## 1 Introduction
The model considers multiple paths and is constrained by the condition that it should satisfy all travel demands. The installing and operating cost is represented by weights that set on the candidate site, and its objective is to minimize the total cost. Moreover, many literatures aim to minimize the total social cost of charging infrastructure [29; 30; 31], which normally includes fixed investment cost, land cost, the construction cost of fast chargers and other costs. In [27; 28; 32], the user's trip feasibility is considered when planning charging stations. Among them, [PERSON] and [PERSON] [27] divided the traffic nodes into main nodes and sub-nodes. First, fast charging stations are placed at all main nodes. Then the remaining charging stations are set, following the principle that the distance between adjacent charging stations should not exceed the maximum travel range of EVs. In [33; 34; 35], data-driven approaches are adopted to plan charging infrastructures. [PERSON] et al. [33] analyzed the impact of different deployment levels of public charging infrastructure on reducing EV range anxiety. [PERSON] et al. [34] considered users' spontaneous adjustments, as well as interactions of traveling and recharging decisions. [PERSON] et al. [35] proposed a data-driven optimization approach based on large-scale GPS trajectory data. When planning fast charging stations, we find that some researchers suggest siting while sizing [17; 36] and others suggest siting before sizing [18; 24; 37]. For sizing fast charging stations, the queuing theory is most commonly applied. In [18; 36], the capacity of the charging station was determined by aiming at the minimum number of chargers and was constrained by the average waiting time. In [14; 24], similarly based on the queuing theory, the capacity was determined by the objective to minimize the sum of the charger cost and the waiting cost of EV users. However, it is difficult to calculate and determine the average arrival rate of EVs and the charger cost, so there would be a very large possibility of inaccuracy in sizing. As a result, a hybrid method based on queuing theory and the greedy algorithm [25] is applied in this paper to determine the capacity of fast charging stations. This method enables us to allocate a certain number of chargers at each station based on the relative system density of stations without any prior knowledge of the arrival rate at each station, which will effectively reduce congestion at charging stations and avoid an unreasonable allocation of resources. This paper centers on planning fast charging stations in urban areas. Its primary purpose of the charging infrastructure is to fulfill the need of EV users, and the subsequent purpose is to minimize the total social cost against a background of low EV penetration nowadays. Therefore, we propose a multi-objective bi-level planning model, consisting of upper and lower models. The upper model addresses the siting problem to maximize the travel success ratio, and the lower model assesses possible plans to obtain the optimal plan based on the satisfaction index and total social cost. The main contributions of this paper are:  
* In this study, we consider the coupling relationship between EV users' travel routes and the location of charging stations. The shortest path would be the best choice, however, when it could cannot meet the traveling demand, we search other routes passing the fast charging stations within a certain deviation so as to analyze the trip feasibility. * In order to simulate the process of users heading for charging stations to charge, we accord priority consideration to charging when the state of charge (SOC) is less than the range anxiety threshold, and then to charge on relatively sufficient battery. Following this method, we obtain the number of EVs charged at each station, which enables us to achieve a more reliable and practical sizing result. * Based on the charging times and deviation, we propose the concept of the satisfaction index.