. (1978) Where do we stand on Maximum Entropy. In Kluwer Academic Press. The Maximum Entropy Formulism (ed. R.D. Levine and M. Tribus) M.I.T. Press. This page intentionally left blank Teletraffic theory RJ Gibbens MA, Dip Math Stat, PhD University of Cambridge Contents Introduction 5/3 Single link models 5/3 Network models 5/6 Dynamic routeing strategies 5/11 Bibliography 5/14 This page intentionally left blank Introduction 5/3 5.1 Introduction process since n either increases by one when a new call is accepted on the link or decreases by one when an existing call clears down. The subject of Teletraffic Theory has a long history dating back to The transition rates for the birth and death process are therefore the work of the Danish mathematician, A.K. Erlang (Brockmeyer, given by Equations 5.1 and 5.2. 1948), first published in 1917. Today the subject has grown enor- mously and is still growing at a rapid pace with research into the (5.1) performance modelling of areas as diverse as, for example, dynamic routeing strategies, cellular mobile radio systems and the applica- q(n,n-1)nn1,...,C (5.2) tion of fast packet switching techniques proposed for use in a broadband integrated services digital network. Hui (1990) is a good A general result, (Kelly, 1979) on birth and death processes gives text for some of these more recent developments. the equilibrium distribution in terms of the birth and death rates, as In Section 5.2 the basic model of a single link in a circuit switched in Equation 5.3 where is determined from the normalisation telecommunication network is studied. This section also introduces condition of Equation 5.4. the important control mechanism of trunk reservation. Section 5.3 shows how the single link models studied in Section (5.3) 5.2 can be incorporated into models of networks of links using the effective link independence approximation to construct the Erlang fixed point systems of equations. These equations allow the inves- tigation of the rich behaviour of dynamic routeing strategies in the (5