I 



THE OCCURRENCE AND EFFECT OF LOCKOUT 275 



per cent of time locked out from the circuit constants. Since this is 

 proportional to the repetition rate, a measure of relative circuit per- 

 formance is obtained in terms of the circuit constants. 



As an example of such calculations let us assume that t,„ = tJ 



= Te = T,.', T — T and T = T\ and /i,„ = h,^ = 2t,„ + a. Then the 

 constants of integration determined in the appendix become, 



a = a, 



b = a -\- T - T, 



c = a + 2" -f T, 



and the probability of a lasting lockout is proportional to 



"a+T+T n^ r'y+T+T 



P 



Xa r^a+T+T n^ r'y+T+T 



p2{y)dy I pi(x)dx + I p2iy)dy I pi{x)dx. (7) 



Values of this probability for a = 0.1 are shown in Fig. 8 as a function 

 of the transmission time T with r, the delay between the suppressors as 

 a parameter and in Fig. 9 as a function tJT with 7" as a parameter. 

 The curves are not extended beyond T — 0.5 since smaller values are 

 thought to cover the range of practical interest. Furthermore, for 

 large values of T there is some evidence that the effect of the transmis- 

 sion time would be noticed by the subscribers with a consequent change 

 in the distributions of resumption and response times. 



These curves indicate that for a constant value of r, the delay be- 

 tween the echo suppressors, there is little change in the probability of 

 lockout as the total delay of the circuit T is increased, and for a constant 

 value of T the probability of lockout is approximately proportional to t. 



To continue with a more specific example, let us consider a telephone 

 connection consisting of two four-wire circuits each equipped with an 

 echo suppressor in the center of the circuit as shown in Fig. 10. In the 

 notation of Fig. 10 the relay hangovers are each equal to r + 0.100 

 and the constants of integration are 



a = 0.100, 



b = 0.100 + r, 



c = 0.100 + 3t. 



Since the two circuits are assumed equal, only lasting lockouts are 

 theoretically possible and the curves of Fig. 8 may then be used to 

 determine p in terms of r as defined by equation (7), which in turn may 

 be used to determine the expected number of lockouts from equation 

 (3). The mean duration of lockout is obtained by inserting the value 



