recursive computation impractical, a second method is available which avoids the direct (5.9) calculation of large factorials. After some re-arrangement Equation 5.12 may be obtained. (5.12) Later the question of how best to compute E(A,C) in such a way as to reduce numerical inaccuracies caused by rounding errors will be considered. First, let us look at some of its properties. Written in this form each successive term in the summation is a In Figure 5.2 the loss probability L= E(A,C) is shown as a function of the traffic intensity p = N/C for C held fixed at the values C = simple multiple of the previous one and so direct calculation of 100, 250, 1000 and 10000. This figure demonstrates the important factorials may be avoided. The final sum is then inverted to give the trunking efficiency effect where for a fixed level of the traffic loss probability. intensity, p, the loss probability, L, decreases with increasing link capacity, C: larger links are more efficient at carrying calls. Also 5.2.2 Multiple priorities and trunk reservation shown in the figure is the limiting case as C increases to infinity which is given by Equation 5.10. Consider again a single link with C circuits but now suppose that there are two independent Poisson arrival streams offered at rates = max ( 1-1.01 (5.10) A1 and A2. Suppose we wish to give priority to the calls at rate A1 over those at rate A2. A very simple mechanism has been devised to implement these priorities known as trunk reservation. In this mech- anism, calls of the low priority stream are only accepted when there 5.2.1.1 Numerical considerations are at least I + 1 free circuits available. In contrast, the high priority calls are accepted so long as there is at least 1 free circuit available. Several methods are available for the efficient and accurate numeri- The integer value, I, is known as the trunk reservation parameter. An cal evaluation of Erlang's loss formula. For small values of C, equivalent notation which is sometimes more convenient is to let C perhaps up to 