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Asymptotically achievable performance in ATM networks

Part of: Computer system organization Operations research and management science Special processes Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

Sem Borst  and
Debasis Mitra
Sem Borst*
Affiliation:
Bell Laboratories
Debasis Mitra*
Affiliation:
Bell Laboratories
*
∗ Postal address: Bell Laboratories, Lucent Technologies, P.O. Box 636, Murray Hill, NJ 07974-0636, USA.
∗ Postal address: Bell Laboratories, Lucent Technologies, P.O. Box 636, Murray Hill, NJ 07974-0636, USA.
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Abstract

The primary objective in the present paper is to gain fundamental understanding of the performance achievable in ATM networks as a function of the various system characteristics. We derive limit theorems that characterize the achievable performance in terms of the offered traffic, the admissible region, and the revenue measure. The insights obtained allow for substantial simplifications in the design of real-time connection admission control algorithms. In particular, we describe how the boundaries of admissible regions with convex complements may be linearized - thus reducing the admissible region - so as to obtain a convenient loss network representation. The asymptotic results for the achievable performance suggest that the potential reduction in revenue is immaterial in high-capacity networks. Numerical experiments confirm that the actual reduction is typically negligible, even in networks of moderate capacity.

Keywords

Achievable performanceATM networksconnection admission controlMarkov decision processesrevenue maximization

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 68M20: Performance evaluation; queueing; scheduling 90B15: Network models, stochastic 90B22: Queues and service 93E20: Optimal stochastic control
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 2 , June 1998 , pp. 568 - 585
Copyright
Copyright © Applied Probability Trust 1998 

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References

[1] Bean, N. G. (1993). Effective bandwidths with different quality of service requirements. In Integrated Broadband Communication Networks and Services, ed. Iversen, V. B., IFIP, 241–252.Google Scholar
[2] Boorstyn, R. R., Suh, J.-K., Kershenbaum, A. and Chennikara, J. (1995). An algorithm for call acceptance based on characterization of sources. Preprint. Polytechnic University, Brooklyn, New York.Google Scholar
[3] Elwalid, A. and Mitra, D. (1993). Effective bandwidth of general Markovian traffic sources and admission control of high speed networks. IEEE/ACM Trans. Netw. 1, 329–343.Google Scholar
[4] Elwalid, A. and Mitra, D. (1995). Analysis, approximations and admission control of a multi-service multiplexing system with priorities. In Proc. INFOCOM '95, Boston MA, pp. 463–472.Google Scholar
[5] Elwalid, A., Mitra, D. and Wentworth, R. H. (1995). A new approach for allocating buffers and bandwidth to heterogeneous, regulated traffic in an ATM node. IEEE J. Sel. Ar. Commun. Special Issue on the Fundamentals of Networking 13, 1115–1127.Google Scholar
[6] Faragó, A., Blaabjerg, S., Ast, L., Gordos, G. and Henk, T. (1995). A new degree of freedom in ATM network dimensioning: optimizing the local configuration. IEEE J. Sel. Ar. Commun. Special Issue on the Fundamentals of Networking 13, 1199–1206.Google Scholar
[7] Gibbens, R. J. and Hunt, P. J. (1991). Effective bandwidths for the multi-type UAS channel. Queueing Systems 9, 17–28.Google Scholar
[8] Hui, J. Y. (1990). Switching and Traffic Theory for Integrated Broadband Networks. Kluwer.Google Scholar
[9] Kelly, F. P. (1991). Effective bandwidths at multi-type queues. Queueing Systems 9, 5–15.Google Scholar
[10] Key, P. B. (1990). Optimal control and trunk reservation in loss networks. Prob. Eng. Inf. Sci. 4, 203–242.Google Scholar
[11] Lippman, S. A. (1975). Applying a new device in the optimization of exponential queuing systems. Operat. Res. 23, 687–710.Google Scholar
[12] Miller, B. (1969). A queuing reward system with several customer classes. Management Sci. 16, 234–245.Google Scholar
[13] Mitra, D., Morrison, J. A. and Ramakrishnan, K. G. (1995). ATM network design and optimization: a multirate loss network framework. In Proc. INFOCOM '96, San Francisco CA, pp. 994–1003.Google Scholar
[14] Reiman, M. I., Wang, J. and Mitra, D. (1995). Dynamic call admission control of an ATM multiplexer with on/off sources. In Proc. 34th CDC, New Orleans LA, pp. 1382–1388.Google Scholar
[15] Ross, K. W. (1995). Multirate Loss Models for Broadband Telecommunication Networks. Springer.Google Scholar
[16] Ross, K. W. and Tsang, D. H. K. (1989). Optimal circuit access policies in an ISDN environment: a Markov decision approach. IEEE Trans. Commun. 37, 934–939.Google Scholar
[17] Weiss, A. (1994). Equivalent bandwidth for a priority system. Unpublished notes.Google Scholar