 different service rates, = (111, um). The production function means the arrival process is memoryless (a Poisson arrival rate), the service of calls is memoryless (a Poisson service rate), there is one server for the calls, and there is no exogenous limit on the size of the queue. The Design and Costs of Networks would be a reduced form with optimal utilization of the m servers. 12 In addi- tion, the queue itself can be limited, with calls blocked and discouraged if they exceed the size of the buffer or waiting room. To represent the production func- tion of a general network, consider a network that serves total traffic Q with some quality level parameters W representing such characteristics as waiting time in a queue and the number of blocked calls. The backbone network has a set of nodes , n} that are connected by a set of links L = {(1, 2), (1, 3), } that is not necessarily complete. Let Kij be the capacity of each link ij in the set of links and let K represent the vector of these capacities. Let the set N represent the switches and other capital equipment associated with the nodes in the backbone network. Assume that the calls are dispatched efficiently given the configuration of the backbone network. Suppose also that the network is efficiently designed and operated given its configuration and the capacity of the links. Although calculating performance measures for complex networks is difficult and can require computer algorithms, suppose that such calculations have been made by network engineers. Then it is possible to describe an economic production function that relates the output of the service provided by the backbone network to the inputs of capital facilities at the nodes and the capacity of the links. Let X, Y, Z represent other economic inputs. Then the network's production function is = F(N, K, X, Y, Z; W). The network production function plays an important role in determining the costs of the network. Changes in the capacity of a link affect the network's quality of service in complex ways. The