Real-Time Electric Taxi Guidance for Battery Swapping Stations Under Dynamic Demand

Abstract

High battery swapping demand from electric taxis and drivers’ subjective station selection often leads to congestion and the uneven utilization of battery swapping stations (BSSs). Efficient vehicle guidance is essential for improving the operational performance of electric taxis. In this study, we have developed a vehicle-to-station guidance model that considers dynamic demand and diverse driver response-time preferences. We have proposed two decision-making strategies for BSS recommendations. The first is a real-time optimization method that uses a greedy algorithm to provide immediate guidance. The second is a delayed optimization framework that performs batch scheduling under high demand. It integrates a genetic algorithm with KD-tree search to handle dynamic demand insertion. A case study based on Beijing’s Fourth Ring Road network was conducted to evaluate the strategies under four driver preference scenarios. The results show clear differences in vehicle waiting times. A balanced consideration of travel distance, waiting time, and cost can effectively reduce delays for drivers and improve station utilization. This research provides a practical optimization approach for real-time vehicle guidance in battery swapping systems.

1. Introduction

The transportation industry is currently the second-largest source of global carbon emissions [1]. Most regions are falling behind in achieving the target of net-zero carbon emissions by 2050 [2]. Electric vehicles (EVs) remain the most cost-effective and commercially viable route to fully decarbonized transportation [3]. Figure 1 shows the EV sales in selected countries and regions from 2017 to 2023. Due to the high frequency and large-scale usage of public transportation, it has become a priority to reduce urban carbon emissions [4]. The Chinese government gives priority to promoting the electrification of vehicles in the field of public transportation, including urban buses, taxis, ride-hailing, and logistics fleets. In this context, electric taxis have gradually become an important part of the urban transportation system [5]. Cities such as Taiyuan, Shenzhen, and Hangzhou have successfully implemented the large-scale adoption of electric taxis [6].

Efficiency and revenue are key priorities for taxi drivers. Unlike conventional charging, the battery swapping model enables replenishment in just 3–5 min, making it more suitable for high-frequency operations [7]. Effective battery swapping station (BSS) allocation is therefore essential to support uninterrupted taxi operations. However, its efficiency is constrained by limited battery availability and dynamic driver demand. In practice, drivers often rely on personal judgment when selecting a BSS, which can lead to congestion and long wait times [8]. Meanwhile, operators managing multiple stations must ensure balanced utilization across all stations to maximize overall efficiency. Thus, it is critical to design a guidance system for BSSs.

Despite the failure of projects such as Battery Place and Tesla in the early development of the battery swap mode, they have been actively promoted in recent years with the continuous expansion of China’s new energy market. By January 2024, China had deployed 3624 swapping stations. Current research on the operation of battery swapping stations primarily focuses on station location optimization [9], battery inventory planning [10], and battery charging schedules [11,12,13]. However, relatively little attention has been given to battery swapping guidance. Existing studies on swapping guidance focus on two main areas: route optimization and multi-factor guidance strategies. In route optimization, early work concentrated on homogeneous fleet optimization [14]. Later studies expanded to heterogeneous fleets, considering factors such as battery life, energy consumption, and degradation costs [15]. Some researchers also explored the impact of drivers’ choices between fast charging and battery swapping on route planning [16,17,18]. But these studies often assume BSSs have unlimited service capacity, overlooking practical constraints such as limited facility capacity and demand-driven queue fluctuations [19].

In multi-factor guidance strategies, research prioritizes factors like the distance between vehicles and stations, congestion levels, and battery availability [20,21]. Sun et al. [22] optimized service probabilities and waiting times using a hybrid queuing network model. However, these methods are often based on offline analysis and fail to capture real-time demand. To tackle this, online recommendation algorithms have been introduced to capture real-time information on vehicle destinations and station queue lengths, thereby optimizing route and station selection [23]. Ni et al. [24] did not directly assign BSSs to customers but instead provided a list of prices for customers to choose from. But the temporal coupling between vehicles and stations creates challenges in dynamic environments and increases computational complexity. So, some studies introduced game theory models to align vehicle distribution with dynamic pricing signals [25]. To improve vehicle–station matching efficiency, Li et al. [26] proposed an online allocation method based on bipartite graph matching. While these methods offer insights for vehicle arrival scheduling, they impose a large computational burden on short time scales. Wang and Hou [8] addressed this issue by proposing a multi-time-scale optimization strategy, allocating overall demand every 15 min and updating recommendations every 10 s to better adapt to dynamic demand.

