The Theory of Probabilities Applied to Telephone Trunking Problems

HE T h e o r y of Probabilities lends itself to the solution of many i m p o r t a n t telephone problems. These problems arise not only in connection with the t r u n k i n g of calls b u t also in statistical studies which underlie the making of f u n d a m e n t a l plans, in studies carried on in physical research and in the m a n u f a c t u r i n g of telephone apparatus. T h e purpose of the present paper is to discuss certain simple types of trunking problems which can readily be handled to a sufficient degree of approximation by well-known probability methods. It would be quite impossible, within the scope of a single paper to give a complete discussion of trunking problems in general. For years 1 it has been known t h a t light could be shed on these problems by the application of probabilities and m a n y articles 2 have appeared on this subject; however the t r e a t m e n t to be found in the literature is, as yet, by no means comprehensive. A b o u t 1905, the development of machine switching systems arrived at a stage where the relative efficiencies of different sizes of t r u n k groups became of prime importance. In designing and engineering machine switching systems, it is necessary to compare the costs of various plans using t r u n k groups of widely different sizes, in order to choose the cheapest arrangement. Some plans use trunk groups as small as 5 and others groups as large as 90. Machine switching development, therefore, gave a great impetus to the application of the T h e o r y of Probabilities to telephone engineering and in the Bell System work along this line has been in progress, systematically, for m a n y years.