THE OCCURRENCE AND EFFECT OF LOCKOUT 



269 



mining the average number of lockouts per hundred seconds and the 

 average duration of lockouts in terms of the circuit constants and ob- 

 taining the per cent of locked out time as the product of these two 

 quantities. 



The average, or expected number of lockouts per hundred seconds 

 can be approximately determined from the circuit constants and the 

 distributions of response and resumption times. It is shown in the 

 appendix that, subject to certain assumptions, the probability of lock- 

 out following a pause is given by 



^ = \ \ p'^^^ p^^y^ ^^ ^y^ 



(1) 



in which ^i(.r) dx and poiy) dy are the probabilities that, following a 

 pause, the resumption time will be between x and x + dx and the re- 



<0 12 



0.5 1.0 



TIME IN SECONDS 



1.5 



2.5 



Fig. 4 — Observed distribution of resumption and response times. 



sponse time will be between y and y + dy. As suitable approximations 

 to these probabilities we may take the observed distributions of re- 

 sumption and response times. Mr. Norwine and Mr. Murphy, in their 

 accompanying paper, ^ give distributions of resumption and response 

 times which are shown in Fig. 4. These distributions are expressed in 

 terms of the total number of resumptions, or responses and conse- 

 quently the data are an approximation to the conditional probability 

 that if a resumption or response has occurred, the resumption or re- 

 sponse time will be between / and t + dt. The use of these data will 



^ Loc. cit. 



