DIALING HABITS OF TELEPHONE CUSTOMERS 35 



line group studied. Additional dial tone tests were made on all other 

 line groups in the office as a check that the delays experienced on the 

 line groups under stud}'- were not due to a sender shortage. The sender 

 data on the tapes were also used for this purpose. Figs. 1(a) to 1(d), 

 and 2(a) to 2(d), inclusive, show for various amounts of load carried, 

 the per cent of dial tone tests encountering delays greater than three 

 and greater than ten seconds for half-hour study periods for the most 

 frequent number of line finders in the tests for each class of service. 



Plotted on each of these figures is a theoretical fitting dial tone tester 

 dela}" curve computed for the indicated dial tone delays and for the 

 f ollowmg j factor values in the generalized trunking formula, determined 

 in a manner to be explained later: 



To indicate the effect of varying j, several curves have been added 

 to Fig. 1(a). Selections of curves for^ = 0, 1 and <» (which correspond 

 to the three commonly used infinite source congestion formulae, Erlang 

 C, Poisson and Erlang B when adapted to the tester's delay problem) 

 are shown. It is clear that with the wide differences in delays which they 

 give for specified loads carried, it is highly desirable to select that j 

 formula for engineering use which most nearly describes the customer 

 actions in any situation being dealt with. In the field of curves shown 

 on Fig. 1(a), the one labelled j = 6.6 was derived in a logical manner 

 from the data, and shows an agreeably satisfactory fit. For example, 

 during a heavy load period when, say, 20 per cent of a dial tone tester's 

 calls are meeting delays greater than 3 seconds, an actual average load 

 of 16.6 erlangs (as showTi by the j = 6.6 curve) would likely be carried. 

 (Load in erlangs equals average number of simultaneous calls.) The 

 Erlang C (j = 0) and Poisson (j = 1) theories would indicate the 

 presence of loads of 15.6 and 16.0 erlangs, respectively, figures clearly 

 too small for the circumstances shown by the data of Fig. 1(a). On the 

 other hand, use of the Erlang B (j = oo ) theory would predict a con- 

 siderably larger load carried, about 17.9 erlangs, than one would prob- 

 ably be justified in assuming here for engineering purposes. 



By grouping the dial tone delay data by bands of load carried, rela- 

 tionships of per cent of test calls encountering varying dial tone delays 



