se effects are mitigated by optimal dispatch of calls over the backbone network, which in turn takes account of possible congestion effects in other parts of the network. The effects of changes in the capacity of a link Kij cannot be presumed to have smooth effects, because of possible discrete effects on network performance. This is even more the case with the addition or removal of a critical link or node, because the configuration of the backbone network will necessarily change. To illustrate these issues, consider a simple backbone network with four nodes and four links, as shown in Figure 2.9. Suppose that distinct sets of calls originate or terminate through node 1 or through node 3, SO that calls are switched either through the path 123 or through the path 143. The performance of the network thus depends on the capacity of all four links. Suppose that any of these links is removed, say for instance the link between nodes 3 and 4. Then, given the way that calls are switched over the backbone network, the link between nodes 1 and 4 becomes useless because it is no longer possible to connect nodes 1 and 3 through node 4. Accordingly, all traffic is switched to links (1,3) and (2, 3). The capacity of 12 This corresponds to an underlying MM M/00 queue. If the queue with m servers is limited to size k, then it is an M/M/m/k queue Networks in Telecommunications Figure 2.9. A backbone network with four nodes and four links. the backbone network is then entirely dependent on the smaller of the capacities of the two links K13 and K23. To give another example, suppose that all four nodes originate and terminate traffic from distinct populations. Again, remove the link between nodes 1 and 4. Then all calls must travel over the remaining three links. One interesting conse- quence of this is that direct connections between nodes 1 and 4 are replaced by the indirect route passing through nodes 3 and 2. Thus, the direct traffic on one link, K14, is added to traffic on each of the other three links. If direct traffic on (1