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A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem

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  • Nie, Yu (Marco)

Abstract

A cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once linearized and augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) to propagate traffic. As a result, we show that CTM-type traffic dynamics can be derived from the original M-N model, when the exit-flow function is properly selected and discretized. The proposed cell-based M-N model has a simple constraint structure and cell network representation because all intersections and cells are treated uniformly. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop's second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many discrete SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.

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  • Nie, Yu (Marco), 2011. "A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 329-342, February.
    • Handle: RePEc:eee:transb:v:45:y:2011:i:2:p:329-342
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