500 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



Table XVI — Approximate Determination of the Variance 



OF Carried Loads; 

 X lower paths, 8 upper paths; offer to upper paths = 3 erlangs 



variance- Corresponding reasoning yields the same conclusion when the 

 offered load before the x paths is non-random. 



A numerical example by Brockmeyer" while clearly insufficient iu 

 establish the degree of the inequality (41), indicates something as to the 

 discrepancy introduced by this approximate procedure. Comparison with 

 the true values is shown in Table XVI. 



In the case of random offer to the 0, 3, 6, 12 "lower paths," the ap- 

 proximate method of equation (41) overestimates the variance of the 

 carried load by nearly two to one (columns 4 and 5 of Table XVI). The 

 exact procedure of (37) is then clearly desirable when it is applicable, 

 that is when random traffic is being offered. For the 8 upper paths to 

 which non-random load is offered (the non-randomness is suggested by 

 comparing the variance of column 6 in Table XVI with the average 

 offered load of 3 erlangs), the approximate formula (41) gives a not too 

 extravagant overestimate of the true carried load variance. Until curves 

 or tables are computed from equation (32), it would appear useful to 

 follow the above procedure for estimating the carried load variance 

 when non-random load is offered. 



8.5. Solution of a Typical Toll Multi- Alternate Route TrunJcing Arrange- 

 ment: Bloomsburg, Pa. 



In Fig. 9 a typical, moderately complex, toll alternate route layout 

 was illustrated. It is centered on the toll office at Bloomsburg, Pa. The 

 loads to be carried between Bloomsburg and the ten surrounding cities 

 are indicated in CCS (hundred call seconds per hour of traffic; 36 CCS = 

 1 erlang). The numbers of direct high usage trunks shown are assumed 

 to have been determined by an economic study; we are asked to find 



