THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 



481 



7.4.1 Correlation of Loss with Peakedness of Components of Non-Ran- 

 dom Offered Traffic 



Common sense suggests that if several non-random parcels of traffic 

 are combined, and their joint proportion of overflow from a trunk group 

 is P, the parcels which contain the more peaked traffic should experience 

 overflow proportions larger than P, and the smoother traffic an overflow 

 proportion smaller than P. It is by no means clear however, a priori, the 

 extent to which this would occur. One might conjecture that if any one 

 parcel's contribution to the total combined load is small, its loss would 

 be caused principally by the aggregate of calls from the other parcels, 

 and consequently its own loss would be at about the general average loss 

 P, and hence not very much determined by its own peakedness. The 

 Murray Hill-6 throwdowai results may be examined in this respect. The 

 mean and variance of each OST-parcel of traffic, for example, arriving 

 at the final ST route was recorded, together with, as noted before, its 

 own proportion of overflow from the ST trunks. The variance/mean over- 

 dispersion ratio, used as a measure of peakedness, is plotted for each 

 parcel of traffic against its proportion of loss on Fig. 37. There is an un- 

 doubted, but only moderate, increase in proportion of overflow with 

 increased peakedness in the offered loads. 



It is quite possible, however, that by recognizing the differences be- 

 tween the service given various parcels of traffic, significant savings in 

 final route trunks can be effected for certain combinations of loads and 

 trunking arrangements. Of particular interest is the service given to a 

 parcel of random traffic offered directly to the final route when compared 



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V/a OF EACH OST PARCEL REACHING ST TRUNKS 



Fig. 37 — Effect of peakedness on overflow of a parcel of traffic reaching an 

 ilternate route. 



