364 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



5 10 15 20 25 30 35 40 45 50 55 60 65 70 



t/h = DELAY IN MULTIPLES OF AVERAGE HOLDING TIME 



Fig. 4 — Distributions of delays on 2 paths by groups of 1000 calls in random 

 delay throwdowns, designed load a. = 0.90. 



per cent of all the calls delayed. The 10 trunk case based on 1500 calls 

 at 0.8 occupancy also shows good agreement to 99.5 per cent of the calls 

 delayed. 



In making throwdown tests of this sort, the criterion for deciding when 

 one has proceeded long enough is rather vague. The usual practice is to 

 summarize the delays at regular intervals and observe at what point 

 it seems likely that making additional tests would not change the results 

 by a sensible amount. For the c = 2 trunk case, six runs of 500 calls 

 each produced the several very different broken line curves of Fig. 3 

 shown superposed on the theoretical delay distribution for a = 0.90. 

 Clearly no one of these by itself could be given much weight. 



Consecutive runs were paired to form three runs of 1000 calls each, 

 as shown in Fig. 4. As one would expect, their spreads have narrowed 

 appreciably. Combining these three runs yielded the dotted curve of 

 Fig. 1, which, of course, has a correspondingly smaller likelihood of 

 sampling error in it. On the basis of such a succession of narrowing 

 spreads, one can, with some feeling of assurance, estimate within what 

 narrow band about the observed curve the true unknown curve (ap- 

 proachable by many more tests) must lie. 



On Figs. 1 and 2 the shapes and positioning of the total throwdown 

 and theoretical curves seldom differ more than 20 per cent on the 

 probability scale down to the P = 0.005 probability level. The dis- 



