48 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



the equivalent expression: 



Ny='j^J{z-\-y) 



(19) 



where A''^ = The average number of waiting calls that drop out per unit 

 of time during the state {z + y). 

 y = The number of waiting calls. 

 z = The number of Hne finders occupied with calls. 

 1/H = A measure of the rate at which calls tend to abandon 

 waiting. 

 f(z -\- y) = The proportion of time that the state {z + y) exists. 



On the tapes we can measure f(z + y) and count A'"^^. Hence H can 

 be determined. The result is a statistical quantity subject to many- 

 chance factors. In the actual analysis of a tape, the composite average 

 value of H was determined for all possible observed states where calls 

 were waiting. By an analogous process, the composite average value 

 of h for all possible observed states where calls were being served by 

 line finders was determined. Also as a side computation, a composite 

 average value of h' for calls that were served by line finders but for 

 which no peg counts were scored was determined. This value of h' is 

 included in h on the basis that data for engineering line finders consist 

 of estimated calls based on peg counts and of holding times which in- 

 clude an allowance for these short holding time calls. The average 

 values of H, h and of the j factor for the four classes of service studied 

 are given in Table III. 



The results for H by individual half hours and by various percentages 

 of dial tone delays greater than three secolids are shown on Figs. 7(a) 

 to 7(d) respectively for the four classes of service. On some of these 

 figures an upward bulge may be noted in the center. This is not con- 

 sidered to be characteristic of the habits of the subscribers but is the 

 overall effect resulting from a number of arbitrary mles followed in 

 making the analysis in order to simplify the work and to offset par- 



Table III 



Message rate individual 

 Message rate two-party 

 Flat rate individual. . . . 

 Coin 



Average Values in Seconds 



24 

 42 

 27 



74 



159 

 243 

 176 

 153 



j = h/H 



6.6 

 5.8 

 6.5 

 2.1 



