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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.
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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 

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Footnotes

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

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