TKUNK REQUIREMENTS IN ALTERNATE ROUTING NETWORKS 291 



costs of the direct and alternate routes are c'oiili()lliii«i. Since load carried 

 l)y a high usage grouj) is a function of the load offered, under the Erlang B 

 assumption, it is apparent that the size of the load between any two toll 

 centers will also limit the possible range of economic CCS values which 

 can be realized. In other words a high usage group to exist at all must 

 have at least one trunk and that one trunk must carry not less than the 

 economic number of CCS required by the cost ratio applying to the case. 

 For example, if a busy-hour load of ()0 CCS is to be carried betw^een 

 offices A and B and the cost ratio indicates an economic CCS of 25 it can 

 be shown that when one trunk is offered 60 CCS it wall carry only 23 

 of the 00 CCS with the Ijalance 37 CCS being o\'erflowed. Under these 

 conditions no direct (HU) group could be economically estabUshed since 

 the efficiencj' of even the first trvmk of such a group would fail to meet 

 the requirement of the case. 



This immediately suggests that a prime requirement in determining 

 whether or not there should be a direct group of any size between two 

 toll centers is a level of load at and abo^-e which a group will prove in 

 and below which, of course, it will fail to prove in. As previously stated 

 the cost ratio betw-een the alternate route and the potential direct group 

 is also a controlling factor. Thus, to determine the economic propriety 

 of establishing a direct (HU) group it is necessary to know the following: 



Cost of path in the alternate route; 



Cost of path in the direct route; 



Efficiency of trunks added to the alternate route; and 



Load offered between toll centers. 



The last three of these items were available to the engineer but the 

 first item could not be known in all cases because the groups comprising 

 the logical alternate routes in some cases were themselves hypothetical. 

 For example, a high usage group betw-een TCI and TC2 in Fig. 5 might 

 have an alternate route via POI or via P02 which routes in turn would 

 depend upon the existence of groups P01-TC2 and TC1-P02, respec- 

 tively. Therefore, it was necessary to "Cut-and-try" in the process of 

 locating high usage groups. This was accomplished by choosing an 

 average cost ratio (and hence an average economic CCS value) which 

 could be used with the known offered loads b(;tween toll centers to test 

 the feasibility of at least one high usage trunk. With this tentative pat- 

 tern of high usage groups the potentially available alternate routes could 

 then be identified. For each high usage-alternate route triangle thus 

 tentatively selected the test of relative costs was applied to verify the 

 economy of the case. Some proposed high usage groups failed to prove 

 in under such test in which cases the uneconomic high usage groups were 



