426 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



wide range of group sizes, and several selections of message holding 

 times. They were constructed following summarization of many obser- 

 vations of load and resultant average delays on ringdown (non-dial) 

 intertoll trunks.^ Fig. 2 shows the permissible occupancy (efficiency) of 

 various trunk group sizes for 6.5 minutes of use per message, for a va- 

 riety of T-schedules. It is perhaps of somfe interest that the best fitting 

 curves relating average delay and load were found to be the well-known 

 Pollaczek-Crommelin delay curves for constant holding time — this in 

 spite of the fact that the circuit holding times were far indeed from 

 having a constant value. 



A second, and probably not uncorrected, observation was that the 

 per cent "No-Circuit" (NC) reported on the operators' tickets showed 

 consistently lower values than were measured on group-busy timing de- 

 vices. Although not thoroughly documented, this disparity has generally 

 been attributed to the reluctance of an operator to admit immediately 

 the presence of an NC condition. She exhibits a certain tolerance (very 

 difficult to measure) before actually recording a delay which would 

 recjuire her to adopt a prescribed procedure for the subsequent handling 

 of the call.* There are then two measures of the No-Circuit condition 

 which are of some interest, the "NC encountered" by operators, and the 

 "NC existing" as measured by timing devices. 



It has long been observed that the distribution of numbers n of simul- 

 taneous calls found on T-engineered ringdown intertoll groups is in re- 

 markable agreement with the individual probability terms of the Erlang 

 "lost calls" formula, 



f n — a ' 



a e 



fin) = ^-^^ (1) 



e 



E- 



n=o n! 



where c = number of paths in the group, 



a' = an enhanced average load submitted such that 

 a'[l — Ei^c(a')] = L, the actual load carried, and 

 Ei^cid') = fie) = Erlang loss probability (commonly called Er- 

 lang B in America). 

 An example of the agreement of observations with (1) is shown in Fig. 

 3, where the results of switch counts made some years ago on many 

 ringdown circuit groups of size 3 are summarized. A wide range of "sub- 



* Upon finding No-Circuit, an operator is instructed to try again in 30 seconds 

 and GO seconds (before giving an NC report to the customer), followed by addi- 

 tional attempts 5 minutes and 10 minutes later if necessary. 



