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A note on the minimum instantaneous cost path of the dynamic traffic assignment problem. (English) Zbl 0842.90033
Summary: We consider an example to show that the minimum instantaneous cost path principle, as suggested by T. L. Friesz, J. Lucque, R. L. Tobin, B.-W. Wie [Oper. Res. 37, No. 6, 893-901 (1989; Zbl 0691.49029)] for generalising Wardrop’s first principle to the dynamic state, may cause some drivers’ routes to “loop”. These looping routes traverse the same link more than once – indeed, in our example six times.

MSC:
90B06 Transportation, logistics and supply chain management
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References:
[1] T. L. Friesz, J. Luque, R. L. Tobin and B.-W. Wie, Dynamic network traffic assignment considered as a continuous time optimal control problem, Operations Research 37(1989)893–901. · Zbl 0691.49029
[2] J.G. Wardrop, Some theoretical aspects of road traffic research, Proc. Instit. Civ. Eng., Part II, 1 (1952) 325–362.
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