The Theory of Probabilities Applied to Telephone 

 Trunking Problems 



By EDWARD C. MOLINA 



THE Theory of Probabilities lends itself to the solution of many 

 important telephone problems. These problems arise not only 

 in connection with the trunking of calls but also in statistical 

 studies which underlie the making of fundamental plans, in studies 

 carried on in physical research and in the manufacturing of telephone 

 apparatus. 



The purpose of the present paper is to discuss certain simple types 

 of trunking problems which can readily be handled to a sufificient 

 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 ^ 

 it has been known that light could be shed on these problems by the 

 application of probabilities and many articles ^ have appeared on 

 this subject; however the treatment to be found in the literature is, 

 as yet, by no means comprehensive. 



About 1905, the development of machine switching systems arrived 

 at a stage where the relative efficiencies of different sizes of trunk 

 groups became of prime importance. 



In designing and engineering machine switching systems, it is 

 necessary to compare the costs of various plans using trunk 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 Theory of Probabilities to telephone engineer- 

 ing and in the Bell System work along this line has been in progress, 

 systematically, for many years. This work has included not only 

 the theoretical solutions of various trunking problems, but has also 

 involved the computation of special probability tables and collec- 

 tion of data by means of which theoretical results have been closely 

 checked. 



In the articles which have hitherto appeared, little or no effort 

 has been made to present the mathematical theory of trunking in a 



' G. T. Blood of the A. T. & T. Co. in 1898 found a close agreement between the 

 terms of a binomial expansion and the results of observations on the distribution 

 of busy calls. The first comprehensive paper was one written by M. C. Rorty in 

 October 1903 and was quite widely circulated within the Bell System. 



2 An excellent bibliography is given by G. F. O'Dell in the P. O. E. E. J. for Octo- 

 ber 1920. 



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