Current research on vehicle battery swapping station (BSS) recommendations faces several limitations. First, existing studies on BSS selection have primarily focused on logistics distribution scenarios where the main objective is to minimize travel distance. In contrast, research on more general electric taxi swapping scenarios and the analysis of multiple influencing factors remains limited. Second, many studies overlook the constraints of BSS service capacity, with some assuming that batteries are always available. Finally, existing research lacks sufficient consideration of randomness factors. The operational randomness of taxis and the stochastic nature of traffic conditions make it difficult to predict the sequence of vehicle arrivals at swapping stations. This often results in arrival conflicts, where actual driver waiting times exceed initial estimates.

Given these theoretical and practical considerations, this paper proposes an optimization framework for electric vehicle battery swapping guidance within an online decision-making context. The main contributions are as follows:

(1)

This paper proposes two optimization methods, real-time optimization and delayed optimization, to provide different guidance strategies for battery swapping station operators. Each method recommends an optimal BSS based on driver preferences and station conditions and plans the best route through path optimization.

(2)

To address dynamic vehicle demand, the proposed framework integrates the A* algorithm and K-nearest neighbor search into both strategies to improve solution speed.

(3)

From a practical perspective, the framework enables personalized station and route recommendations based on driver requests. This alleviates BSS congestion while enhancing system efficiency and user satisfaction.

The remainder of this paper is organized as follows: Section 2 presents the model formulation. Section 3 introduces two optimization approaches and solution methods for the problem. In Section 4, case studies are presented for performance analysis. Finally, Section 5 summarizes the key insights from this study and offers suggestions for future research.

2. Problem Description and Formulations

2.1. Problem Definition

The core problem addressed in this paper is how to guide vehicles under dynamic demand while considering the resource limitations of swapping stations. Initially, vehicle swapping requests are unknown. The dispatching center receives a request for information for vehicles at different locations and time periods. Once a dynamic request appears, details such as request time, vehicle location, and remaining battery level become available. For the initial set of known requests, swapping station allocation can be performed in the planning phase. However, as vehicles travel, new emerging dynamic requests may necessitate adjustments to the original decisions. This randomness in time and location affects station status, rendering initial decisions suboptimal and requiring real-time adjustments.

As shown in Figure 2, this problem is defined on a directed graph $G=(V,A)$, where $V$ represents the set of nodes, including demand points $V_D$ and swapping stations $V_S$, and $A$ represents the set of arcs between nodes. Suppose the day is divided into $T$ time periods. At time $t$, $E{V}_1$ makes a swapping request at $D_1$, and $E{V}_2$ makes a swapping request at $D_2$. In the initial stage, the swapping route for $E{V}_1$ might be $D_1-D_3-S_2$. At time $t+1$, $E{V}_3$ and $E{V}_4$ are located at nodes $D_3$ and $D_1$, respectively. When $E{V}_3$ makes a swap request, $E{V}_1$ is still traveling between nodes 1 and 3, and $E{V}_3$ swap route becomes $D_3-S_2$. At this point, a situation arises where the $E{V}_1$ actual wait time upon arrival is longer than initially estimated, resulting in a conflict in reaching the destination.

Arrival conflicts primarily arise due to the system’s inability to accurately predict future battery swap requests. The limited capacity of swapping stations creates a coupling effect between vehicles and stations. As dynamic demand increases, unresolved arrival conflicts accumulate, further increasing queue lengths and reducing station service efficiency. In light of this, this paper examines the guidance problem for battery swapping stations under dynamic vehicle demand, with the goal of enhancing the immediate service capacity of swapping stations.

