426 BELL SYSTEM TECHNICAL JOURNAL 



The values in Table I indicate that, when a liberal number of trunks, i.e., 

 ten trunks, is provided, the numerical difiference between the results of the 

 two formulae is small and the results of either formula can be used as an 

 approximation of the number of calls affected by an all-tru,iks-busy con- 

 dition. There are undoubtedly repetitious attempts, but because the 

 number is small their effect can be neglected. 



When, however, there is a serious shortage of trunks, as when only fiV'e 

 trunks are provided, the numerical difference between the theoretical results 

 of the two formulae is large. In addition, the repetitious attempts will be 

 too numerous to ignore. Some of the repetitious attempts will encounter 

 all trunks busy again and again. Other repetitious attempts will seize idle 

 trunks thereby causing new calls to encounter all trunks busy. The effect is 

 cumulative. Neither the Poisson nor the Erlang B Formula indicates to 

 what extent the repetitious attempts take place nor their effect. A pre- 

 liminary glimpse at the results of this study indicates that 150 calls of 100 

 seconds average holding time when submitted during an hour to five trunks 

 become inflated by 99 repetitious attempts and appear as 249 calls being 

 submitted to the trunks. Of these 249 calls, 108 encounter all trunks busy. 

 Of the 108 calls, 99 become the aforementioned repetitious attempts and 

 nine are abandoned. It is evident that neither formula presents this 

 picture. For studies considering the effect of overloads due to trunk short- 

 ages, this is the type of information needed. A new approach is required to 

 obtain such data. To do this, it is desirable to examine the habits of dial 

 subscribers who have encountered busies. 



The Dialing Behavior of Subscribers upon Encountering a Busy 



In order to investigate the grade of service given to dial subscribers when 

 trunk shortages occur it is desirable to know something about their behavior 

 when they encounter all-trunks-busy signals. Specifically there are four 

 items that need investigation; these are: — 



1. How soon after encountering an all-trunks-busy signal does the sub- 



scriber redial his call? 



2. What percentage of the subscribers make subsequent attempts? 



3. How do the time intervals between successive subsequent attempts 



compare with each other; that is, are they about the same or do they 

 differ widely? 



4. What differences, if any, exist between classes of subscribers? 



The first three items are answered from the results of service observations. 

 The fourth item is answered indirectly. 



The service observations consisted of 1,107 cases where line busies were 

 observed (except for 35 cases of all-trunks-busy signals). Observations on 



