Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T22:35:06.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Coupled Processor: A Second-Order Continuous-State-Space Model

Published online by Cambridge University Press:  27 July 2009

Haruhisa Takahashi
Haruhisa Takahashi
Affiliation:
Department of Communications and Systems The University of Electro-Communications Chofu, Tokyo, 182 Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

A second-order continuous-state-space model for two-dimensional queueing systems is developed in this article. A particular problem is treated but the results can apply to some other two-dimensional queueing problems directly. The generating function for the model is obtained by applying a Riemann boundary value problem and leads to a computationally feasible solution.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 2 , April 1990 , pp. 277 - 298
Copyright
Copyright © Cambridge University Press 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Coffman, E.G. & Mitrani, I. (1975). Selecting a scheduling rule that meets prespecified response time demands. Proceedings of the 5th Symposium on Operating Systems Principles, Austin, TX.Google Scholar
Fayolle, G. & Iasnogorodski, R. (1979). Two coupled processors: The reduction to a RiemannHubert problem. Zeitschrift für wahrscheinlichkeitstheorie und verwandte. Gebiete 47: 325–351.CrossRefGoogle Scholar
Konheim, A.G., Meilijson, I. & Melkman, A. (1981). Processor-sharing of Two Parallel Lines. Journal of Applied Probability 18: 952–956.CrossRefGoogle Scholar
Cohen, J.W. & Boxma, O.J. (1983). Boundary value problems in queuing system analysis. New York: North-Holland.Google Scholar
Feller, W. (1954). Diffusion processes in one dimension. Transactions of the American Mathematical Society 77: 1–31.CrossRefGoogle Scholar
Gelenbe, E. (1975). On approximate computer system models. Journal of the Association for the Computing Machinery, 22: 261–269.CrossRefGoogle Scholar
Coffman, E.G. & Reiman, M.I. (1983) Diffusion approximations for computer/communication systems. In Iazeolla, G., Courtois, P.J., & Hordijk, A. (eds.) International Workshop on Applied Mathematics and Performance Reliability Models of Computer Communication Systems. Amsterdam: North-Holland, pp. 169–188.Google Scholar
Whitt, W. (1971). Weak convergence theorems for priority queues: Preemptive resume discipline. Journal of Applied Probability 8: 74–94.CrossRefGoogle Scholar
Harrison, J.M. (1973). A limit theorem for priority queues in heavy traffic. Journal of Applied Probability 10: 907–912.CrossRefGoogle Scholar
Takahashi, Y. (1986). Mean-delay approximation for a single server priority queue with general low-priority arrival process. Transactions of the IECE Japan (Section E) E69: 1173–1179.Google Scholar
Foschini, G.J. (1981). Equilibria for diffusion models of pairs of communicating computers - symmetric case. IEEE Transactions Infor Theory lT-28: 273–284.CrossRefGoogle Scholar
Gakhov, F.D. (1966). Boundary value problems. Oxford: Pergamon Press.CrossRefGoogle Scholar
Ito, K. (1952). Probability theory. Tokyo: Iwanami.Google Scholar
Takahashi, R. (1979). Complex analysis. Tokyo: Tchikuma.Google Scholar
Malyshev, V.A. (1972). An analytical method in the theory of two-dimensional positive random walks [translated from Sibirskii]. Mathematicheskii Zhurnal 13(6): 1314–1329.Google Scholar
Takahashi, H. & Takahashi, Y. (1989). Notes on conservation laws for preemptive priority queues. Transactions of the IECE, Japan Vol. E72, No. 8, 08.Google Scholar
Takahashi, H. Stationary multidimensional diffusion process with jump-return motion. Submitted for publication to Stochastic Processes and Their Applications.Google Scholar