Abstract
Application of the first jump separation technique for analysis of the tandem queueing system with high-intensive renewal arrival process, infinite number of servers and general service time distribution is presented in the paper. An equation for characteristic function of the multi-dimensional joint distribution of the number of customers at the system stages is derived. The equation is solved under an asymptotic condition of the infinite growth of the arrival rate. It is shown that the distribution under study can be approximated by the multi-dimensional Gaussian distribution. Numerical example shows the range of the approximation applicability.
This work is performed under the state order No. 1.511.2014/K of the Ministry of Education and Science of the Russian Federation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Gnedenko, B.W., König, D. (eds.): Handbuch der Bedienungstheorie: II. Formeln und andere Ergebnisse. Akademie-Verlag, Berlin (1984)
Grachev, V.V., Moiseev, A.N., Nazarov, A.A., Yampolsky, V.Z.: Tandem queue as a model of the system of distributed data processing. Proc. of TUSUR 2(26), part 2, 248–251 (2012) (in Russian)
Balsamo, S., De Nitto Personè, V., Inverardi, P.: On using Queueing Network Models with finite capacity queues for Software Architectures performance prediction. Performance Evaluation 51(2-3), 269–288 (2002)
Heindl, A.: Decomposition of general tandem queueing networks with MMPP input. Performance Evaluation 44(1-4), 5–23 (2001)
Kim, C., Dudin, A., Klimenok, V., Taramin, O.: A Tandem BMAP/G/1 → ∙ /M/N/0 Queue with Group Occupation of Servers at the Second Station. Mathematical Problems in Engineering 2012, Article ID 324604 (2012)
Gómez-Corral, A.: A Tandem Queue with Blocking and Markovian Arrival Process. Queueing Systems 41, 343–370 (2002)
Kingman, J.F.C.: On Queues in Heavy Traffic. Journal of the Royal Statistical Society. Series B 24(2), 383–392 (1962)
Korolyuk, V.S., Korolyuk, V.V.: Stochastic models of systems. Kluwer, Dordrecht (1999)
Bocharov, P.P., Pechinkin, A.V.: Queueing theory. RUDN, Moscow (1995) (in Russian)
Nazarov, A.A., Moiseeva, S.P.: The Asymptotical Analysis Method in Queueing Theory. NTL, Tomsk (2006) (in Russian)
Moiseev, A., Nazarov, A.: Investigation of high intensive general flow. In: Proc. of the IV International Conference, Problems of Cybernetics and Informatics (PCI 2012), pp. 161–163. IEEE, Baku (2012)
Kolmogorov, A.: Sulla determinazione empirica di una legge di distribuzione. Giornale Dell’ Intituto Italiano Degli Attuari 4, 83–91 (1933)
Moiseev, A.N., Nazarov, A.A.: Asymptotic analysis of a multistage queuing system with a high-rate renewal arrival process. Optoelectronics, Instrumentation and Data Processing 50(2), 163–171 (2014)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Moiseev, A. (2014). The First Jump Separation Technique for the Tandem Queueing System GI/(GI/ ∞ )K . In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds) Information Technologies and Mathematical Modelling. ITMM 2014. Communications in Computer and Information Science, vol 487. Springer, Cham. https://doi.org/10.1007/978-3-319-13671-4_34
Download citation
DOI: https://doi.org/10.1007/978-3-319-13671-4_34
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13670-7
Online ISBN: 978-3-319-13671-4
eBook Packages: Computer ScienceComputer Science (R0)