340 
The N.Z. Journal of Science and Technology. 
[Nov. 
is complete — Stout Street, Courtenay Place, Newtown, Kelburn, Hutt and 
Petone, Khandallah, Wadestown, Karori, Brooklyn, Island Bay, Miramar ; 
the Auckland area for Wellesley Street, Bemuera, Ponsonby, Mount Eden, 
Devonport, Takapuna, Birkenhead, Onehunga. 
Trunks. 
The number of trunks and attendant switches needed between groups 
of machines, whether in the same office or in different offices, is very 
necessary to ascertain, as in either case they determine the first cost of the 
exchange equipment, and, where used between offices, the cost of cable- 
pairs. 
As many switches must be supplied in any group as there are connec¬ 
tions to be established simultaneously. It is of great importance to supply 
the correct number of switches for such maximum traffic, as a lack of switches 
inevitably entails a delay or a failure to establish connections, and an excess 
of switches involves depreciation and maintenance of costly and useless 
equipment. 
The problem of predicting the maximum number of simultaneous con¬ 
nections, corresponding with a given number of calls passing at a given 
rate, is one that closely resembles those treated by the mathematical doctrine 
of probability. Expressed mathematically, it concerns the relation existing 
between the total number of events in a period occurring on a chance basis 
and the number of the events existing simultaneously, such event having 
a given duration. As switches must be provided for the total number 
existing simultaneously, it is the maximum number of events existing 
simultaneously during the period that must be determined. 
Such maxima will vary with the time of duration of each event. Maxima 
will increase as the time of duration increases. Maxima will also vary with 
the degree of accuracy or failure-frequency that was premised. A given 
maximum will be exceeded less often than a maximum of smaller magnitude. 
In a switchboard, for example, it may happen only once a week that more 
than ten cord circuits are simultaneously in use, but it would happen only 
once in six months that more than fourteen are in use. The larger maximum 
is exceeded more rarely ; in other words, the failure-frequency decreases 
with the large maxima. 
The probability calculations investigating these relations resulted in a 
series of charts, which were deduced purely from the mathematical theory. 
The question was then raised whether actual telephone traffic is so distri¬ 
buted in the ordinary telephone exchange that it is accurately represented 
by the mathematical curves deduced. A careful comparison of the cal¬ 
culated results with those obtained from a study of actual telephone traffic 
under varying conditions showed that there is a close agreement. It is not 
a surprise that such close agreement should be found, as American operating 
companies have for years used similar curves for predicting simultaneous 
maxima for given traffic data, upon which basis toll-lines were then con¬ 
structed. Besides permitting the accurate prediction of the number of 
machines required in any group for a given busy-hour traffic, these curves 
and formulae enable the investigator to study the larger problem of junction- 
group efficiency and its effect on the economical size of machine. 
