Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-17T02:33:21.092Z Has data issue: false hasContentIssue false
  • English
  • Français

A mathematical model and related problems of optimal management and design in a broadband integrated services network

Published online by Cambridge University Press:  17 February 2009

Suzanne P. Evans
Suzanne P. Evans
Affiliation:
Teletraffic Research Centre, Dept. of Applied Mathematics, University of Adelaide, S.A. 5001.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper describes a mathematical model for a broadband integrated services network offered traffic of many different types. Performance measures are introduced related to revenue generation and overall grade-of-service, providing criteria for the optimal management of resources. Simple asymptotic expressions are derived for quantities termed the “implied costs”, which measure the effect on performance of changes in parameters that are controllable by network management, or that are subject to variation. These implied costs may be used, both to implement optimal bandwidth allocation polices, and also to indicate which services may share a single facility without adversely affecting performance, and which might require a dedicated facility. Asymptotic results are also used to examine how to make efficient use of capacity that is shared between calls with fluctuating bit-rate requirements.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 2 , October 1989 , pp. 150 - 175
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Addie, R. G., “B-ISDN protocol architecture and network reliability”, Proc. 3rd ATERB FPS Workshop (1988).Google Scholar
[2]Addie, R. G., Burgin, J. L. and Sutherland, S. L., “Information transfer protocols for the broadband ISDN”, Proc. GLOBECOM'88 (1988) 716–720.Google Scholar
[3]Addie, R. G. and Warfield, R. E., “Teletraffic engineering of new network structures”, Proc. 2nd Australian Teletraffic Research Seminar (1987).Google Scholar
[4]Burman, D. Y., Lehoczky, J. P. and Lim, Y., “Insensitivity of blocking probabilities in a circuit-switched network”, J. Appl. Prob. 21 (1984) 850–859.CrossRefGoogle Scholar
[5]Evans, S. P., “Integration of services and bandwidth allocation in a B-ISDN network”, Teletraffic Research Centre, University of Adelaide Rep. TRC 22(1988).Google Scholar
[6]Hunt, P. J. and Kelly, F. P., “On critically loaded loss networks”, Adv. Appl. Prob. 21 (1989).CrossRefGoogle Scholar
[7]Hunt, P. J., “Implied costs in loss networks”, Adv. Appl. Prob. 21 (1989).CrossRefGoogle Scholar
[8]Kaufman, J. S., “Blocking in a shared resource environment”, IEEE Trans. Commun. Vol. COM-29 (10) (1981) 1474–1481.CrossRefGoogle Scholar
[9]Kelly, F. P., “Blocking probabilities in large circuit-switched networks”, Adv. Appl. Prob. 18 (1986) 473–505.CrossRefGoogle Scholar
[10]Kelly, F. P., “Routing in circuit-switched networks: shadow prices and decentralization”, Adv. Appl. Prob. 20 (1988) 112–144.CrossRefGoogle Scholar
[11]Lasdon, L. S., Optimization theory for large systems (Macmillan, New York, 1970)Google Scholar
[12]Lundry, M. and Mees, A., “Convergence of the annealing algorithm”, Math. Programming 34 (1986) 111–124.CrossRefGoogle Scholar
[13]Mitra, D., Romeo, F. and Sangiovanni-Vincentelli, A., “Convergence and finite-time behaviour and simulated annealing”, Adv. Appl. Prob. 18 (1986) 747–771.CrossRefGoogle Scholar
[14]Morrison, D. F., Multivariate statistical methods (McGraw-Hill, 1967).Google Scholar
[15]Rao, C. R., Linear statistical inference and its applications (Wiley, New York, 1965).Google Scholar
[16]Roberts, J. W., “A service system with heterogeneous user requirements—application to multiservice telecommunications systems”, in Performance of data communications systems and their applications (ed. Pujolle, G.), (North-Holland, 1981) 423–431.Google Scholar
[17]Rockafellar, R. T., “Convex programming and systems of elementary monotonic relations”, J. Math. Anal. Appl. 19 (3) (1967) 543–564.CrossRefGoogle Scholar
[18]Wolfe, P., “Methods of nonlinear programming”, in Recent advances in mathematical programming (eds. Graves, R. L. and Wolfe, P.), (McGraw-Hill, New York, 1963) 67–86.Google Scholar
[19]Zuckerman, M. and Kirton, P., “Queueing analysis of a B-ISDN switching system”, Proc. 3rd ATERB FPS Workshop (1988).Google Scholar