ANNEX C
                                     (to Recommendation E.506)
                           Description of a top down procedure
               Let
               XT  be the traffic forecast on an aggregated level,
               Xi  be the traffic forecast to country i,
               eq \o(\s\up4(^),s)T     the estimated standard deviation of the aggregated
                  forecast,
               eq \o(\s\up4(^),s)i     the estimated standard deviation of the forecast to 
                  country i.
         Usually
                       XT eq \i\su(i, , )!Unexpected End of Expression. Xi,           (C-1)
         so that it is necessary to find a correction
                                  [X`i] of [Xi] and [X`T] of [XT]
         by minimizing the expression
                      Q = a0(XT - XT`)2 + eq \i\su(i, , )!Unexpected End of Expression. 
         ai(Xi - Xi`)2                         (C-2)
         subject to 
                                            XT` = i Xi`                               (C-3)
         where a and [ai] are chosen to be
                      a0 = eq \f(1,\o(\s\up4(^),s)\s(2,T)) and ai = eq \f(1,\ 
         o(\s\up4(^),s)\s(2,i))   i = 1, 2, . . .                                    (C-4)
               The solution of the optimization problem gives the values [X`i]:
                      Xi` = Xi - eq \o(\s\up4(^),s)\s(2,T) \f(\i\su( ,i, ) Xi - XT,\i\su( 
         ,i, ) \o(\s\up4(^),s) + \o(\s\up4(^),s))(C-5)
               A closer inspection of the data base may result in  other  expressions  for
         the coefficients [ai], i = 0, 1, . .  .  On  some  occasions,  it  will  also  be
         reasonable to use other criteria for finding  the  corrected  forecasting  values
         [X`i]. This is shown in the top down example in Annex D.
               If, on the other hand, the variance  of  the  top  forecast  XT  is  fairly
         small, the following procedure may be chosen:
               The corrections [Xi] are found by minimizing the expression
                      Q` = eq \i\su(i, , )!Unexpected End of Expression. ai (Xi - Xi`)2 (C- 
         6)
         subject to
                      XT = eq \i\su(i, , )!Unexpected End of Expression. Xi`         (C-7)
               If ai, i = 1, 2, . . . is  chosen  to  be  the  inverse  of  the  estimated
         variances, the solution of the optimization problem is given by
                      Xi` = Xi - eq \o(\s\up4(^),s)\s(2,i) eq \f(\i\su( , , ) Xi - 
         XT,\i\su( , , )\o(\s\up4(^),s)\s(2,i)) (C-8)





























                                                        Fascicle II.3 - Rec. E.506   PAGE1