 blocking state correspond- ing to many calls being carried on two-link routes and a low Now examine the issue of implied costs (see Kelly, 1990) in the blocking state corresponding to only a few calls carried over two context of fixed routeing strategies. Suppose that the circuit links with the majority carried on one-link routes. switched network consists of links labelled k = 1,2, K with link k comprising Ck circuits. A subset r U {1, 2, ..., K} identifies a route. Trunk reservation has been found to be an ideal way of preventing Calls requesting route r arrive as independent Poisson processes of this bistable behaviour in the network performance and for provid- rate Vr. A call requesting route r is blocked and lost if on any link k ing more efficient use of network resources. In Figure 5.7 the loss E r there are no free circuits. Otherwise, the call is connected and probability, L, is shown as a function of r for values M = 1 and 5, simultaneously holds one circuit on each link k E r for the holding a = 110, and C = 120. Observe that a value of r in a broad range will period of the call. The call holding period is independent of earlier give close to optimal performance. arrival times and holding periods; holding periods of calls on route Now consider the effect of increasing the number of retries M. r are identically distributed with unit mean. Write R for the set of Figure 5.8 shows the loss probability for varying a and C = 120 and possible routes. for various values of the retry parameter M. The curves are obtained The Erlang fixed point equations for this set up are as in Equation by choosing the optimal choice of r for each traffic (as in Figure 5.35 and the proportion of calls requesting route r that are lost is given by Equation 5.36. Network models 5/9 0 05- Trunk reservation parameter, r Figure 5.7 Optimal choice of r (5.35) W(v;C) = , (5.37) (5.36) (5.38) Suppose that a call accepted on route I generates an expected revenue w. The rate of return from the network will be as in ...., c) be the unique