2.2. The Vehicle Guidance Model for BSS

This chapter introduces a realistic road network model. According to the China Urban Road Engineering Design Code (CJJ 37-2012), roads are classified into four categories: expressways, arterial roads, secondary roads, and branch roads. Considering actual traffic capacity, this study selects expressways, arterial roads, and secondary roads to construct the road network model. The sets used in the model are defined in

Table 1. Variable definition.

Sets	Definition
$V$	Set of all nodes on a directed graph G
$V_D$	Set of demand nodes
$V_S$	Set of bss nodes
$R$	Type of road
$K$	Set of vehicles
$U$	The number of batteries in the BSS
$T$	Set of periods
Parameters
$e_{ik}$	Battery level of vehicle k at node i
$d_{ij}$	Distance from node i to node j
$v_{ij}^t$	Speed of a vehicle between nodes i and j at time t
${\omega }_{ijt}^r$	Battery consumption per unit distance for an electric vehicle on road type r at different times t
${\epsilon }_{ij}^t$	Battery consumption of a vehicle traveling between nodes i and j at time t
$a_{ik}$	Arrival time of vehicle k at node i
$l_{ik}$	Departure time of vehicle k from node i
${\tau }_{ik}$	Total travel time of vehicle k to reach node i
$w_{sk}$	Total waiting time of vehicle k at swapping station S
$y_{ijr}$	$\mathrm{Indicator} \mathrm{that} \mathrm{arc} (i,j)$ belongs to road type $r$
$c_1$	Travel time cost for a vehicle
$c_2$	Cost of vehicle waiting time
$p{e}_t$	Unit price of battery swapping at time t
$p{s}_t$	Battery swapping service fee at time t
$b{e}_{skt}$	Amount of electricity needed to recharge the battery swapped by vehicle k at station s during time t
$c{s}_k$	Battery swapping cost for vehicle k
$ts$	Time required for the swapping operation
${tf}_{su}$	Time required to fully charge each battery u at swapping station s
$\mu$	Battery charging rate
Decision Variables
$h_{usk}$	Binary variable, 1 if vehicle $k$ selects battery $u$ at swapping station $s$, 0 otherwise
$x_{ijk}$	Binary variable, 1 if vehicle $k$ travels through arc $(i,j)$, 0 otherwise
$z_{sk}$	Binary variable, 1 if vehicle $k$ equals 1 if vehicle $s$, 0 otherwise

.

Objective:

$$\max C={\displaystyle \sum _{s\in V_s}{\displaystyle \sum _{k\in K}{c}_1{\tau }_{sk}{z}_{sk}}}+{\displaystyle \sum _{s\in V_s}{\displaystyle \sum _{k\in K}{c}_2{w}_{sk}{z}_{sk}}}+{\displaystyle \sum _{k\in K}c{s}_k}$$

(1)

s.t.

$${\displaystyle \sum _{s\in V_s}{z}_{sk}}=1,\forall k\in K$$

(2)

$$x_{isk}\le z_{sk},\forall i\in V_D,\forall s\in V_s,\forall k\in K$$

(3)

$$e_{jk}\le e_{ik}-d_{ij}{x}_{ijk}{\epsilon }_{ij}^t+M(1-x_{ijk}),\forall i,j\in V,\forall k\in K,\forall t\in T$$

(4)

$${\epsilon }_{ij}^t={\displaystyle \sum _{r\in R}{\omega }_{ijt}^r{y}_{ijr}},\forall i,j\in V,\forall t\in T$$

(5)

$${\displaystyle \sum _{r\in R}{y}_{ijr}=1},\forall i,j\in V$$

(6)

$$e_{sk}>0.1E,\forall s\in V_s,\forall k\in K$$

(7)

$$a_{jk}\ge a_{ik}+{\displaystyle \frac{d_{ij}}{v_{ij}}}M(1-x_{ijk}),\forall (i,j)\in V$$

