DELAY CURVES FOR CALLS SERVED AT RANDOM 



119 



For a = 0.9, results for four exponentials have also been obtained 

 and compare with those of Table V as follows {k = number of ex- 

 ponentials) : 



It is somewhat surprising that two exponentials should do as well as 

 they do for large values of v (in fact for 2; = 12 and 14 better than three) ; 

 a similar behavior appears in the following comparison of approxima- 

 tions on the Mellor basis, again for a = 0.9 



From these comparisons, it appears a relatively small number of 

 exponentials is sufficient for engineering purposes. The curves of Fig. 1 

 are those for three exponentials, for uniformity. 



BIBLIOGRAPHY 



1. Erlang, A. K., L0sning af nogle Problemer fra Sandsynlighedsregningen af 



Betydning for de automatiske Telefoncentraler. Elektroteknikeren 13, p. 5, 

 1917; The Life and Works of A. K. Erlang. Copenhagen, pp. 138-155, 1948. 



2. Molina, E. C, Application of the Theory of Probabilities to Telephone Trunk- 



ing Problems, Bell System Tech. Jl., 6, pp. 461-494, 1927. 



3. Mellor, J. W., Delayed Call Formulae when Calls Are Served in a Random 



Order. P.O.E.E.J. 25, pp. 53-56, 1942. 



4. Vaulot, E., Delais d'attente des appels tdl^phoniques trait^s an hazard. Comp- 



tes Rend. Acad. Sci. Paris 222, pp. 268-269, 1946. 



5. Pollaczek, F., La loi d'attente des appels t^l^phoniques, Comptes Rend. Acad. 



Sci. Paris 222, pp. 353-355, 1946. 

 6 Riordan, J., Triangular permutation numbers. Am. Math. Soc, Proc, 2, pp. 

 429-432, 1951. 



