Abstract
This paper reviews some recent advances in the use of queueing network models for computers and communications networks. It emphasizes the relation between the martingale approach and quasi-reversibility. A brief discussion of optimal design and control is included.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. Arley and V. Borchsenius, On the theory of infinite systems of differential equations and their application to the theory of stochastic processes and the perturbation theory of quantum mechanics, Acta Mathematica, 76, (1945), p. 261–322
F. Baskett, M. Chandy, R. Muntz and J. Palacios, Open, closed and mixed networks of queues with different classes of customers, Journal of the A.C.M., 22 (1975), p. 248–260.
R. Boel, P. Varaiya and E. Wong, Martingales on jump processes; II: Applications, SIAM Journal on Controls, 13 (1975), p. 1022–1061.
R. Boel and P. Varaiya, Optimal control of jump processes, SIAM J. on Control and Optimization, 15 (1977), p. 92–119.
R. Boel, Martingale methods for the semi-Markov analysis of queues with blocking, in preparation.
P. Brémaud, La méthode des semi-martingales en filtrage quand l’ observation est un processus ponctuel marqué Séminaire de Probabilités X, Lecture Notes in Mathematics, vol. 511, p. 1–18, Springer 1976.
P. Brémaud, On the output theorem of queueing theory, via filtering, J. Applied Probability, 15 (1978), p. 387–405
P. Brémaud, Streams of a M/M/l feedback queue in statistical equilibrium, z. Wahrscheinlichkeitstheorie u. verw. Geb., 45 (1978), p. 21–33
P. Courtois, Decomposability — queueing and computer system applications, Academic Press, 1977.
W. Feller, An introduction to probability theory and its applications, volume 2, 2nd. ed., Wiley, 1971
J. Jackson, Networks of waiting lines, Operations Research, 5 (1957), p. 518–521.
F. Kelly, Reversibility and stochastic networks, Wiley, 1979
D. Kennedy, Some martingales related to cumulative sum tests and single-server queues, Stochastic Processes and their Applications, 4 (1976), p. 261–269
L. Kleinrock, Queueing systems, vol. I: Theory, 1975; vol. II: Computer applications, 1976, Wiley.
H. Kobayashi and A. Konheim, Queueing models for computer communications system analsyis, IEEE Trans, on Communications, COM — 25 (1977), p. 2129.
B. Melamed, Characterization of Poisson traffic streams in Jackson queueing networks, Advances in Applied Probability, 11 (1979), p. 422–439.
M. Sobel, Optimal operation of queues, in Mathematical Methods in Queueing Theory, A.B. Clarke, ed., Lecture Notes in Economics and Mathematical Systems, vol. 98, Springer, 1973.
J. Walrand and P. Varaiya, Interconnections of Markov chains and quasi-reversible queueing networks, to appear in: Stochastic Processes and their Applications, 10 (1980)
J. Walrand and P. Varaiya, Flows in queueing networks; a martingale approach; preprint, 1979.
M. Yadin and S. Zacks, Adaptation of the service capacity in a queueing system which subjected to a change in the arrival rate at unknown epoch, Technical Report no. 30, Dept. of Math, and Stat., Case Western Reserve University, 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 D. Reidel Publishing Company
About this paper
Cite this paper
Boel, R. (1981). Stochastic Models of Computer Networks. In: Hazewinkel, M., Willems, J.C. (eds) Stochastic Systems: The Mathematics of Filtering and Identification and Applications. NATO Advanced Study Institutes Series, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8546-9_9
Download citation
DOI: https://doi.org/10.1007/978-94-009-8546-9_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-8548-3
Online ISBN: 978-94-009-8546-9
eBook Packages: Springer Book Archive