DELAYED EXPONENTIAL CALLS SERVED IN RANDOM ORDER 



361 



10" 



10 15 20 25 30 35 40 45 50 55 60 



t/h = DELAY IN MULTIPLES OF AVERAGE HOLDING TIME 



65 



Fig. 1 — Distribution of delays. Theory versus throwdown, delayed calls han- 

 dled at random, c — 2 paths, a = 0.90, 3000 throwdown calls. 



THROWDOWN CHECKS 



Before calculating a field of curves for working purposes it was thought 

 desirable to make at least a modest throwdown test, or traffic simulation, 

 at these high occupancies to observe the agreement of theoretical delays 

 with those determined by a trial in which the theoretical assumptions 

 would be closely followed. This has now been performed at two trunk 

 group sizes, c = 2 paths, loaded by approximately a = 1.8 erlangs or 

 an occupancy of a = 0.90, and c = 10 paths at an occupancy of ap- 

 proximately a = 0.80. 



For these throwdo^^^ls, random origination times were obtained 

 through use of Tippett's Random Numbers. An hour was visualized as 

 being composed of 100,000 (or, as in one case, 1 million) consecutive dis- 

 crete intervals, numbered serially. Choosing 5 (or 6) digit random num- 

 bers then provided the start times of the subscribers' bids for service. 



Likewise holding times were chosen by random numbers from an 

 exponential universe by dividing it into 100 equal probability segments 

 and assigning each a number from 00 to 99. A central value of holding 

 time was chosen to represent the range of cases within each segment. 

 The last segment, number 99, on the long tail was further subdivided 

 into 100 parts in order to give more definition in the long call lengths 

 which are believed to be critical. 



I 



