DELAY CURVES FOR CALLS SERVED AT RANDOM 117 



Table IV — Symmetric Functions for Exponential Sums, Mellor 



Approximation 



k = 2 ai = 3+a A; = 3 ai = 6 + 3« 



a2 = 2 a2 = 11 + 5a + 2a^ 



a3 = 6 



A- = 4 ai = 10 + 6a: 



a2 = 35 + 26a + 11«' 



as = 50 + 26a + 14a2 + Ga^ 



a4 = 24 



A - 5 ai = 15 + 10a 



a2 = 85 + 80a + 35a2 



as = 225 + 200a + 125a2 + 50a3 



ai = 274 + 154a + 94a2 + 54a3 + 24a* 



a, = 120 



A: = 6 ai = 21 + 15a 



a2 = 175 + 190a + 85a2 



as = 735 + 855a + 585a2 + 225a3 



a4 = 1624 + 1604a + 1194a2 + 704a3 + 274a4 



as = 1764 + 1044a + 684a2 + 444a3 + 264a* + 120a5 



as = 720 



that sketched above, and without determining Rs and Rq . Notice that 



which may be proved independently. All values in Table III satisfy 

 the recurrence relation 



hj = [k - (k - l)a]h-ij +[k+ (k- l)a]h-ij-i (35) 



— {k — 1) ahk-2,j-2 



which also satisfies the boundary relations for a = and 1 given above 

 for all values of k. 



The corresponding symmetric functions for the Mellor approximation 

 are given in Table IV. These have the recurrence relation 



akj = ak-i,j + [/c + (/c - l)a]ak-i,j-i - (k - 1) W-2.i-2 (36) 



For a = 0, the values are the signless Stirling numbers of the first 

 kind, that is, the numbers given by the expansion of 



(1 + x)(l + 2x) ••• (1 + kx). 



For a = 1, the results are the same as for the exact case, as given above. 



