532 BELL SYSTEM TECHNICAL JOURNAL 



is no possibility of the line being busy; the only faults a subscriber may 

 properly find with the service (over and above transmission troubles) 

 are that "the called party is busy" on another line, and "he does not 

 answer," conditions beyond the control of the interconnecting system. 

 For a very small number of subscribers all in close proximity such a 

 scheme would and does serve admirably. As soon as the number of 

 subscribers, "«," is increased, however, the number of lines, which 



equals —^ — ^ -, goes up at an enormous rate, almost as the square 



of the number of subscribers. Since a major element of the cost is in 

 direct variation with the number of lines this plan, even on a modest 

 scale, is quickly prohibited. 



Nevertheless, if a truly universal service is to be furnished it must 

 not only be possible for any subscriber to communicate directly with 

 any other, but it must be easily possible. This problem was solved 

 by the development of the central office plan of interconnection. 



Elementary Studies 



We may represent a simplified central office exchange system by the 

 line diagram of Fig. 2. Two sets of 100 subscribers, A and B, may 

 make calls to the opposite set via the 10 "trunks" C} A line which 

 connects an individual subscriber to his central office exchange is 

 unique in that it will never be used except when he is talking. The 

 lines C, however, which are provided for establishing connections 

 between the telephones in one office and those in the other may well 

 carry calls originated by a large number of subscribers. Thereupon 

 it is readily seen that one interoffice line (or trunk, as we shall hereafter 

 call it) may easily attain a very much higher efficiency, as measured 

 by the per cent time it is in use, than an individual subscriber's line. 

 \\'hen one subscriber is not using a particular trunk it is available 

 for use by another; thus we make one trunk do the w^ork for which 

 two or more lines were required in the original arrangement of Fig. 1. 



To obtain this increased call carrying capacity per trunk and the 

 consequent savings due to reduction in the total number of trunks, 

 it is necessary to forego one particular advantage: we cannot be ab- 

 solutely sure that there will be an idle trunk available when each 

 subscriber desires to place his various calls. For it is possible, although 

 very improbable, that all of the subscribers might want to call one 

 another simultaneously, and having far fewer trunks than subscribers 

 in either office many would fail to get immediate service. The 



1 For our purpose it is unnecessary to consider how two subscribers within the 

 set A, or the set B, may be interconnected. 



