THE OCCURRENCE AND EFFECT OF LOCKOUT 277 



pends upon the characteristic time intervals in conversational speech. 

 The values which have been calculated with experimentally determined 

 constants are shown to agree with the observed values. 



The average duration of lockouts has been found to be proportional 

 to the hangovers of the relays effective in lockout. 



Since the per cent of time locked out is equal to the product of the 

 average number of lockouts per hundred seconds and the average dura- 

 tion of lockouts, it may be determined in terms of the circuit constants, 

 and used as one of the criteria of the relative performance of the circuits 

 under consideration. 



Specific examples of such calculations have been used to illustrate the 

 relations between the expected number of lockouts and the circuit con- 

 stants, and between the repetition rate and the constants of a particular 

 circuit configuration. 



Subject to certain restrictions on the relations between the circuit 

 constants, it appears that the number of lockouts and the resulting in- 

 crease in repetition rate are approximately proportional to the delay 

 included between the echo suppressors. 



In conclusion I wish to express my appreciation to my associates who 

 have contributed to this study; in particular to Dr. G. R. Stibitz who 

 first developed the theoretical approach to the problem, to Mr. W. R. 

 Bennett and Mr. B. D. Holbrook who have contributed to the extension 

 of this approach, and to Mr. A. C. Norwine and Mr. O. J. Murphy who 

 obtained the distribution functions used in the calculations and con- 

 ducted the experimental work. 



Appendix 

 To assist in formulating an expression for the probability of lockout 

 a number of simplifying assumptions have been made, as follows: 



Pauses in speech are sufficiently separated to be considered as 

 independent events, or in other words the sequence of events oc- 

 curring at one pause have no effect upon those occurring at another. 



Following a pause each speaker can start speaking only once and 

 only one of three events can occur. 



1. The original speaker regains control of the circuit. 



2. The other speaker obtains control of the circuit. 



3. Lockout occurs. 



Resumption and response times are independent. 



The distributions of response and resumption times are inde- 

 pendent of the delay of the circuit and the disposition of the echo 

 suppressor. 



The operate times of the suppressors are sufficiently small to be 

 neglected. 



