267 Congestion Probabilities in a Circuit-Switched Integrated Services Network Zbigniew Dziong Institute of Telecommunications, Warsaw University of Technologv, Nowowiejska 15/19, 00-655 Warsaw; Poland James W. Roberts Centre National d'Etudes des T~l&ommunications, 38-40, rue du G~n&al Leclerc, 92131 lssy les Moulineaux, France Received 10 January 1987 Revised 3 May 1987 We derive recurrence relations enabling the direct calculation of the joint distribution of the number of busy channels in a circuit-switched network whose offered traffic streams require a variable number of channels on each link. Approximate congestion probability calculation methods are developed based on the estimation of marginal link occupancy distributions taking account of link traffic correlation. These approximations are tested on a number of simple two-link examples. Keywords: Integrated Services Digital Network, End-to-End Blocking, Multi-Rate Circuit Switching, Joint Occupancy Distribu- tion, Link Traffic Correlation. I. Introduction We consider the problem of evaluating congestion probabilities in circuit-switched telecommunication networks when the number of channels seized by a call on each link of its path is a variable determined by Zbigniev Dziong was born in Poland in 1952. He received his M.Sc. and Ph.D. degrees from the Warsaw University of Technology, Poland in 1974 and 1980, respectively, both in Electrical Engineering. He is currently an Assistant Professor at the Warsaw University of Technology where he lectures on digital switching systems and modelling and performance evaluation of telecommunications systems. His current research interests include modelling and optimisation of communication networks, teletraffic theory and system design methodology based on the CCITT defined System Description Language. He has taken sabbatical leave at the Centre National d'Etudes des T~16communications, France (six months in 1985/1986) and at the Department of Communication Systems, Lund Institute of Technology, Sweden (three months in 1987). James W. Roberts received the B.Sc. degree in Mathematics from the University of Surrey, United Kingdom n 1970. He worked from 1971 to 1975 in the Teletraffic Division of the British Post Office before moving to Zrance to join the company SOCOTEL. He has been with the Centre National d'Etudes des T616communica- ions since 1978 where he has worked on different aspects of teletraffic and performance evaluation. His :urrent interests include the performance evaluation problems arising in multiservice networks with )articular emphasis on the integration of high bit rate services. North-Holland Performance Evaluation 7 (1987) 267-284 0166-5316/87/$3.50 © 1987, Elsevier Science Publishers B.V. (North-Holland)