THE INTERCONNECTION OF TELEPHONE SYSTEMS 



533 



analyses necessary to determine the theoretical probability (or the 

 proportion of times in the long run) that a particular subscriber will 

 find all of a group of trunks busy are well known ; and tables and curves 

 are available showing for wide ranges of loads and numbers of trunks 

 the probability of a particular subscriber finding them all in use.^ 



-CENTRAL OFFICE EXCHANGES- 



L 



n 



10 TRUNKS 





SJ B 



Fig. 2 — A simplified central office interconnection system. 



In Fig. 3 is shown the load, a, in average simultaneous calls which 

 theoretically may be submitted to c trunks so that, on the average, one 

 one-hundredth (P = .01), or one one-thousandth {P = .001), of all 

 the calls submitted will find no idle trunk available. By replotting 

 Fig. 3 to show as in Fig. 4 the average load carried per trunk (efficiency) 

 we see that a large group of trunks is relatively much more efficient 

 than a smaller one. 



For example, to carry a load of a = 41 at P = .01 we should provide 

 a single group of 57 trunks, while if we are required to carry the same 

 total load over groups of c = 16 trunks, we shall need five such groups 

 or a total of 80 trunks. That this should be so may become clearer 

 by considering, say 20 trunks, first as a complete group and then as 

 two split groups or subgroups of 10 trunks, each carrying one-half of 



2 "The Theory of Probabilities Applied to Telephone Trunking Problems," by 

 E. C. Molina, Bell System Technical Journal, November, 1922. 



