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THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



i.a 



^O 0.2 



EQUIVALENT 

 RANDOM THEORY 



ERLANG THEORY- 



1 2 3 4 5 6 7 8 9 10 It 12 13 14 15 16 17 

 ALTERNATE ROUTE (OST) NUMBER 



Fig. 28 — Comparison of theoretical and throwdown overflows from a number 

 of first alternate routes. 



were obtained by 36-second switch counts of those calls from each OST 

 group which had come to rest on subsequent alternate routes. 



On Fig. 28 is shown a summary of the observed and calculated pro- 

 portions of "lost" to "offered" traffic at each OST alternate route group. 

 As may be seen from the figure and the last four columns of Table V, 

 the general agreement is quite good ; the individual group variations are 

 probably no more than to be expected in a simulation of this magnitude. 



An assumption of randomness (which has sometimes been argued as 

 returning when several overflows are combined) for the load offered to 

 the OST's gives the Erlang Ei loss curve on Fig. 28. This, as was to be 

 expected, rather consistently understates the loss. 



Since "switch-counts" were made on the calls overflowing each OST, 

 the distributions of these overflows may be compared with those esti- 

 mated by the Negative Binomial theory having the mean and variance 

 predicted abo\'e for the overflow. Fig. 29 shows the individual and cumu- 

 lative probability distributions of the overflow simultaneous calls from 

 the first two OST alternate routes. As will be seen, the agreement is 

 quite good even though this is traffic which has been twice "non-ran- 

 domized." Comparison of the observed and calculated overflow means 

 and variances in Table V indicates that similar agreement between 

 observed and theoretical fitting distributions for most of the other OST's 

 would be found. 



7.3.2. Comparison of Equivalent Random Theory with Field Results on 

 Simple Alternate Routing Arrangements _ 



Data were made available to the author from certain measurements 

 made in 1941 by his colleague C. Clos on the automatic alternate routing 

 trunk arrangement in operation in the Murray Hill-2 central office in 

 New York. Mr. Clos observed for one busy hour the load carried on 



