This paper investigates a hybrid management policy of road tolls and tradable credits in mixed road networks with both public and private roads. In the public sub-network, a tradable credit scheme is applied to mitigate traffic congestion. In the private sub-network, tolls are collected by the private company, but the toll levels and toll locations are determined by the government. The purpose of toll charge is two-fold: on the one hand, the government uses it as a tool for mitigating congestion; on the other hand, a threshold of revenue should be guaranteed for the profitability of the private company. A bi-level programming model is formulated to minimize the total travel time in the network by taking into account the user equilibrium travel behaviour and the revenue requirement of private firms. To obtain a global optimum solution, the bi-level model is transformed into an equivalent single-level mixed integer linear program that can be easily solved with commercial software. Numerical examples are provided to demonstrate the effectiveness of the developed model and the efficiency of the proposed algorithm. It is shown that the mixed management schemes can achieve favourable targets, namely, joint implementation of road tolls and tradable credits can effectively mitigate traffic congestion and meanwhile maintain reasonable revenue for the private company.
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