DELAY CURVES FOR CALLS SERVED AT RANDOM 113 



Mo) may be fitted exactly by solution of 2k equations of form (25), as 

 will be shown. 



The first approximation (k = 1) is the order of arrival curve, say 



F,{u) = 6-^'-"^" 



which has Ai = Xi = 1, Ak = Xk = 0, k > 1, and matches Mo and Mi . 

 The next approximation (/c = 2) is determined from equations 



Ai + A2 =1 



AiXi + ^-20:2 = 1 



Aixl + A2X2 = R2 



Aixl + A2XI = R^ 



Eliminating A2 from successive pairs, 



Ai (xi — 0:2) = 1 — X2 



AiXi (xi — X2) = R2 — X2 



Aixl{xi — X2) = R-i — R2X2 



Eliminating Ai from these, 



2:1 + 0:2 — 0:1X2 = R2 



(26) 



{xi + X2)R2 — 0:10:2 = Ri 



or, writing ai = 0:1 + 0:2 , 02 = 0:1X2 , so that x^ — aiX -\- a2 = {x — Xi) 



{x — X2) 



ai — a2 = R2 



(26a) 



aiR2 — a2 = Rz 

 From the first of the second set of equations, and from symmetry (or 

 from Ai + A2 = I) 



1—0:2 



Ai = 

 A2 = 



Xi — X2 



1 - xi 



X2 — Xi 



(27) 



f Taking R2 and R^ from Table II, it turns out that 



Xi"' = 1 - VW^ = 2Ai 

 X2~' = 1 + vW2 = 2A2 



(28) 



