472 BELL SYSTEM TECHNICAL JOURNAL 



and the average delay on calls delayed is 



Case II — Holding Times Constant 

 Write X, the number of calls encountered by "A^," in the form 



X — nc -\- m — \, 



where n and m are positive integers such that m > r. In the Fig. 3 

 below these wc + w — 1 calls are shown in groups arranged according 



o 1 



-y o m 



c * t 



# W c ♦ m 



2 C 



2 c ♦ 1 

 *2 { 2 c • m 



3 c 



#n-1 



n c + 1 



n c • m - 1 = X 



n c ♦ m 



\ 



Operator no m lakes 

 care of these calls. 



dt 



Call under 

 consideration. 



Fi(.. .3 



to the order in which they originated. The first c calls are occupying 

 the trunks. Then n — \ groups, each consisting of c waiting calls, 

 are shown and finally a remainder of m — 1 waiting calls; our par- 

 ticular call "X" is the {nc + m)th. in order of time. 



Now evidently, as indicated in the figure, trunk number m will 



i 



