Abstract
A modification of the iterative Takahashi—Takami method is discussed to calculate the distribution of the number of requests in the closed multiphase queueing systems. A method is proposed for calculating the moments of waiting time distribution. The results of the calculations are compared with those obtained from a simulation model.
The research described in this paper was partially supported by state research 0073-2018-0003.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Vishnevsky, V.M.: Theoretical bases of designing computer networks. Technosphere, Moscow (2003). (in Russian)
Bhat, U.N.: An Introduction to Queueing Theory. Springer, New York (2015)
Bolch, G., Greiner, S., de Meer, H., Trivedi, K.: Queueing Networks and Markov Chains: Modeling and Performance Evaluation with the Computer Science Applications. Wiley, Hoboken (2006)
Shin,Y.W., Moon, D.H. Sensitivity and approximation of M/G/c Queue: Numerical Experiments. In: 8 th International Symposium on Operational Research and its Applications, China, pp. 140–147 (2009)
Ryzhikov, Y.I.: Iterative method for calculating multi-channel service systems — bases, modifications and marginal capabilities distribution (in Russian). In: Proceedings of the 9th Russian Multiconference on Management Problems. Information Technologies in Management. State Scientific Center of the Russian Federation “Concern Elektropribor”, pp. 224–233, SPb (2016)
Ryzhikov, Y.I.: Modifications and perspectives of the matrix-geometric progression method (in Russian). Ibid., pp. 234–243
Seelen, L.P.: An algorithm for Ph/Ph/c queues. Eur. J. of Oper. Res. 23, 118–127 (1986)
Takahashi, Y., Takami, Y.: A Numerical Method for the Steady-State Probability of a GI/G/c Queuing System in a General Class. J. Operat. Res. Soc. Jpn 19(2), 147–157 (1976)
Ryzhikov, Y.I.: A package of programs for the calculation of systems with queues and its testing. In: Proceedings of the SPIIRAN. Issue 7. Science, pp. 265–284, SPb (2008) (in Russian)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Ryzhikov, Y. (2019). Calculation of the Closed Multi-channel Queueing Systems. In: Silhavy, R. (eds) Cybernetics and Algorithms in Intelligent Systems . CSOC2018 2018. Advances in Intelligent Systems and Computing, vol 765. Springer, Cham. https://doi.org/10.1007/978-3-319-91192-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-91192-2_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91191-5
Online ISBN: 978-3-319-91192-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)