,4) was 100 calls, then combined traffic on the other three links increases by 300 calls. Removing link (1, 4) also removes the possibility of indirect traffic that would travel on that link if there were congestion on any of the other three links. Therefore, removing one link affects service quality throughout the network. The stress on the network is far greater than the traffic that traveled on the missing segment. Again, the nodes and links of the backbone network form an integrated system. Removal of a critical node or link has effects on final network output that are not easily isolated to the specific network element. 3. Production Functions for a Multioutput Network The production function of a network applies also to multiple outputs. Suppose the network produces J outputs. Then H(Q1,..., , QJ, N, K, X, Y, Z) =0 is a production function specifying the outputs Q1 QJ that are produced using a network with nodes N, links with capacities K, and other economic The Design and Costs of Networks inputs X, Y, and Z. The list of outputs of the network can represent many things, including A set of point-to-point connections, such as city pairs; A set of outputs of varying service qualities, such as regular and priority ser- vice; A set of services distinguished by types of uses of the network, such as local versus long distance; A set of distinct services, such as data versus voice transmission or wireline versus mobile service; or A set of services distinguished by the classes of customers who receive that service, such as residential, commercial, and industrial customers. The production function not only illustrates tradeoffs between inputs as alter- native ways to produce particular outputs. The production function also illustrates tradeoffs between outputs for given levels of inputs. This latter tradeoff is known as the production possibility frontier (PPF). It must be emphasized that networks have limited capacities. Technological innovations such as computerized switching and optical transmission have vastly 