Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T08:08:50.441Z Has data issue: false hasContentIssue false
  • English
  • Français

Teletraffic engineering for product-form circuit-switched networks

Published online by Cambridge University Press:  01 July 2016

Keith W. Ross  and
Danny Tsang
Keith W. Ross*
Affiliation:
University of Pennsylvania
Danny Tsang*
Affiliation:
University of Pennsylvania
*
∗Postal address: Department of Systems, University of Pennsylvania, Philadelphia, PA 19104, USA.
∗∗Present address: Department of Mathematical Statistics and Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3JJ.
Get access Rights & Permissions [Opens in a new window]

Abstract

We develop a performance modeling methodology for product-form circuit-switched networks. These networks allow for: arbitrary topology and link capacities; Poisson and finite population arrivals; multiple classes of calls, each class with a different route and bandwidth requirement; conference as well as point-to-point calls. The methodology is first applied to generalized tree networks, which consist of multiple access links feeding into a common link. Each access link may support multiple ‘long-distance' classes (requiring circuits only on the access link and on the common link) and multiple ‘local' classes (requiring circuits only on the access link). For generalized tree networks an efficient algorithm is given to determine the blocking probabilities. The methodology is then applied to hierarchical tree networks, where traffic is repeatedly merged in the direction of a root node.

We also establish a ‘Norton' theorem for product-form circuit-switched networks. This theorem implies that for any given calling class, the entire network can be replaced by an Erlang loss system with a state-dependent arrival rate, without modifying the equilibrium probabilities for the particular calling class.

Keywords

TELEPHONE NETWORKSREVERSIBILITYCONVOLUTION ALGORITHMSNORTON'S EQUIVALENT
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 657 - 675
Copyright
Copyright © Applied Probability Trust 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.)

Footnotes

Research supported partially through AT & T grant 5-27628 and partially through NSF Grant NCR-8707620.

References

[1] Aho, A. V., Hopcroft, J. E. and Ullman, J. D. (1974) The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass.Google Scholar
[2] Arthurs, A. and Kaufman, J. S. (1979) Sizing a message store subject to blocking criteria. In Performance of Computer Systems, ed. Arato, M., Butrimenko, A., and Gelenbe, E., North-Holland, Amsterdam, 547–564.Google Scholar
[3] Bachle, A. (1973) On the calculation of full available groups with offered smoothed traffic. In Proc. 7th Internat. Teletraffic Conference, Stockholm, 223/1–223/6.Google Scholar
[4] Brockmeyer, E., Halstrom, H. L. and Jensen, A. (1948) The Life and Works of A. K. Erlang. The Copenhagen Telephone Co., Copenhagen.Google Scholar
[5] Burman, D. Y., Lehoczky, J. P., and Lim, Y. (1984) Insensitivity of blocking probabilities in a circuit-switching network. Adv. Appl. Prob. 21, 850–859.CrossRefGoogle Scholar
[6] Chandy, K. M., Herzog, U. and Woo, L. S. (1975) Parametric analysis of queueing networks. IBM J. Res. Devel., 19, 43–49.CrossRefGoogle Scholar
[7] Dziong, Z. and Roberts, J. W. (1987) Congestion probabilities in a circuit-switched integrated services network. Performance Evaluation 7, 267–284.CrossRefGoogle Scholar
[8] Jagerman, D. L. (1974) Some properties of the Erlang loss function. Bell Syst. Tech. J. 53, 525–551.Google Scholar
[9] Kaufman, J. S. (1981) Blocking in a shared resource environment. IEEE Trans. Comm. 29, 1474–1481.Google Scholar
[10] Kelly, F. (1986) Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob. 18, 473–505.Google Scholar
[11] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
[12] Mitra, D. (1987) Asymptotic analysis and computational methods for a class of simple, circuit-switched networks with blocking. Adv. Appl. Prob. 19, 219–239.Google Scholar
[13] Roberts, J. W. (1981) A service system with heterogeneous user requirements. Performance of Data Communications Systems and their Applications, 423–431.Google Scholar
[14] Ross, K. W. and Tsang, D. (1989) Optimal circuit access policies in an ISDN environment: a Markov decision approach. IEEE Trans. Comm. 37, 934–939.Google Scholar
[15] Ross, K. W. and Tsang, D. (1989) The stochastic knapsack problem. IEEE Trans. Comm. 37, 740–747.CrossRefGoogle Scholar
[16] Ross, K. W. and Yao, D. D. (1988) Monotonicity properties of the stochastic knapsack. IEEE Trans. Inf. Theory. To appear.Google Scholar
[17] Schwartz, M. (1987) Telecommunication Networks: Protocols, Modeling and Analysis. Addison-Wesley, Reading, Mass. Google Scholar
[18] Schwartz, M. and Kraimeche, B. (1983) An analytic control model for an integrated node. In Infocom 83, San Diego, 540–546.Google Scholar
[19] Tsang, D. and Ross, K. W. (1989) Algorithms for determining exact blocking probabilities in tree networks IEEE Trans. Comm. To appear.Google Scholar
[20] Whitt, W. (1985) Blocking when service is required from several facilities simultaneously. AT&T Tech. J. 64, 1807–1856.Google Scholar