(8)

$$t{f}_{su}\ge l_{sk}+{\displaystyle \sum _{s\in V_s}{\displaystyle \sum _{u\in U}\frac{0.9E-e_{sk}}{\mu }{h}_{usk}}},\forall k\in K$$

(9)

$$w_{sk}=\max (a_{sk},l_{s,k-1},\min (t{f}_{s1},t{f}_{s2},\dots ,t{f}_{su}))-a_{sk},\forall u\in U,\forall s\in V_s,\forall k\in K$$

(10)

$${\displaystyle \sum _{s\in V_s}{\displaystyle \sum _{u\in U}{h}_{usk}}=1},\forall k\in K$$

(11)

$$c{s}_k={\displaystyle \sum _{s\in V_s}{\displaystyle \sum _{t\in T}b{e}_{skt}}}(p{e}_t+p{s}_t)z_{sk}$$

(12)

$${\displaystyle \sum _{t\in T}b{e}_{skt}}={\displaystyle \sum _{s\in V_s}(0.9E-e_{sk})z_{sk}},\forall k\in K$$

(13)

$$\left\{\begin{array}{l}{\omega }_{ijt}^1=0.247+{\displaystyle \frac{1.52}{v_{ij}^t}}-0.004v_{ij}^t+2.992\times {10}^{-5}{v}_{ij}^t\\ {\omega }_{ijt}^2=-0.179+0.004v_{ij}^t+{\displaystyle \frac{5.492}{v_{ij}^t}}\\ {\omega }_{ijt}^3=0.21+{\displaystyle \frac{1.531}{v_{ij}^t}}-0.001v_{ij}^t\end{array}\right.$$

(14)

The objective function minimizes the total battery swapping cost for vehicles, including travel time to the BSS, waiting cost at the BSS, and the battery swapping fee. Constraint (2) ensures that each vehicle selects only one swapping station. Constraint (3) ensures the consistency of the movement between nodes and swapping station selection. Constraint (4) represents the vehicle’s battery level upon arrival at a node, describing the battery consumption under different times and road types. Constraint (5) represents the per-unit distance battery consumption between nodes $i$ and $j$ at time $t$. Constrain (6) ensures that nodes $i$ and $j$ belong to only one type of road. Constraint (7) indicates that upon arrival at a swapping station, the battery level of vehicle $k$ must be greater than 10% of the battery’s capacity. Constraint (8) calculates the arrival time of vehicle $k$ at node $j$. Constraint (9) denotes the time required for each battery at the swapping station to reach full charge. This value continuously changes as vehicles arrive and depart from the station. Constraint (10) defines the waiting time $w_{sk}$ for vehicle $k$ at swapping station $s$. Whether a vehicle can begin swapping depends on two conditions. First, whether there is an available queue position for the vehicle, and second, whether there is a sufficiently charged battery. The availability of swapping service is determined by the departure time $l_{s,k-1}$ of the preceding vehicle. The availability time of a battery depends on its charging duration, and each vehicle upon arrival will obtain a set of fully charged battery times $(t{f}_{s1},t{f}_{s2},\dots ,t{f}_{su})$. Thus, the vehicle’s waiting time is the difference between the earliest available service time and its arrival time at the swapping station. Constraint (11) indicates that each vehicle can only select one battery to swap at the station. Constraint (12) represents the swapping cost for vehicle $k$ at the swapping station. Since the charging process generally spans multiple time periods, the battery will be recharged over several intervals until it reaches the vehicle’s requirements, as shown in Constraint (13). Constraint (14) represents battery consumption during vehicle travel.

3. Solution Method

Drivers have different expectations for the response time of battery swapping services. Some prefer immediate recommendations, while others can accept short delays for better results. Peak-hour demand often leads to station congestion and uneven resource use. To address this, we propose two guidance strategies: real-time optimization and delayed optimization. The real-time strategy provides instant recommendations and periodic updates. The delayed strategy collects requests over fixed intervals and processes them in batches, which is more effective during high-demand periods.

