DIALING BEHAVIOR OF SUBSCRIBERS 425 



• York City Service Observing Bureaus during the winter of 1943-44. These 

 observations dealt with the behavior of subscribers who encounter a busy 

 on a dialed call. This behavior is assumed to apply to the situation when 

 subscribers encounter an all-trunks-busy condition. 



Inadequacy of the Poisson and Erlang B Formulae To Express 

 « THE Situation wtien Shortages Occur in Trunk Groups 

 Handling Subscriber Dialed Calls 



In connection with the provision of trunks in the exchange plant, two sets 

 of trunk-call-carrying-capacity tables are currently in use. One set of these 

 tables is computed from the Poisson Formula and the other from the Erlang 

 B Formula. The Poisson tables are used for trunk groups carrying non- 

 alternate route traffic, whereas the Erlang B tables are used for trunk 

 groups carrying traffic subject to alternate routing. 



The assumption underlying the Poisson Formula, when a shortage of 

 trunks occurs, is that of a partial delay. A call which encounters all trunks 

 busy waits but not longer than a holding time mterval for a trunk to become 

 available. 



The corresponding assumption underlying the Erlang B Formula is that of 

 no delay. A call which encounters all trunks busy is cleared out. The call 

 may be abandoned by the subscriber or advanced to an alternate route. 



With respect to non-alternate route trunk groups handling subscriber 

 dialed calls neither of the above two assumptions is realized in practice. 

 When all trunks are busy, the dial equipment is arranged to return an all- 

 trunks-busy signal to the subscriber rather than hold the call pending the 

 outcome of a subsequent test for an idle trunk. The subscriber upon 

 encountering an all-trunks-busy signal does not necessarily abandon the call. 

 In most cases he redials the call. 



The degree by which the assumptions are not realized depends upon the 

 relative number of trunks that are provided for a given volume of traffic. 

 For instance if, during an hour, 150 calls having an average holding time of 

 100 seconds are submitted to ten trunks and an equivalent volume of traffic 

 is submitted to five trunks, the following theoretical results follow from the 

 Poisson and Erlang B Formulae: — 



