 solution of the systems of Equation 5.37 where a is given by Equation 5.38. equations given by Equation 5.39. M=Infinity Arrival rate, l Figure 5.8 Loss probability with varying number of retries, M 5/10 Teletraffic theory (5.39) 5.3.3.2 Decentralised adaptive routeing strategy Note that the implied cost, Ck, can be written in the form shown in The values of 2 and Pk are given by Equations 5.40 and 5.41. Equation 5.46 (where Sr is given by Equation 5.47) in terms of observables such as the carried traffics on routes and links. (5.40) traffic on route link (Ck+s,) (5.46) (5.41) r:kEr jEr-k (5.47) Thus, Pk is simply the traffic offered to link k under the approxi- Hence, we may construct over time estimates of the implied costs mation procedure. It may be proved that Equations 5.42 and 5.43 ck and surplus values S. This might be achieved by using, for hold. example, moving average estimators. Suppose that the loss prob- ability, L, on route r has also been estimated by similar means. A call offered to route r will generate a net expected revenue of (1 - (5.42) L). Should this quantity be negative for any route then that route should be avoided: more revenue will be lost elsewhere in the network than can be generated by accepting calls on this route. (5.43) Otherwise, traffic should be shared out between possible routes so as to reflect the net expected revenues (1-L)s,- Routes with higher values of (1-L)s than others should receive an increased share of the traffic. Adjustments to routing patterns made on this basis will need to be gradual since the effect of increasing the traffic to a route The definition of Erlang's loss formula can be extended to non- will be to push up the loss probability of the route and the implied integral values of capacity C by linear interpolation and at integer cost c along that route, and hence reduce the net expected revenue values of C, define the derivative of W(v; C) with respect to Ck to (1-L)s be the left derivative. Equation 5.42 shows that the effect of increasing the offered