348 BELL SYSTEM TECHNICAL JOURNAL 



the right. The general scheme of Fig. 3 is not too far from standard methods, 

 although the contact load on the memory elements is still impractical. In 

 actual panel, crossbar and step-by-step systems the equivalents of the 

 memory boxes are given limited access to the lines in order to reduce the 

 contact loads. This reduces the flexibility of interconnection, but only by 

 a small amount on a statistical basis. 



4. Rel.\tiox to Information Theory 



The formula M = 2S log .V can be interpreted in terms of information 

 theory.- When a subscriber picks up his telephone preparatory to making 

 a call, he in effect singles out one line from the set of .Y, and if we regard 

 all subscribers as equally likely to originate a call, the corresponding amount 

 of information is log X . When he dials the desired number there is a second 

 choice from N possibilities and the total amount of information associated 

 with the origin and destination of the call is 2 log N. With S possible simul- 

 taneous calls the exchange must remember 25 log iV units of information. 



The reason we obtain the "separate memory" formula rather than the 

 absolute minimum memory by this argument is that we have overestimated 

 the information produced in specifying the call. Actually the originating 

 subscribers must be one of those not already engaged, and is therefore in 

 general a choice from less than N. Similarly the called party cannot be 

 engaged; if the called line is busy the call cannot be set up and requires no 

 memory of the type considered here. When these factors are taken into 

 account the absolute minimum formula is obtained. The separate memory 

 condition is essentially equivalent to assuming the exchange makes no use 

 of information it already has in the form of current calls in remembering 

 the next call. 



Calculating the information on the assumption that subscribers are 

 equally likely to originate a call, and are equally likely to call any number, 

 corresponds to the maximum possible information or "entropy" in com- 

 munication theory. If we assume instead, as is actually the case, that certain 

 interconnections have a high a priori probability, with others relatively 

 small, it is possible to make a certain statistical saving in memory. 



This possibility is already exploited to a limited extent. Suppose we have 

 two nearby communities. If a call originates in either community, the 

 probability that the called subscriber will be in the same community is 

 much greater than that of his being in the other. Thus, each of the exchanges 

 can be designed to service its local traffic and a small number of intercom- 

 munity calls. This results in a saving of memory. If each exchange has N 

 subscribers and we consider, as a limiting case, no traffic between exchanges, 



■' C. K. Shannon, "A Mathematical Theory of Communication," Bell Svstem Technical 

 Journal, Vol. 27, |)|). ,?70 42.^, and 62.S 6,S6, July and October 1948, 



