在用户均衡(UE)用户和Cournot-Nash (CN)用户组成的异质性交通网络中, UE用户中出行者的目的是最小化自身出行成本, 属于同一CN用户的出行者之间完全合作, 属于不同CN用户的出行者之间完全竞争, CN用户的目的是最小化其所有出行者的总出行成本. 构建了弹性需求下UE-CN混合交通均衡分配的变分不等式模型, 分别运用放缩法和非线性规划方法得到了弹性需求下UE-CN混合交通均衡分配的效率损失上界. 在此基础上, 运用解析推导方法得到了收费机制下UE-CN弹性需求混合交通均衡分配的效率损失上界. 研究结论表明, 放缩法得到的效率损失上界表达式只和用户均衡时的社会总收益与社会总剩余之比有关; 用非线性规划方法得到的效率损失上界表达式不仅与用户均衡时的社会总收益与社会总剩余之比有关, 而且还与CN用户的数量相关. 收费机制下UE-CN弹性需求混合交通均衡分配的效率损失上界表达式与路段出 行时间成本函数类、路段收费机制、用户均衡时的社会总收益(社会总剩余最大时 的社会总收益)与用户均衡时的社会总剩余之比相关.

Consider a heterogeneous traffic network simultaneously with user equilibrium (UE) player and Cournot-Nash (CN) players, the users under UE player aim to minimize her/his own travel cost, the users belonging to the same CN player can fully cooperate with each other and different players will fully compete with each other. The users of one CN player aim to minimize their own total travel cost while compete with users of other players. The variational inequality (VI) model for UE-CN mixed traffic equilibrium with elastic demand is presented; the upper bound of the efficiency loss of this mixed traffic equilibrium is obtained by the scaling method and the nonlinear programming method, respectively. Then, the efficiency loss of UE-CN mixed traffic equilibrium with elastic demand under road pricing is investigated by analytically derived. It is shown that the upper bound of efficiency loss obtained by the scaling method only depends on the ratio of user benefit and the total social surplus at traffic equilibrium state, the upper bound of efficiency loss obtained by the nonlinear programming method depends on the number of the CN players besides the aforementioned factors. The upper bound of efficiency loss of UE-CN mixed traffic equilibrium with elastic demand under road pricing depend on the type of link travel time cost function, the road pricing scheme, the ratio of user benefit at traffic equilibrium state (user benefit at system optimum state) and the total social surplus at traffic equilibrium state.