540 BELL SYSTEM TECHNICAL JOURNAL 



empirical investigations of the graded multiple problem.^ These have 

 included successively or progressively-graded multiples as well as 

 those involving only a single set of subgroups feeding into a simple 

 group of common trunks. They conclude that for more than two 

 subgroups the successive grades are somewhat advantageous and the 

 highest efficiencies are to be gotten when there is " a smooth progression 

 from individuals to commons." That is, the number of trunks in each 

 subgroup of individuals, pairs, fours, eights and commons, should be 

 very nearly equal, and in general "no grading should be used, if it can 

 be avoided, in which the actual number of circuits required to the next 

 rank exceeds half the maximum possible number. ^ An 18-group 

 grading, for example, should not be used when more than 90 circuits 

 are required. . . . These specific data are, of course, with reference 

 only to the gradings of 10-contact switches." 



Finally, a very interesting field of study has been opened up through 

 the design of an artificial traffic machine by Messrs. E. A. Elliman 

 and R. W. Eraser of the Standard Telephones and Cables, Ltd.^" In 

 the particular machine constructed two group gradings with all arrange- 

 ments of individuals and commons up to hunts of 25 could be simu- 

 lated. In the single examples given of straight and graded groups 

 the results showing the load per trunk appear to be closely in accord- 

 ance with their expected values. If a more flexible mechanism could 

 be devised and tested to insure concordance with practice a most 

 valuable contribution to the art of trunking would be made. 



In the Mathematical Appendix I of this paper Mr. E. C. Molina 

 sets forth the analytical theory for simple (single-stage) symmetrical 

 graded multiples as originated and practiced (with certain modifica- 

 tions to be mentioned later) by the Bell System. The present method 

 of estimating the probability of loss, knowing the arrangement of 

 trunks and the average load submitted per subgroup, is the natural 

 outgrowth of several preliminary formulas each of which was closely 

 studied and compared with the actual conditions to be met in 

 operation. 



The four governing assumptions which need careful scrutiny in the 

 final formula presented in this paper are : 



1. The holding time of all calls is assumed to be constant. 



2. A call not receiving immediate service is held in waiting for its 

 normal holding time period, and if an available trunk becomes idle it 

 will occupy it till this period is completed. This is usually referred to 

 as the "lost calls held" assumption. 



8G. F. O'Dell: "An Outline of the Trunking Aspect of Automatic Telephones." 

 The Journal of the Institntioji of Electrical Engineers, vol. 65, February, 1927. 



9 By "next rank" is meant, for instance, second selectors followmg first selectors. 



10 Elliman and Fraser: "An Artificial Traffic Machine for Automatic Telephone 

 Studies." Electrical Communication, October, 1928. 



