If you had known User Equilibrium ([Wardrop (1952)]) and Beckmann Formulation [Beckmann et al.(1956)], you would have no doubt about the correctness of the Chapter 4 in the paper. Besides, you can write a much more concise proof of the first algorithm by the nonlinear description in Chapter 4.
Wardrop, John Glen. "ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH." Proceedings of the institution of civil engineers 1.3 (1952): 325-362.
Beckmann, Martin, Charles B. McGuire, and Christopher B. Winsten. Studies in the Economics of Transportation. No. 226 pp. 1956. 78.155.199.200 (talk) 03:58, 30 June 2019 (UTC)
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