Essential Components of the Solution Set for Multiclass Multicriteria Traffic Equilibrium Problems

Wardrop [1] introduced the famous user equilibrium principle for traffic network, which is a scalar equilibrium principle. Smith [2] investigated that a Wardrop's user equilibrium flow is equivalent to the solution of a class of variational inequalities when the travel cost function is a scalar function. Recently, many researchers have proposed equilibrium models based on multicriteria consideration or vector-valued cost functions. Chen and Yen [3] first proposed (weak) vector equilibrium principle for a vector traffic network without capacity constraints, which is a generalization of the classic Wardrop's user equilibrium principle. In [4], Yang and Goh investigated equivalent relations between vector variational inequalities and vector equilibrium flows based on vector equilibrium principle. Daniele et al. [5, 6] studied a traffic equilibrium problem with capacity constraints in dynamic case and obtained sufficient and necessary conditions for a traffic equilibrium flow. Lin [7] extended weak vector equilibrium principle to the case of capacity constraints of arcs and showed that there exists at least one essential components of the solution set for traffic equilibrium problems with capacity constraints of arcs. However, all the researches mentioned above assumed that the users in the traffic network are homogenous. In reality, we have to group users in different classes due to their differences in the income, age, gender, education, travel destination, and so on. Nagurney [8], Nagurney and Dong [9] discussed MMTE problem without capacity constraints with fixed demand and elastic demand, respectively, and