utility of choosing charging station $j$ given that service provider $k$ has been chosen; $\overline{W}_{k}^n$ and $\overline{V}_{j,k}$ are linear weighted combinations of attributes of the charging stations and the EV owner.

Note that the retail charging price and the charging time are two factors differentiating the three charging services. In addition, we assume the income of EV owners will also play a role in choosing charging services. In contrast to our previous work [@mywork], we use a different formula to calculate $\overline{W}_k^n$ here.

$$\overline {W}_k^n =\alpha \frac{1}{t_k}+\beta \frac{p_k}{i_n},$$

where $t_k$, $p_k$ and $i_n$ represent, respectively, the average charging time, the retail charging price, and the income of the $n$-th EV owner; and $\alpha, \beta$ are the corresponding weighting coefficients. This model is similar to Ben-Akiva and Lerman’s utility model in their study of public transportation mode [@transmode]. The value of $\alpha$ is positive because shorter charging time implies a better charging service experience; therefore, leading to higher utility. The value of $\beta$ is negative because a higher retail charging price results in less utility. However, the retail charging price is divided by the income, which reflects that the retail charging price for the EV owners becomes less important as their 