40 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



The individual contributions of these four factors to discrepancies 

 between theory and observation are not easy to assess. The first three 

 explain a tendency for test calls to get ahead of calls already waiting 

 for dial tone. On Figs. 3 to 6, inclusive, additional theoretical dial 

 tone delay curves, curves B, for the case where a dial tone tester 

 always gets first in line are shown. Even these curves tend to lie above 

 the curves of the observed data on Figs. 4 and 5 where ten line finders 

 were available; they more nearly agree with the observed data on Fig. 3 

 where twenty line finders were available, and they lie below the observed 

 data on Fig. 6 where 34 line finders were available. This is an indication 

 of the fact that with higher traffic loads (which occurred on the larger 

 line finder groups) a test call will encounter more competition from 

 other calls and therefore will have a lesser chance of gaining precedence 

 over all of the other calls. The fourth factor indicates that the call 

 attempts served on line finders consist of two distinct holding time 

 universes and not just one, as was assumed in the development of the 

 dial tone tester formula. The effect of the presence of both a short and 

 long holding time universe of calls would be to introduce a change of 

 slope in the delay curves which may be seen in Figs. 3 to 6 to be at about 

 t = 4 seconds. There is reason to believe that the same cause may have 

 been responsible for the tendency of the observed delay curves to fall 

 away from the theoretical at the lower levels of load carried. 



Due to the reasons given above and to the fact that the dial tone 

 delay observations were made by the test call method, the above re- 

 sults may not directly describe service from the customer's point of 

 view. Conny Palm has developed the following formula which gives a 

 slightly different measure of customers' dial tone service. It indicates 

 the proportion of calls which have neither received dial tone nor have 

 dropped out at time t. 



POO = POO) yWJAa/j)e.p i-t/H)] ^^p (_^/^) ^^„) 

 y(c/j, a/j) 



Curves for this formula are shown plotted on Fig. 1(a) and at C on 

 Figs. 3 to 6. They are quite close in many cases to the observed dial 

 tone tester results. It would appear that a sufficiently good estimate 

 of the customer's dial tone service, whatever its precise definition, can 

 be obtained by the dial tone tester method. 



Recently revised tables for the capacity of step-by-step line finders 

 have been published for Bell System use based on Palm's formula using 

 a factor of j = 5. This was selected as being slightly conservative for 



