TRUNK REQUIREMENTS IN ALTERNATE ROUTING NETWORKS 281 



carrying the load from the originating office to each distant office would 

 be at a minimum. This rccjuired some means of determining how much 

 load would be carried by the direct trunks when offered a given load 

 and consequently how much of that load would l)c overflowed to the 

 alternate route. For this purpose, a formula* known as the Erlang B 

 "lost-calls-cleared" assumption was used. This formula states for a given 

 random offered load, the amount of load which will be carried by each 

 of a number of trunks, n, tested in succession provided that the calls 

 failing to be carried on the first attempt (the lost calls) are not reoffcrcd 

 within the hour during which the first offering took 'place. The condition 

 italicized is extremely important to the problem since it requires that 

 calls lost on the direct high usage group, i.e., the calls overflowed to the 



Fig. 2 — Illustration of sim]jle interlocal trunk network arranged for alter- 

 nate routing. 



alternate route, must be disposed of without delay on the alternate route 

 or routes. In the New York City trials it was assumed that the then 

 current basis of provision of trunks in each leg of the alternate route 

 (final groups AT and TN, Fig. 2) namely, with a probability of delay 

 of one per cent. (P.Ol) would, as a practical matter, satisfy the condition 

 that calls overflowing from AX should be cleared. It should be mentioned 

 in passing that the results of the trials substantiated the reasonableness 

 of this assumption. 



A typical Erlang B distribution is shown in Fig. 3, Curve A wherein 

 the load carried by each of n=l-4 trunks is shown for the condition of 240 

 offered CCS. Thus, assuming the load to be offered in succession to 

 trunks 1, 2, 3, etc., in that order, it will be seen that the first trunk 

 carries the most load, the second trunk somewhat less, the third still less 

 until the fourteenth trunk carries about 0.5 per cent of the total. By 



* A. K. Erlang, Solution of Some Problems in the Theory of Prohahilities of 

 Significance in Automatic Telephone Exchanges, Post Office Electrical Engineers' 

 Journal, 10, 1917. 



