442 BELL SYSTEM TECHNICAL JOURNAL 



successive entries of 19 significant figures of ^^ (Tables of the Exponential 

 Function — WPA — 1939). The numbers drawn and their functions in the 

 study are as follows: 



A set of 1,000 six-digit numbers was taken from the last six digits of 

 entries of e^ from x = 0.4000 to a: = 0.4999. These 1,000 six-digit numbers 

 were arranged in numerical order to give the placing time of 1,000 simulated 

 calls. The first digit in every number was used to represent the hour and 

 the last five digits the hundred- thousands part of the hour when a particular 

 call was placed. The randomness of this particular draw was checked by 

 determining the differences between successive placement times and then 

 arranging the differences in numerical order. The results were plotted on 

 a cumulative basis on Fig. 5, where a visual comparison can be made with 

 theoretical results. 



A set of 1,000 seven-digit random numbers between 0,000,000 to 4,166,667 

 inclusive were taken from the last seven digits of entries of e^ from x = 0.5000 

 to X = 0.7344. Numbers above 4,166,667 were disregarded. These seven- 

 digit numbers when arranged in numerical order accounted for the total 

 holding time of all the calls. The difference between successive numbers 

 arranged in numerical order, furnished 1,000 individual holding times. 



A third set of 1,000 random numbers were taken from two sources in 

 the e* tables. These 1,000 numbers contained a variable number of digits. 

 These numbers were for use when calls encountered all trunks busies in order 

 to determine which calls were to be resubmitted and to determine the time 

 interval for resubmitting a call. Previously, it was estimated from Fig. 3, 

 that 90% of the subscribers after encountering a busy redial their call. 

 This estimate was used by assigning to the numerals 1 to 9 in the third set of 

 random numbers the characteristic that a call may make a subsequent 

 attempt if it encounters an all trunks busy and by assigning to the numeral 

 the characteristic that the call drops out if it encounters an all trunks busy. 

 About 10% of the 1,000 numbers show a numeral in the first place and 

 hence no further digits are needed because the call drops out. The remain- 

 ing 90% of the numbers show numerals from 1 to 9 in the first place and 

 hence may make a second attempt. If an all trunks busy is encountered on 

 the second attempt, a numeral from 1 to 9 in the second place determines 

 that a third attempt may be made while the numeral determines that the 

 call drops out. This process is repeated for each place of each number in 

 the third set of 1,0(K) random numbers until the numeral appears. The 

 number of consecutive places showing only numerals from 1 to 9, indicates 

 the total number of attempts that a particular call might make before it 

 drops out. Thus for a particular number the numerals might be 4720. 

 In this case, three subsequent attempts can be made. Another number 

 might be 834650. In this case, five subsequent attempts can be made. 



