Theories for Toll Traffic Engineering in 



the U.S.A.* 



By ROGER I. WILKINSON 



(Manuscript received June 2, 1955) 



Present toll trunk traffic engineering practices in the United States are 

 reviewed, and various congestion formulas compared with data obtained on 

 long distance traffic. Customer habits upon meeting busy channels are noted 

 and a theory developed describing the probable result of permitting subscribers 

 to have direct dialing access to high delay toll trunk groups. 



Continent-wide automatic alternate routing plans are described briefly, 

 in which near no-delay service will permit direct customer dialing. The 

 presence of non-random overflow traffic from high usage groups co7nplicates 

 the estimation of correct quantities of alternate paths. Present methods of 

 solving graded multiple problems are reviewed and found unadaptable to the 

 variety of trunking arrangements occurring in the toll plan. 



Evidence is given that the principal fluctuation characteristics of overflow- 

 type of non-random traffic are described by their mean and variance. An 

 approximate probability distribution of simultaneous calls for this kind of 

 non-random traffic is developed, and found to agree satisfactorily with theo- 

 retical overflow distributions and those seen in traffic simidations. 



A method is devised using ^^ equivalent random''^ traffic, which has good 

 loss predictive ability under the "lost calls cleared" assumption, for a diverse 

 field of alternate route trunking arrangements. Loss comparisons are made 

 with traffic simulation residts and with observations in exchanges. 



Working curves are presented by which midti-alternate route trunking 

 systems can be laid out to meet economic and grade of service criteria. Exam- 

 ples of their application are given. 



Table of Contents 



1 . Introduction 422 



2. Present Toll Traffic Engineering Practice 423 



* Presented at the First International Congress on the Application of the 

 Theory of Probability in Telephone Engineering and Administration, Copen- 

 hagen, June 21, 1955. 



421 



