Commenced in January 2007
Paper Count: 30076
About Analysis and Modelling of the Open Message Switching System
Abstract:The modern queueing theory is one of the powerful tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing systems, arising in the networks theory and communications theory (called open queueing network). The authors of this research in the sphere of queueing theory present the theorem about the law of the iterated logarithm (LIL) for the queue length of a customers in open queueing network and its application to the mathematical model of the open message switching system.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072146Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 987
 N. H. Bingham, Variants of the law of the iterated logarithm. Bulletin London Mathematical Society, 18, 1986, 433-467.
 D.L. Iglehart Multiple channel queues in heavy traffic. IV. Law of the iterated logarithm. Zeitschrift f ┬¿ur Wahrscheinlicht-Keitstheorie und Verwandte Gebiete, 17, 1971, 168-180.
 F.I. Karpelevich and A.I. Kreinin, Heavy traffic limits for multiphase queues. American Mathematical Society, Providence, 1994.
 Knessl C., Tier C. (1999a). Two tandem queues with general renewal input. I and II. SIAM J. Appl. Math., 59(6), 1917-1959, 1960-1997 (electronic).
 Knessl C., Tier C. (1999b). A diffusion model for two tandem queues with general renewal input. Comm. Statist. Stochastic Models, 15(2), 299-343.
 Ya. Kogan and A. Pukhalskii, On tandem queues with blocking in heavy traffic. Performance-84 (Paris, 1984), North-Holland, Amsterdam,1985, 549-558.
 Ya. Kogan and A. Pukhalskii, Tandem queue with finite intermediate waiting room and blocking in heavy traffic. Problems Control Inform. Theory, 17(1), 1988, 3-13 (in Russian).
 S. Minkevi╦çcius, On the law of the iterated logarithm in multiphase queueing systems, Lithuanian Mathematical Journal, 35, 1995, 360 -369
 S. Minkevi╦çcius, On the law of the iterated logarithm in multiphase queueing systems. II,Informatica, 8, 1997a, 367 - 376.
 S. Minkevi╦çcius, Complex transient processes in multiphase queueing systems. Lietuvos Matematikos Rinkinys, 37(4), 1997b, 519-531 (in Russian).
 S. Minkevi╦çcius and G. Kulvietis. Application of the law of the iterated logarithm in open queueing networks 2011 (to be published)
 L. L. Sakalauskas and S. Minkevi╦çcius, On the law of the iterated logarithm in open queueing networks. European Journal of Operational Research, 120, 2000, 632 - 640.
 V. Strassen, An invariance principle for the law of the iterated logarithm. Zeitschrift f┬¿ur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 3, 1964, 211-226.