1030 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



the following differential difference equations: 



[O if X < 8 



P^ix) + nP,{x) = 

 P,'{x) + \P,{x) = 



-(a+m)<s 



if X > 5, 



if X > 5, 



P2{x - 8)fjLe 

 if X ^ d 

 Prix - 8)\e~''^''' 

 F'(x) + (X + M)/^(.r) = \P,{x) + fiP.ix), 

 Pi(0) = P2(0) - F(0) = 1. 



These have been solved on a general purpose analog computer with i 

 the aid of a lumped-element approximate delay line for a number of : 

 cases. We have chosen for illustrative purposes the parameters A = 5, 

 M = 10, 5 = 0.02, and L ^ 1. The exact solution, together with various 

 approximations to be described in the sequel, is plotted in Fig. 8, where 

 the exact solution is labelled yi . 



1.0 



0.9 



0.8 



LU 

 (J 



z 

 111 

 9 



u 



z 



o 

 o 



o 



z 



IL 



o 



0.7 



0.6 



0.5 



0.4 



0.3 



0.2 



0.1 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



L 



Fig. 8 — Probability of no coincidences between two one-dimensional Poisson 

 patterns with X = 5, m = 10, if 5 = 0.02. 



