DELAYED EXPONENTIAL CALLS SERVED IN RANDON ORDER 383 



t/h, we have 



P{>t/h) = P(>0) F{u) = (7(c, a) F{u) (4) 



Values of P(>0) = C{c, a) are given for a wide range of a and c in Fig. 

 21. The appUcation of equation (4) is quite simple. 



Illustration 1 . Suppose it is desired to obtain the probabihty of a call 

 being delayed more than 3 holding times on a 10 trunk group without 

 storage or gating circuits, and which carries a = 9 erlangs. Here t/h = 

 3.0, c = 10,a = 0.9. Then u = ct/h = 30, and reading on Fig. 20 with 

 this value of u, and a = 0.9, we find F{u) = 0.080. Fig. 21 provides 

 C{c, a) = 0.67 for a = 9 and c = 10. Substituting in equation (4), 



P(>3 hold times) = 0.67 (0.080) = 0.053, 



which checks the value read directly from the c = 10 curves of Fig. 15. 

 Illustration 2. With an occupancy of a = 0.65 on 15 paths what is the 

 probability of meeting a delay greater than one holding time when 

 delayed calls are served in random order? Calculate u = ct/h = 15. 

 Enter with this abscissa on Fig. 20, and interpolating between the 

 a = 0.6 and 0.7 curves, read F{u) = 0.022. Fig. 21 shows for a = 0.65(15) 

 = 9.75 and c = 15, C(c, a) = 0.085. Hence 



P(>1 hold time) = 0.085(0.022) = 0.0019. 



