Application of the Theory of Probability to Telephone 

 Trunking Problems 



* By EDWARD C. MOLINA 



IF telephone plants were provided in such quantities that when a 

 subscriber makes a call there would be immediately available 

 such switching arrangements and such trunks or paths to the desired 

 point as may be necessary to establish the connection instantly, it 

 would require that paths and switching facilities be provided to meet 

 the maximum demand occurring at any time, wdth the result that 

 there would be a large amount of plant not in use most of the time. 



Obviously, this would result in high costs, particularly in cases of 

 long circuits or where the switching arrangements are complex. 



Sound telephone engineering requires, therefore, that we approach 

 this condition only in so far as it is practical and economical to do so, 

 consistent with good telephone service to the subscriber. To take 

 an extreme case — if enough toll lines were provided between New 

 York and San Francisco so that no call w'ould ever be delayed because 

 of busy lines or busy switching arrangements, the rates it would be 

 necessary to charge would be prohibitive, although the speed of service 

 would be very good. Obviously, it is necessary to adopt a compromise 

 between the number of circuits and amount of equipment and the time 

 required to complete a call. 



Handling traffic on any other than an instantaneous basis is generally 

 spoken of as handling it on a "delayed basis," even though this delay 

 may be, and generally is, inappreciable to the subscriber. While 

 most of the traffic is handled practically on a no-delay basis, there are 

 certain kinds that are handled on a "delayed basis," such as 



1. Calls handled by toll lines, when all toll lines happen to be busy. 



2. Calls served by senders or line finders in machine switching systems. 



3. Calls handled by operators; the delays implied here being due to 



the time required by an operator to perform her functions 

 apart from delays due to limitations of equipment. 



For traffic handled in this manner it is desirable to have formulas or 

 curves for determining the percentage of calls delayed and the average 

 delay on calls delayed. The product of these two figures will give, 

 of course, the average delay on all calls. 



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