DELAY CURVES FOR CALLS SERVED AT RANDOM 115 



Using Table II for values of the R's, it is found that 



• ai = (18 -7a- 2a') (2 - a)-\3 - 2a)-' 



^2 =18 (2 - a)"'(3 - 2a)-' (31) 



as = 6 (2 - a)-\3 - 2a)-' 



a;i , a;2 and 0^3 are then the roots of the cubic equation 



x^ — aix' + a2X — aa = 



The coefficients Ai , i = 1, 2, 3 are determined from equations like 



A = ^2 — {xi + x^ + 3:2X3 /„ s 



(:ci — 2:2) (xi — 0:3) 



For the fourth approximation, matching 8 moments, the equations 

 for the symmetric functions are 



CLiRz — (I2R2 ~h ^3 — cii = R\ 



aiRi — aiRz -\- a^H^ — a^ = Rt, 



cliRq — cLiRh ~\~ clzRa ~ CI4R3 = Ri 



and 0:1 , a:2 , Xz and x^ are roots of the quartic equation 



x^ — aix^ + a2X^ — azx -\- a4 = 



Coefficients Ai are determined from equations like 



. _ Rz — (x2 -{• X3 + Xi)R2 + (x2a;3 + 3:23:4 + x^x^) — ^2X3X4 ,^4) 

 (xi — 0:2) (xi — a:3)(a:i — 0:4) 



It may be noted that 



3:2 + xs + X4 = ai — xi 



X2XZ + 0:23:4 + 3:33:4 = a2 — xi(ai — xi) 



3:23:33:4 = az — Xi[a2 — Xi{a — Xi)] = a^i 



which gives the general structure. 



It is worth noting that equations (33) may be used to determine the 

 7^'s if the a's may be determined otherwise. As a matter of fact, they 

 have led to the determination of Rt and Ri in the following way. The 



(33) 