3.1. Real-Time Optimization for Vehicle Guidance

This section introduces a real-time optimization framework to guide vehicles to battery swapping stations under dynamic demand conditions, as shown in Figure 3. The framework integrates real-time allocation and rolling optimization to adapt to continuously changing station statuses and vehicle requests.

In the initial phase, vehicle requests are addressed immediately upon generation using a greedy algorithm. This approach minimizes the total battery swapping costs, encompassing travel time, waiting time, and swapping fees. After assigning a swapping station, the shortest path from the vehicle’s current location to the selected station is determined based on real-time traffic conditions.

To account for changes in station states and newly generated requests, rolling optimization is performed at fixed intervals. During each interval $\Delta t$, the system combines pending requests from the previous period with newly generated requests. All requests are then reassigned to their optimal stations, and travel paths are recalculated based on the latest system information.

Figure 4 provides an example of real-time optimization. At time $t$, vehicle $E{V}_1$ sends a battery swap request. Based on the road segment speeds $v_{ij}^t$ at time $t$ and the current status of swapping stations, $EV1$ is initially assigned to station $s_1$ with the shortest path $D1-D2-D4-S1$. At time $t+1$, the position of $EV1$ is updated to node $D_4$. Considering the updated station status and road conditions, a new swapping station assignment is made. Simultaneously, vehicle $E{V}_2$ generates a new swap request at node $D_3$. Taking into account the updated road speeds, the request from $E{V}_2$, and the latest station status, the final path for $E{V}_1$ is adjusted to $D1-D2-D4-S2$.

Additionally, when reallocating a swapping station and recalculating a vehicle’s route after $\Delta t$, it is crucial to determine the vehicle’s starting node. As shown in Figure 5a, if the vehicle reaches node 2 exactly at time $\Delta t$, node 2 is set as the starting node. However, if the vehicle is still on the road segment and has traveled a distance $d_{12}+d_{2j^{\prime }}$, as show in Figure 5b, the end node of that segment, node 4, is set as the starting node for the updated route.

3.2. Delayed Optimization for Vehicle Guidance

To meet different user preferences in vehicle guidance, this study proposes a delayed optimization strategy. Unlike real-time optimization, which processes each vehicle request immediately, delayed optimization aggregates requests within a short decision window (e.g., 5 min) to achieve a more efficient and globally optimized solution. For example, in the online retail industry, more orders may be received during the delay period, which provides more information for the e-commerce provider to make better decisions [27,28]. The delayed optimization strategy addresses dynamic vehicle demand by dividing the continuous optimization problem into sequential static decision cycles. This framework consists of two key stages: global optimization for vehicle allocation and dynamic demand insertion.

3.2.1. Genetic Algorithm Optimization

Figure 6 presents the framework of the delayed optimization strategy. At the start of each decision interval, all battery swapping requests within the interval are processed together. These requests are globally optimized using the genetic algorithm. The goal is to minimize the vehicle travel distance, battery swapping costs, and waiting time while considering station capacity constraints. Each solution is encoded as a chromosome, where vehicle assignments to battery swapping stations (BSSs) are represented as integers corresponding to station nodes in the network. After optimization, the assignment results of vehicles to swapping stations are obtained, forming an expected arrival queue. As shown in Figure 6, during the $[0,1]$ time period, 11 vehicle requests are optimized. Based on the expected arrival time of the vehicles, arrival queues are formed at two swapping stations, and battery swapping is conducted on a first-come, first-served basis.

3.2.2. Dynamic Demand Insertion Using KD-Tree

In subsequent decision intervals, as new vehicle requests are dynamically generated, they need to be inserted into the previously optimized solution. As shown in Figure 6, during the time interval $[1,2]$, vehicles $k1-k5$ have arrived at the BSS, while vehicles $k6-k11$ have been scheduled but have not yet arrived. These arrived and expected-to-arrive vehicles form queues at each BSS. Newly generated vehicle demands $k12-k14$ are dynamically inserted into these queues based on the distance of the vehicles from the BSS.

