Optimum network call-carrying capacity

A telephone network with switching and trunk congestion is considered. An optimization problem expressed in terms of mean numbers of calls and mean rates of flow of calls in various categories of service throughout the network is formulated. The maximum mean number of talking calls given by this optimization problem is an upper bound on the mean number of talking calls which could be carried by the network using theoretically optimum network management. Examples are given suggesting that the upper bound is close to values which actually can be attained. The optimum of the problem is achieved by controls which (i) restrict the number of calls coming into the network from the end offices and (ii) route appropriate fractions of the remaining calls over the various possible routes.