2000 Fiscal Year Final Research Report Summary
Approximation of Queueing Networks : Theory and Applications
| Project/Area Number |
11640138
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kanagawa University |
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Principal Investigator |
YAMADA Keigo Faculty of Engineering, Kanagawa University, Professor, 工学部, 教授 (90111369)
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| Co-Investigator(Kenkyū-buntansha) |
ABE Yosihiro Faculty of Engineering, Kanagawa University, Professor, 工学部, 教授 (10159452)
KINO Issei Faculty of Science, Kanagawa University, Professor, 理学部, 教授
NARITA Kiyomasa Faculty opf Engineering, Kanagawa University, Professor, 工学部, 教授 (10211450)
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| Project Period (FY) |
1999 – 2000
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| Keywords | queueing system / approximation theory / integral of renewal process / diffusion approximation / Bessel process / large deviation theory / fractal Brownian motion / multi layer queueing system |
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| Research Abstract |
(A) The development of the theory of diffusion approximation and applications (1) The conditions under which the stohastic integrals with respect to renewal processes converge to Ito integrals were clarified. The result was applied to the diffusion approximation of queueing systems with vacations which were modeled as non-Markov processes and we showed that the approximation processes were sticky reflecting Brownian motions. This fact was applied to establish a method of evaluating cost performances of queueing networks. (2) Occupation time problems for Bessel proceses with constant drifts and Levy processes were studied, and we extended the results obtained by Papanikolau and T.Yamada by treating the more large class of occupation functions. We also showed that as the limit processes for occupation times, it is possible to obtain the fractional derivatives and integrals of local times of Bessel processes and Levy processes. By applying these results, we obtained a method of evaluating
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the cost and reliability performances when these are expressed as the additive functionals of processes in queueing systems.
(B) Application of large deviation theory to queueing systems (1) We analysed the asymptotics and singular pertarvation for the distributions of first passage times of Ehrenfast type Markov models. (2) An analysis was done for stochastic pertarvation of the solutions of Duffing type Lorez equations. We also analysed the solutions of these equations when Brownian motions are replaced by fractional Brownian motions. These results was applied for developing a method of analysis of queueing systems having long dependence arrivals.
(C) Stability of multi-layer queueing systems (1) Developed was a method for predicting SMP type systems of queueing networks, and the applicability of this method was verified by using real data of networks. (2) A method was developed for obtaining an approximation of limiting distribution of stochastic behavior of two layer queueing systems. Less
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