To address this challenge, this study proposes a KD-tree nearest-neighbor search method, adopting a “station-to-vehicle” approach instead of the traditional “vehicle-to-station” strategy. The traditional approach, where vehicles select the nearest BSS, has two significant limitations. First, from the perspective of accessibility and distance cost, drivers do not need to perform a global search across all BSSs, as this results in significant, unnecessary computational overhead. Second, this method does not fully consider the positions of other vehicles, potentially leading to station selection conflicts. Therefore, the “station-to-vehicle” approach is employed, where each BSS proactively identifies and allocates the nearest vehicle to itself. The key steps are as follows:

Step 1: Constructing the KD-Tree. Vehicle demand points are split into dimensions (e.g., latitude and longitude). The median value of the data is selected as the root node, with lower and higher values assigned to the left and right subtrees, respectively. This recursive process forms a balanced KD-tree structure.

Step 2: Nearest-Neighbor Search. Starting from the root node, the search traverses the tree to identify the nearest vehicle demand point to the BSS. The Haversine formula or other distance metrics are applied to calculate the spherical distance between the BSS and vehicle points.

Step 3: Updating the KD-Tree. Once a vehicle is assigned to a BSS, it is removed from the KD-tree. This prevents duplication and ensures subsequent searches reflect only unallocated vehicles.

Step 4: Generating a New Solution. The updated vehicle assignments are integrated into the optimization framework. The newly inserted demands form an optimized queue for each BSS, which is further refined through the global optimization process using the genetic algorithm.

4. Numerical Simulation

4.1. Scenario Description

This case study addresses the recommendation of battery swapping stations (BSSs) for electric vehicles (EVs) under stochastic traffic conditions. The scenario is set within Beijing’s Fourth Ring Road, including expressways, arterial roads, and secondary roads. The network consists of 46 nodes and 71 road segments, as shown in Figure 7. Triangular nodes (12, 19, and 38) represent the locations of the BSS, while circular nodes denote road intersections where multiple battery swapping requests are randomly generated.

With the development of traffic technology and big data, traffic status data have emerged as an effective tool for studying traffic flow and related issues [29]. Such data include information on real-time traffic flow, speed, and congestion levels. This paper chooses Baidu Maps as the primary data source for traffic conditions. Python 3.7.0 and web scraping techniques are used to obtain traffic status data for specific time periods via HTTP request libraries and URL parameters. The data are gathered at 5 min intervals, covering the time period from 00:00 to 23:20.

Distances between road segments are measured using Baidu Maps’ distance measurement tool. Sample distances are provided in

Table 2. Distance between sections.

Road Segment	Distance (km)	Road Segment	Distance (km)
1–2	1.3	14–26	2.45
1–12	0.87	15–16	2.2
2–3	3.2	15–27	2.7
2–13	0.88	16–17	1.9
3–4	2	16–28	2.44
3–15	0.87	17–18	1.2

. Detailed data are provided on GitHub.

Based on the Baidu Map travel big data platform and the Python programming language, we obtained the travel speeds of various road segments at different times. Due to the high update frequency of the traffic network and the large data volume,

Table 3. Speed of each section at 18:00.

Road Segment	Average Speed	Road Type
1–2	31.807	secondary road
1–12	30.06	expressway
2–3	35.351	secondary road
2–13	17.344	secondary road
3–4	25.787	expressway
24–35	25.074	arterial road

provides sample travel speeds for each road segment at 18:00. Detailed data are provided on GitHub.

4.2. Analysis of Numerical Results

This section analyzes vehicle guidance and optimization strategies for BSSs under varying driver preferences. The performance of a BSS is influenced by multiple factors, as outlined in the case study scenario. Based on the objective function defined in Section 2.2 (Equation (1)), drivers prioritize factors differently, which affects their selection of BSSs and travel routes. To reflect these differences, four preference scenarios are considered, ranking the importance of travel time (T), swapping cost (C), and queuing wait time (W). The scenarios are shown in

Table 4. Factor priorities in the four scenarios.

