ファーネス法によるOD表の修正における2,3の問題について

概要

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We have the Furness Method as the simple method for the modification of an OD table of traffic when we are to obtain the future OD table based upon the present OD table. The method can be applied to most of the OD tables. But in a few cases, we can not use the method for the modification. As a matter of fact, for example, when all of the distributed traffics which originate from the ith region T_<i1>, T_<i2>,……, T_<in> are 0, or those which are destinated to the ith region T_<1j>, T_<2j>,……, T_<nj> are 0, we cannot get the adequate future OD table by the Furness method, where T_<ij> is the traffic from the ith region to the jth region, and n is the total number of the regions observed. We have some other cases in which we cannot use the method. When we apply the method to an OD table, in general, the distributed traffics in the OD table will be changed. If we introduce the equation : T_<ij>^<(s)>=T_<ij>^*+ΔT_<ij>^<(s)> we can show the relation between T_i., T_<.j>, T_<i.>^*, and T_<.j>^* by relatively simple equations (equations (4.5), (4.8), (4.12), and (4.13)), where T_<ij>^<(s)> is the traffic from the ith region to the ith region obtained by the sth step of the modification, T_<ij>^* is the future traffic obtained by Furness method, ΔT_<ij>^<(s)> is T_<ij>^<(s)> -T_<ij>^*, Ti. is Σ^^n__<j=1> T_<ij>, T_<.j> is Σ^^n__<i=1>T_<i.>,^* is Σ^^n__<j=1>T_<ij>^*, and T_<.j>^* is Σ^^n__<i=1>T_<ij>^*.