several hundreds of circuits, E(A,C) can be computed be the capacity available to calls of priority i or lower so that C1 = using the recursive formula of Equation 5.11 and E(A,0) = 1. C and C2 =C-I. C=100 C=250 C=1000 C=10000 C=Infinity Figure 5.2 Erlang's blocking formula Single link models 5/5 Again, a birth and death process can be used to model the system. 5.2.2.1 Optimality criterion for r The transition rates are now given by Equations 5.13 and 5.14. Consider the situation given by Equations 5.17 and 5.18. (5.13) q (n,n+1)= (5.17) q(n,n-1)n n1, (5.14) (5.18) B2(+) - k=C-r The equilibrium distribution, using the general result in Equation 5.3 is given, after some re-arrangement, by Equation 5.15, where is determined by Equation 5.16. Then B (r) and B,(r) are the blocking probabilities to the high and low priority streams respectively when the trunk reservation par- ameter level is set at the value r. (5.15) A criterion for choosing r, which is applicable in much of the work n=0,....,C-r n=C-r+1,.... C to follow on control in routeing strategies in fully connected net- works, is to minimise with respect to I the expression of 5.19. (5.19) (5.16) = = 1 This would correspond to a valuation by the link that the carrying of a low priority call is worth just half the carrying of a high priority The above procedure to avoid computing large factorials in Er- call. Here we think of high priority calls as the directly routed calls lang's loss formula can also be used here to calculate the distribution and the low priority calls as the overflow calls using two links. In Figure 5.3 the value of I minimising expression 5.19 is illus- Two criteria for selecting the trunk reservation parameter r will trated with 21 held fixed in such a way that E(A,C) = 1% for two now be considered. values of C. C=500 C=100 10000 Overflow traffic, As Figure 5.3 Optimality criterion 5/6 Teletraffic theory The value of expression (5.19) is relatively insensitive to r above A rationale for choosing the trunk reservation parameter is then to 