Scenario	Factor Priority Order	Description
1	T > C > W	Travel time is most important
2	W > C > T	Queuing time is most important
3	C > W > T	Swapping cost is most important
4	T = C = W	Equal weighting

.

In Beijing, most battery-swapping taxis are BAIC New Energy vehicles. This study selects the EU300 model as the case vehicle, which has a battery capacity of 45.3 kWh and a maximum range of 300 km. Charging standards differ among operators. After querying prices through a charging APP, this paper calculated the average prices for different time periods (peak, valley, and off-peak) and used them to determine the parameter values. The battery charging rate is affected by the power of the charging pile, which typically ranges from 40 kW to 120 kW for fast charging. According to [25], the charging rate is set to 1.25 kWh/min. The specific values are in

Table 5. BSS parameter information.

Parameter	Initial Value
Number of BSSs	4
Number of Batteries	10
Charging Price	Off-peak: 0.8 CNY/kwh, Peak: 1.1 CNY/kwh, Valley: 0.6 CNY/kwh
Service Fee	0.35 CNY/kwh
Charging Power	1.25 kWh/min

.

Due to the uncertain timing of battery swapping demand generated by electric taxis, we define a demand generation rate, $\lambda$, representing the average number of vehicles requesting battery swaps per period, which is similar to the arrival rate in queuing theory. A random function is used to generate vehicle demand times randomly within each period. The case study includes 360 vehicles, with a simulated time period from 06:00 to 22:00. The demand generation rates for each period are shown in

Table 6. Demand generation rate of each period.

Time Period	Demand Generation Rate	Time Period	Demand Generation Rate
[06:00–07:00]	10	[14:00–15:00]	30
[07:00–08:00]	10	[15:00–16:00]	20
[08:00–09:00]	10	[16:00–17:00]	20
[09:00–10:00]	20	[17:00–18:00]	20
[10:00–11:00]	30	[18:00–19:00]	30
[11:00–12:00]	30	[19:00–20:00]	20

.

Based on taxi operation patterns and the battery swapping demand distribution reported in [8], the demand settings for this case study were determined.

4.2.1. Comparison of Vehicle Waiting Times

Assuming that BSS batteries are immediately recharged after each swap, driver preferences are modeled by assigning different weights to the objective functions. Two optimization methods, real-time optimization and rolling optimization, are applied for analysis. Through experiments,

Table 7. Solution results under four preference scenarios.

Optimization Method	Scenario	Average Waiting Time (min)	Vehicles Waiting > 20 min	Average Waiting Time at Each BSS
Method 1: Real-Time Optimization	1	11.83	89	[0.41, 17.99, 10.62]
	2	4.60	19	[4.86, 5.40, 3.51]
	3	7.95	44	[4.6, 13.11, 3.74]
	4	4.48	18	[1.6, 6.07, 4.60]
Method 2: Delayed Optimization	1	12	89	[0.3, 19.3, 11.55]
	2	1.07	0	[0.98, 0.90, 1.28]
	3	8.62	62	[0.52, 14.79, 5.36]
	4	2.10	0	[1.09, 2.98, 1.83]

presents the key indicator results for different objective weights under four preference scenarios.

By comparing the results across the four preference scenarios, we observe that for both optimization methods, the trends in vehicle waiting time, the number of vehicles exceeding the tolerance for waiting, and the average waiting time at the BSS are consistent. However, there are differences in the optimization effects.

In Scenario 1, drivers prioritize the nearest BSS. Due to the limited service capacity of each station, this leads to excessive load at the stations and longer queuing wait times. The optimization effects of Method 1 and Method 2 are similar, with 24% of vehicles having wait times exceeding 20 min and a small number waiting for nearly an hour (see Figure 8).

In Scenario 2, drivers prioritize reducing queuing wait times. This objective achieves a balanced distribution of traffic across the three BSSs. Method 2 performs significantly better than Method 1. In Method 1, 5% of vehicles have wait times exceeding 20 min, while in Method 2, this percentage is 0 (see Figure 9).

