.4) setting of symmetric fully connected networks. This section on network based results ends with two bounds on the overall best possible behaviour of dynamic routeing strategies. Section 5.4 presents some of the dynamic routeing strategies that Hence, from Equations 5.1 and 5.2 one can obtain Equations 5.5 have been either implemented or proposed for real networks. This and 5.6. is an area which has received much attention over the last decade and is one in which teletraffic theory has provided the models and (5.5) understanding leading to more efficient, flexible and reliable net- works. (5.6) 5.2 Single link models 5.2.1 Erlang's loss formula In summary, the equilibrium distribution for the utilisation, n, of The first model to be considered is the classical model for a single a single link is given by Equation 5.7. link in a circuit switched network. Suppose that the arrival process of calls offered to a link is a Poisson process of rate A. Let the holding times of calls be exponentially distributed with a mean of 1 (5.7) independently of the arrival process. Suppose that the link has a (n=0,1,...,C) capacity of C circuits. See Figure 5.1 and Chapter 3 for an introduc- tion to the theory of stochastic processes applied to queueing net- works. This system may be modelled by the stochastic process, n, the number of circuits occupied by the link with n taking values in the In particular, the probability, L, that an arriving call finds the link range 0 to C inclusive. It can be seen that n is a birth and death full to capacity is °C given by Equation 5.8. Capacity C Traffic I Figure 5.1 Single link model 5/4 Teletraffic theory (5.8) E(A,C)= (5.11) This result can be derived by substituting the expression for Equation 5.8 is known as Erlang's loss formula and is undoubtedly E(A,C) given in Equation 5.9 and simplifying the resulting ex- the most widely used result in teletraffic theory. The standard pression. notation E(A,C) for the quantity given in Equation 5.9 will be used. For larger values of C, which make a 