywordsQueuing system Limited resources Probabilistic characteristics Insensitivity
The reported study was supported by the Russian Science Foundation, research project No. 16-11-10227. We thank Prof. Valeriy Naumov for the methodic assistance and scientific guidance in the preparation of this chapter, as well as for the constant and invaluable attention to our scientific work.
- 3.Naumov, V.A., Samouylov, K.E.: On the modeling of queuing systems with multiple resources. Bull. Peoples Friendsh. Univ. Rus. Math. Inf. Sci. Phys. 1(3), 58–62 (2014)Google Scholar
- 4.Naumov, V., Samuoylov, K., Sopin, E., Andreev, S.: Two approaches to analysis of queuing systems with limited resources. In: Proceedings of 7th international congress on ultra modern telecommunications and control systems and workshops, 585–588 (2014)Google Scholar
- 6.Naumov, V., Samuoylov, K., Sopin, E., Yarkina, N., Andreev, S., Samuylov, A.: LTE performance analysis using queuing systems with finite resources and random requirements. In: Proceedings of 8th international congress on ultra modern telecommunications and control systems and workshops, 100–103 (2015)Google Scholar
- 9.Naumov, V., Samuoylov, K., Sopin, E.: On the insensitivity of stationary characteristics to the service time distribution in queuing system with limited resources. In: Proceedings of 9th international workshop on applied problems in theory of probabilities and mathematical statistics, 36–40 (2015)Google Scholar