hieved. In a case study of a 24 node network model it was reported that with DNHR the trunk cost was reduced by about 15% compared with fixed routeing strategies. In international net- (5.56) works even greater savings of the order of 25% have been reported. 5.4 Dynamic routeing strategies 5.4.2 Learning automata Advances in the technology of modern telecommunication systems Learning automata schemes have been applied to telephone rou- have led to considerable interest in schemes which can dynamically teing problems (see Narenda, 1983). They continually offer calls control the routeing of calls within a network. The purpose of such across the available routes r = 1, 2,...,R, say, for calls between each dynamic routeing schemes is to adjust routeing patterns within the source destination node pair according to a probability distribution network in accordance with varying and uncertain offered traffics, (pr:r=1,2,...,R). This probability distribution is updated over time to make better use of spare capacity in the network resulting from according to the acceptance or rejection of offered calls. A scheme dimensioning upgrades or forecasting errors, and to provide extra can thereby reward a route on which a call is successful and punish flexibility and robustness to respond to failures or overloads. a route on which a call fails. Two approaches in particular have received considerable atten- For example, the learning automation scheme called up- tion. In the United States, AT&T (see Ash, 1981) implemented a dates the route selection probabilities as follows. If route i is chosen scheme called Dynamic Non-Hierarchical Routeing (DNHR) which at time step n and the call is successful then Equations 5.57 and 5.58 uses traffic forecasts for different times of day in a large scale are used. 5/12 Teletraffic theory Boston San Francisco Chicago Phoenix Miami Figure 5.9 DNHR alternative routes (n+1)=p(n)a1-p(n)] (5.57) via a tandem node. The call is attempted on this route with trunk reservation applied against it on both link