434 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



I 



This formula provides a means for estimating the grade of service 

 which customers might he expected to receive if asked to dial their calls 

 over moderate-delay or high-delay trunk groups. For a circuit use length 

 of 150 seconds, and an average return time of 250 seconds (as on Fig. 6), 

 both exponential, the load-versus-proportion-NC curves for 6 and IG 

 trunks are given as curves (3) on Fig. 7. For example with an offered 

 (= carried) load of a = 4.15 erlangs on 6 trunks we should expect to find 

 27.5 per cent of the total attempts resulting in failure. 



For comparison with a fixed return time of NC-calls, the IF-formula 

 curves for exponential returns of 30 seconds (s = 5) and 250 seconds 

 (s = 0.6) averages are shown on Fig. 5. The first is far too severe an 

 assumption for operator performance, giving NC's nearly double those 

 actually observed (and those given by theory for a 30-second constant 

 return time). The 250-second average return, however, lies only slightly 

 above the 30-second constant return curve and is in good agreement with 

 the data. Although not logically an adequate formula for interpreting 

 Peg Count and Overflow registrations on T-engineered groups under 

 operator dialing conditions, the IF-formula apparently could be used for 

 this purpose with suitable s-values determined empirically. 



3.1. Comparison of Some Formulas for Estimating Customers' NC Service 



on Congested Groups 



, 1 

 As has been previously observed, a large proportion of customers who 



receive a busy signal, return within a few minutes (on Fig. 6, 75 per cent 

 of the customers returned within 10 minutes). It is well known too, that 

 under adverse service conditions subscriber attempts (to reach a par- 

 ticular distant office for example) tend to produce an inflated estimate 

 of the true offered load. A count of calls carried (or a direct measurement 

 of load carried) will commonly be a closer estimate of the offered load 

 than a count of attempts. An exception may occur when a large propor- 

 tion of attempts is lost, indicating an offered load possibly in excess even 

 of the number of paths provided. Under the latter condition it is diffi- 

 cult to estimate the true offered load by any method, since not all the 

 attempts can be expected to return repeatedly until served; instead, a 

 significant number will be abandoned somewhere through the trials. In 

 most other circumstances, however, the carried load will prove a reason- 

 ably good estimate of the true offered load in systems not provided with 

 alternate paths. 



This is a matter of especial interest for both toll and local operation 

 in America since principal future reliance for load measurement is ex- 



