a low threshold. Thus, while minimising the value of r can be quite relate a and C by Equation 5.23, where B > 0 is a fixed constant, sensitive to the precise values of C, 2 l' and 22 close to optimal and to take the trunk reservation parameter, R(C), as in Equation 5.24 for some constant K with 1 < K < 1/B. performance over a wide range of values of C, 21 and 22 can be obtained by quite a crude choice of the parameter r. E(A,C) = B (5.23) R (C) = min{r:B(A,C,r)s = KB} (5.24) 5.2.2.2 Secondary criterion for r Suppose that fresh traffic alone would suffer a blocking prob- A further criterion which may be applied to selecting the trunk ability of B. Then the trunk reservation mechanism with parameter reservation parameter r is as follows. The approach begins by first r = R(C) chosen in accordance with this criterion ensures that the recognising that the offered traffics in a network are in practice very blocking probability for fresh traffic under arbitrary conditions of uncertain and large low priority overflow traffics may occur. Trunk overflow traffic is no worse than K times that without overflow reservation may then be used to guarantee performance in the worst traffic. Figure 5.4 gives some examples of R(C) with several values case conditions of infinite overflow traffic, where the number of of the parameter K. circuits in use on a link is forced to remain in the states {C-r, C}, where r > 0 is the trunk reservation parameter. Then the transi- tion rates for the birth and death process are simply as in Equations 5.20 and 5.21. Network models g(n,n+1)=n=C-,.,-1 = (5.20) 5.3.1 Erlang fixed point q(n,n-1)nn=C-r1,, (5.21) In section 5.2 models of a single link was described. In this section the scope will be broadened to investigate models of networks of If B(A,C,r) is the blocking probability for fresh traffic under these links. The simplest, and most commonly used, approach to creating circumstances then Equation 5.22 may be obtained. a model of a network of links is to use an approximation that blockings on li