raffic non Suppose now that calls arrive to be connected between nodes i and coincidence whereby not all the nodes in the network reach their j(i,j=1,2,..,).) = as a Poisson process with rates hij and that as the peak traffic at the same time of day. In international networks, and pair {i, j} varies it indexes independent Poisson streams. Suppose in trunk networks of geographically large countries, such hourly non also that a connected call has a duration which is arbitrarily dis- coincidence is due to the presence of multiple time zones. tributed with unit mean, is independent of earlier arrival times and Figure 5.9 shows an example of how this might operate in prac- call durations and of the node pair {i, j}, and is unknown to the tice. Traffic between Boston and Miami during the morning peak dynamic routeing strategy at the time of the call arrival. Let L be the period may experience congestion on the direct route. A sequence overall network loss probability. Then it may be shown that a lower of alternative routes for this time of day might be to attempt bound on L is provided by l, the optimum attained in the linear overflowing via Chicago, then to try via Phoenix and then finally programme of expression 5.54 subject to expressions 5.55 and 5.56. San Francisco using links which are only lightly congested with direct traffic thanks to the time zone effect which makes the peak (5.54) periods for traffic between San Francisco and Boston and between minimise San Francisco and Miami, say, occur a few hours later in the day. In DNHR these patterns are calculated in a network management centre at intervals of months with weekly updates using data on traffics and circuit capacities provided by the nodes. This procedure is integrated within a large scale optimisation procedure for updat- iES,jES ing the link capacities to cope with the growth in forecasted traffic demands. By taking advantage of idle capacity which can be found (5.55) in the network due to traffic non coincidence overall network cost savings can be ac