THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 435 



pected to be placed on automatically processed TUR data, and as the 

 TUR is a switch counting device the results will be in terms of load 

 carried. Moreover, the quantity now obtained in many local exchanges 

 is load carried.* Visual switch counting of line finders and selectors off- 

 normal is widely practiced in step-by-step and panel offices; a variety of 

 electromechanical switch counting devices is also to be found in crossbar 

 offices. It is common to take load-carried figures as equal to load-offered 

 when using conventional trunking tables to ascertain the proper pro- 

 vision of trunks or switches. Fig. 7 compares the NC predictions made by 

 a number of the available load-loss formulas when load carried is used as 

 the entry variable. 



The lowest curves (1) on Fig. 7 are from the Erlang lost calls formula 

 El (or B) with load carried L used as the offered load a. At low losses, 

 say 0.01 or less, either L or a = L/[l — Ei(a)] can be used indiscrimi- 

 nately as the entry in the Ei formula. If however considerably larger 

 losses are encountered and calls are not in reality "cleared" upon meet- 

 ing NC, it will no longer be satisfactory to substitute L for a. In this 

 circumstance it is common to calculate a fictitious load a' to submit to 

 the c paths such that the load carried, a'[I — Ei^dd')], equals the desired 

 L. (This was the process used in Section 2 to obtain " % NC existing.") 

 The curves (2) on Fig. 7 show this relation ; physically it corresponds to 

 an initially offered load of L erlangs (or L call arrivals per average hold- 

 ing time), whose overflow calls return again and again until successful 

 but without disturbing the randomness of the input. Thus if the loss 

 from this enhanced random traffic is E, then the total trials seen per 

 holding time will be L(l + ^ + ^' -f • • •) = L/(l - E) = a', the ap- 

 parent arrival rate of new calls, but actually of new calls plus return 

 attempts. 



The random resubmission of calls may provide a reasonable descrip- 

 tion of operation under certain circumstances, presumably when re-trials 

 are not excessive. Kosten^ has discussed the dangers here and provided 

 upper and lowxr limit formulas and curves for estimating the proportions 

 of NC's to be expected when re-trials are made at any specified fixed 

 leturn time. His lower bounds (lower bound because the change in con- 

 gestion character caused by the returning calls is ignored) are shown by 

 open dots on Fig. 7 for return times of 1.67 holding times. They lie above 

 curves (2) (although only very slightly because of the relatively long 

 return time) since they allo\\- for the fact that a call shortly returning 



* In fact, it is difficult to see how any estimate of offered load, other than carried 

 load, can be obtained with useful reliability. 



