Memory Requirements in a Telephone Exchange

A G E N E R A L telephone exchange with N subscribers is indicated schematically in Fig. 1. The basic function of an exchange is that of setting up a connection between any pair of subscribers. In operation the exchange must "remember," in some form, which subscribers are connected together until the corresponding calls are completed. This requires a certain amount of internal memory, depending on the number of subscribers, the maximum calling rate, etc. A number of relations will be derived based on these considerations which give the minimum possible number of relays, crossbar switches or other elements necessary to perform this memory function. Comparison of any proposed design with the minimum requirements obtained from the relations gives a measure of the efficiency in memory utilization of the design. Memory in a physical system is represented by the existence of stable internal states of the system. A relay can be supplied with a holding connection so t h a t the armature will stay in either the operated or unoperated positions indefinitely, depending on its initial position. It has, then, two stable states. A set of N relays has 2 s possible sets of positions for the armatures and can be connected in such a way that these are all stable. The total number of states might be used as a measure of the memory in a system, but it is more convenient to work with the logarithm of this number. T h e chief reason for this is that the amount of memory is then proportional to the number of elements involved.