366 BELL SYSTEM TECHNICAL JOURNAL 



relatively simple analysis a measure of the reliability of such an estimate 

 can be obtained. If in addition for the same period a record is kept on a 

 call- or peg-count meter of the number of calls passing over the group, it 

 is possible also to obtain estimates of the average call holding time and the 

 reliability of such an average. 



Direct measurement of holding times or switch counts should naturally 

 be made on groups during periods which are presumably typical of those 

 toward which the engineering is ultimately directed. Usually, although 

 not always, this will be the busy or busiest hours of the day during the 

 busy season of the year. In order to decide intelligently how long a period 

 needs to be studied in any given case some knowledge of the persistence of 

 the same holding time universe is necessary. This might be obtained 

 through relatively small holding time samples made in the hours of interest 

 every day for several weeks in the busy season. If spottiness or "lack of 

 control" is not apparent, the problem will be comparativeh' simplified. 

 If trends are present, however, it will be necessary to investigate their 

 nature (such as whether some one day of the week shows high holding 

 times) and apportion the main sampling procedure in a fashion to give 

 these peculiarities their proper weighting. 



It will be of interest to examine in this respect certain limited data at 

 hand taken by the pen register method some years ago on an inter-ofiice 

 trunk group in Newark, New Jersey. The kind of examination made 

 here will serve to indicate the procedure which may be found suitable in 

 some degree for application to other groups whose characteristics are 

 relatively little known. 



II — Preliminary Study of Newark Data 



It has long been known that local subscriber call holding times, /, follow 

 remarkably closely the simple exponential frequency distribution, 



fiOdt = ke^"dt, (1) 



where - = the average holding time." This was found to be substantially 

 k 



true of the data collected on the inter-office trunk group in Newark as 

 shown in Fig. 1 for 7385 calls observed in 19 hours having loads in the 

 range 15.0-16.0 average simultaneous calls. The fit of the exponential 

 curve having an average equal to the observed average of 2.380 minutes is 

 seen to be quite good. It may be further noted that in the exponential 

 distribution the standard deviation, a, equals the mean /. In practice a 



^ A. K. Erlang apparentl}- was the first to notice this holding time distribution, "Nvt 

 Tidsskrift for Matematik" (Denmark), 1909. 



