THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 475 



curve. The superposed single line is the corresponding estimate by EE, 

 theory of the hour-to-hour call losses. As may be seen, theory and ob- 

 servation are in good agreement both point by point and on the average 

 over the range of losses from 0.01 to 0.50. The dashed line shows the 

 prediction of final route loss for each hour on the assumption that the 

 offered traffic A' was random. Such an assumption gives consistently low 

 estimates of the existing true loss. 



As of interest, a series of heavy dots is included on Fig. 31. These are 

 the result of calculating the Poisson Summation, P{C,L), where L is the 

 average load carried on, rather than offered to, the C trunks. It is inter- 

 esting that just as in earlier studies in this paper on straight groups of 

 intertoll trunks (for example as seen on Fig. 7), the Poisson Summation 

 with load carried taken as the load offered parameter, gives loss values 

 surprisingly close to those observed. Also, as before, this summation has 

 a tendency to give too-great losses at light loadings of a group and too- 

 small losses at the heavier loadings. 



; 7.4 Prediction of Traffic Passing Through a Midti-Stage Alternate Route 



Network 



I In the contemplated American automatic toll switching plan, wide 

 I advantage is expected to be taken of the efficiency gains available in 

 i multi-alternate routing. Thus any procedure for traffic analysis and 

 prediction needs to be adaptable for the . more complex multi-stage 

 arrangements as well as the simpler single-stage ones so far examined. 

 Extension of the Equivalent Random theory to successive overflows is 

 easily done since the characterizing parameters, average and variance, 

 of the load overflowing a group of paths are ahvays available. 



Since few cases of more than single-stage automatic alternate routing 

 are yet in operation in the American toll plant, it is not readily possible 

 to check an extension of the theoiy with actual field data. Moreover col- 

 lecting and analyzing observations on a large operating multi-alternate 

 route system would be a comparatively formidable experiment. 



However, in New York city's local interoffice trunking there is a very 

 considerable development of multi-alternate routing made possible by 

 the flexibility of the marker arrangements in the No. 1 crossbar switching 

 system. None of these overflow arrangements has been observed as a 

 whole, simultaneously and in detail. The Murray Hill-2 data in OST 

 groups reviewed in Section 7.3.2 were among the partial studies which 

 have been made. 



In connection with studies made just prior to World War II on these 



