A Model for System Optimum Dynamic Traffic Assignment with Minimum-Envy Allocations

초록

With real-time information having become readily available, dynamic traffic assignment models can assume an optimal traveler behavior where travelers select the fastest travel option based on current traffic conditions (greedy assumption), known as the Dynamic User Optimum (DUO). This assumption is valid when we only consider the availability of real-time traffic information. However, we can postulate that this is not a dynamic system-optimal solution (DSO) since greedy behavior does not improve the efficiency of a system. A service provider in the future who designs “transportation as a service” will devise a platform that maximizes the efficiency of a system while minimizing agents’ complaints from unfairness. When a system allows travelers to exchange their travel information with others, travelers might feel envious of others who have a faster route. Also, the feeling of unfairness might differ by drivers concerning his/her preference. To model a fair and efficient allocation of transportation supply for heterogeneous travelers, we employ Envy models which were initially employed for a fair division problem in the context of the fair cake-cutting problem in the 1940s (Barbanel 2005). Envy-Freeness implies that each agent believes that their allocation is greater than or at least the same as the share of others. Each player, in turn, is satisfied with an allocated piece of cake according to their preference. Thus, an EF region exists if there is a certain level of heterogeneity of preference(Gamow and Stern, 1958, Varian, 1974). Our goals regarding dynamic cases are maximizing system efficiency while minimizing agents’ envy. This chapter will address the following questions: 1) how to find the best alternatives under dynamic traffic demands and conditions, 2) how unfairness is evoked by efficient transportation, 3) how to obtain the best pricing policy for minimizing envy.