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As of December 2022, there were 119,000 gas stations, 10,800 gas stations and 4,488,000 charging piles nationwide, while the number of vehicles reached 312 million, including 11.49 million new energy vehicles. The imbalance between transportation energy supply and energy replenishment demand leads to crowded queues of vehicles at some stations and idle resources in others. How to reduce the phenomenon of large queues and improve the utilization rate of idle resources is the key to alleviating the imbalance between supply and demand.

Therefore, from the perspective of spatio-temporal equilibrium of urban transportation energy supply stations, multi-energy supply station cooperation is established in view of the phenomenon of large spatio-temporal differences among different energy supply stations, and corresponding inducing strategies are adopted for energy supplement vehicles in the road network, so that part of queued users go to energy supply stations with fewer vehicles, so as to balance the supply and demand of transportation energy in the region. On this basis, the income distribution of urban transportation energy supply station is discussed.

The total revenue after the cooperation was 13,095, an increase of 22.9%. Secondly, in terms of distribution rationality, three impact factors are selected and Shapley correction value is used to distribute the total income. Compared with independent operation, both sites have a certain degree of increase.

Traffic congestion at energy supply stations is closely related to the number, location and number of vehicles at energy supply stations. Therefore, using a cooperative approach of energy trading cannot solve the queuing problem. In addition, there are a few research results on the equalization of energy supply station services considering time-of-use pricing. However, these studies do not consider the vehicular grooming at congested stations. As far as the authors know, there are no relevant research results in the research on the service equilibrium of energy supply stations based on cooperative games.

This paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as a Wasserstein metric arising from optimal transport theory.

The authors spell out the basis and rationale for using Wasserstein metrics on the data space of (random) probability measures.

In elaborating the new statistical analysis of non-Euclidean data sets, the paper illustrates the generalization of traditional aspects of statistical inference following Frechet's program.

Besides the elaboration of research methodology for a new data analysis, the paper discusses the applications of Wasserstein metrics to the robustness of financial risk measures.