In Scenario 3, drivers prioritize reducing costs. Drivers choose battery swapping stations with lower overall costs, which may also lead to excessive load at a particular station and increased wait times. In this scenario, the optimization results of Method 1 and Method 2 are largely similar (see Figure 10).

In Scenario 4, a comprehensive approach is taken, considering distance, cost, and wait time equally. This multi-factor balancing scenario achieves a more equitable distribution of vehicle wait times. Method 2 significantly outperforms Method 1 in this case. Under Method 1, 5% of vehicles experience wait times exceeding 20 min, whereas under Method 2, this percentage drops to 0 (see Figure 11).

The above analysis of two optimization methods under four different preference scenarios leads to the following main conclusions:

(1)

Balancing factors such as distance, wait time, and cost leads to better outcomes. Vehicle wait times vary significantly across different preference scenarios.

(2)

Delayed optimization outperforms real-time optimization. Real-time decisions focus on immediate responses. However, without communication between vehicles, decisions rely only on current information. This can result in longer wait times for some vehicles upon reaching a BSS. Delayed optimization, by contrast, emphasizes inter-vehicle cooperation. It uses prediction and strategic planning to optimize BSS selection, achieving more efficient resource allocation.

4.2.2. Comparison of Fully Charged Battery Counts at BSSs

Figure 12 and Figure 13 show the fully charged battery count variations across three battery swapping stations (Stations 12, 19, and 38) under real-time and delay optimization. Both methods display similar overall trends, with battery counts decreasing during morning (06:00–10:00) and afternoon (16:00–20:00) peaks and increasing at midday and night. This aligns with the typical daily fluctuation in swapping demand.

Real-time optimization (Figure 12) relies solely on current data, leading to an imbalanced distribution. During peak times, battery counts at Stations 19 and 38 drop sharply, while Station 12 remains stable, indicating uneven resource use that may increase wait times and reduce efficiency.

In contrast, delayed optimization (Figure 13) achieves a more balanced resource distribution by forecasting vehicle arrivals, resulting in uniform battery availability across stations, especially during peak periods (e.g., 10:45–11:10). This reduces individual station loads, lowering wait times and improving service efficiency.

In summary, delayed optimization better balances resources, which is suitable for stable demand patterns, while real-time optimization provides quicker responses, fitting dynamic demand scenarios.

5. Conclusions and Future Work

Addressing the operational practices of battery swapping stations and incorporating the uncertainty in electric taxi movements, this paper constructs a comprehensive optimization framework for vehicle-to-station assignment under dynamic demand. The framework effectively mitigates station congestion caused by resource limitations and conflicting vehicle demands. The main conclusions are as follows:

(1)

This study introduces two optimization methods: real-time optimization and delayed optimization. Real-time optimization uses a greedy algorithm to rapidly generate decisions based on real-time vehicle locations and BSS statuses. This strategy is suitable for drivers who prioritize immediate battery swapping. In contrast, delayed optimization emphasizes cooperative effects, combining genetic algorithms and KD-tree-based rapid insertion techniques to achieve global optimization within fixed time windows. This method is more suited to scenarios requiring coordinated scheduling.

(2)

Case study analysis demonstrates that considering travel distance, waiting time, and swapping cost can significantly enhance swapping service efficiency. Further analysis reveals differences in station selection between the two methods, reflecting the impact of real-time information and shared data on decision-making.

(3)

From a management standpoint, a centralized dispatch system is essential for efficient station scheduling. Additionally, developing a user-friendly driver application can effectively improve user experience, thereby facilitating resource allocation and service quality improvements.

This study has several limitations. First, it assumes that replaced batteries are immediately recharged after swapping. However, this setting ignores electricity pricing, an important factor for station operators when managing charging costs. Second, the model assumes that drivers fully comply with the recommended assignments. In future work, electricity pricing and driver behavior can be incorporated to support more flexible decision-making. Additionally, this study does not address emergency demands, such as those from ambulances and emergency vehicles. The suddenness of emergency demands may disrupt regular queuing processes. Future research can focus on resource allocation and priority management under emergency conditions.