Optimal allocation of channels in an alternate route communication network [Comments on]

Recently, it has been reported that the Hakimi Theorem, quoted as Theorem 1 in the above named-paper (ibid., vol. CS-12 pp. 185-190, June 1964), does not hold in the general case. The theorem, however, is still true in so-called bi-path networks discussed by D.T. Tang (1964). In case of bi-path networks, the argument in the original paper is sound. However, in general networks, some modifxation must be made. In that case, a more fundamental relation can be readily derived from the definition of branch capacity. The commentor derives a new expression that should be used in place of (6) in the original paper Consequently, Theorem 2 of the original work should be changed as noted herein. A more detailed treatment of the problem is found in Ling et al. (Inst. Elect. Commun. Engrs. Japan, vol. 48, pp. 40-48, January 1965 (in Japanese), to be translated into English and published by the IEEE in Electronics and Communzeataons an Japan).