With the explicit consideration of user heterogeneity,i.e.,each user has a different value of time(VOT),this paper examines the system efficiency and social equity of toll revenue redistribution in a bi-mode transportation system.Three schemes of distributing the road toll revenue are proposed,which respectively consider efficiency,equity,as well as efficiency and equity together.With mild assumptions,we prove that the number of auto-motorists decreases and the total social cost increases with transit subsidy share when only marginal operating cost of the transit is covered by its fare.However,when average fixed cost of the transit is further covered,the total social cost is a "U" shape curve against the transit subsidy share.Numerical results show that the well designed toll revenue redistribution schemes can make the system more equitable while keeping high efficiency.With the increase of user heterogeneity,the Gini coefficient becomes larger while the total social cost goes down.
