A Novel Max-Pressure-Driven Integrated Ramp Metering and Variable Speed Limit Control for Port Motorways

Abstract

In recent years, congestion on port motorways has become increasingly frequent, significantly constraining transportation efficiency and contributing to higher pollution emissions. This paper proposes a novel max-pressure-driven integrated control (IFC-MP) for port motorways, inspired by the max pressure (MP) concept, which continuously adjusts the weights of ramp metering (RM) and the variable speed limit (VSL) based on pressure feedback from the on-ramp and upstream, assigning greater control weight to the side with higher pressure. A queue management mechanism is incorporated to prevent on-ramp overflow. The effectiveness of IFC-MP is verified in SUMO, filling the gap where the previous integrated control methods for port motorways lacked micro-simulation validation. The results show that IFC-MP enhances bottleneck throughput by approximately 7% compared to the no-control case, optimizes the total time spent (TTS) by 26–27%, and improves total pollutant emissions (TPEs) by about 11%. Compared to strategies that use only RM and VSL control, or activate VSL control only after RM reaches its lower bound, the time–space distribution of speed under IFC-MP is more uniform, with smaller fluctuations in bottleneck occupancy. Additionally, IFC-MP maintains relatively stable performance under varying compliance levels. Overall, the IFC-MP is an effective method for alleviating congestion on port motorways, excelling in optimizing both traffic efficiency and pollutant emissions.

1. Introduction

Port motorways in large ports often experience substantial spatiotemporal variability [1] in traffic flow, particularly during operations associated with vessel arrivals and departures. This variability frequently leads to localized congestion [2,3] at critical segments, such as major junctions, posing serious challenges to terminal logistics and freight mobility. The traffic stream is predominantly composed of container trucks, which are larger, have constrained maneuverability [4], and exhibit slower acceleration and deceleration capabilities, thereby aggravating congestion. Congestion not only reduces the traffic efficiency and capacity of these roads [5,6] but also results in substantial pollutant emissions [7,8], thereby causing significant environmental impacts. Accordingly, to ensure the efficient operation of port motorways, it is essential to adopt effective traffic control measures to address congestion issues.

Numerous motorway traffic control methods have been proposed in previous studies to mitigate congestion. Among these, ramp metering (RM) [9,10] and variable speed limit (VSL) control [11,12] have emerged as two of the most direct and effective measures validated in real-world implementations. However, when applied independently, each method offers only limited benefits under certain conditions. For instance, the storage space available at on-ramps is constrained by their physical length, often necessitating the use of queue management techniques to prevent overflow [13]. Similarly, VSL control on motorways faces its own set of limitations: the speed limits are subject to a prescribed minimum [14], and its effectiveness is highly dependent on the selected application area [15]. When either of these control methods reaches its control limit, it can provide further improvements in control outcomes.

Therefore, an increasing number of researchers have proposed integrated control approaches [16,17] combining RM and VSL control to address the limitations associated with their independent application. These integrated control strategies can be divided into feedforward control and feedback control. Feedforward methods typically rely on advanced techniques such as model predictive control (MPC) [18,19,20,21] or optimal control based on a second-order traffic flow model [22], which require accurate demand forecasts and reliable model validation, or machine learning (ML) based optimal control [23,24], which often operate as black-box systems dependent on large volumes of historical data for training. Although effective under certain conditions, these approaches face challenges on port motorways, where heterogeneous traffic flows fluctuate with port operation schedules [1]. The nonlinear relationship between traffic demand and port activities undermines prediction reliability and complicates model validation. Additionally, the high computational complexity of feedforward approaches hinders their real-time application in such uncertain environments.

In contrast, rule-based feedback control offers a more practical solution by adjusting control actions based on the system’s current state, without relying on demand predictions or complex model calibrations. However, most existing feedback control strategies for integrated systems implement VSL control only after RM has reached its lower bound [25,26]. On port motorways, where container trucks dominate, this rule may lead to queue overflow when on-ramp demand is high, and the delayed activation of VSL control may hinder timely congestion mitigation when mainstream demand is high as container trucks require additional time to decelerate. Consequently, it is necessary to develop a method that can simultaneously activate RM and VSL control and continuously adjust their integration based on feedback from mainstream and on-ramp demands, so as to better adapt to the characteristics of port motorways.

In the process of searching for integration rules, we identified that the competition between mainstream and on-ramp flows on port motorways is similar to the competition for downstream traffic resources at urban intersection approaches. The most widely used strategy for addressing intersection congestion is the max pressure (MP) strategy [27]. The core idea is to define the pressure at a node as the difference between upstream and downstream flows and prioritize releasing the direction with the highest pressure to delay the formation of congestion [28,29,30]. Based on this theory, we considered whether the idea of MP could be applied to integrate RM and VSL control to alleviate congestion on port motorways.

Since traffic flow at intersections is discontinuous, the flow with the highest pressure can be prioritized. However, on port motorways with continuous flow, it is not possible to release just one direction. Therefore, we propose a novel MP-driven integrated method where RM and VSL control are assigned weights based on the pressure levels of mainstream and on-ramp flows, with a higher pressure receiving a larger weight. At the same time, we recognize that RM solely based on this weight may lead to queue overflow. We introduce a queue management mechanism that places a greater reliance on VSL control once the queue reaches a predefined limit.

The effectiveness of this method needs to be evaluated through experimentation, making it essential to summarize the existing research in traffic simulation studies. It was found that previous research has evaluated RM through micro-simulation, by Abuamer, Woong Cho and Lee [31,32,33], and VSL control, by Du and Papamichail [34,35], as well as intersection signal control, by Owais and Almutairi [36,37]. However, there is a lack of research using micro-simulation to assess integrated control strategies for motorway traffic. For port motorways, in addition to total time spent, an important metric for evaluating the effectiveness of the methods is pollutant emissions, which need to be accurately assessed through micro-simulation. Therefore, further micro-simulation studies are crucial for evaluating integrated control strategies in port motorway contexts.

Building upon the above analysis, the main contribution of this study is the development of a novel max-pressure-driven integrated ramp metering and variable speed limit control (IFC-MP) method tailored to port motorways. Different from traditional MP applications that prioritize a single movement with the highest pressure at signalized intersections with discrete traffic flows, IFC-MP separately calculates pressures for the mainstream and on-ramp and converts them into control weights for the continuous-flow environment of port motorways, enabling RM and VSL control to be adjusted simultaneously and proportionally. Moreover, unlike existing integration strategies that typically alternate between RM and VSL control, IFC-MP uses pressure-based weights to enable parallel and balanced regulation of both controls. This unified framework improves adaptability to varying traffic conditions while maintaining operational stability. The effectiveness of IFC-MP is evaluated through micro-simulation, with both traffic efficiency and pollutant emissions used to comprehensively assess its suitability for port motorways.

The remainder of this paper is structured as follows after the introduction: Section 2 provides a brief review of motorway traffic control methods, including RM, VSL control, and their integration. Section 3 details the proposed integrated control strategy for port motorways. Section 4 describes the simulation experimental design and presents a comparative analysis of the simulation results across different control strategies in various scenarios, along with a stability analysis of the proposed strategy under varying compliance levels. The conclusion is drawn in the final Section 5.

2. Motorway Traffic Control Methods

This section outlines the basic ideas of two motorway traffic control methods: ramp metering (RM) ([16] for an overview) and variable speed limit (VSL) control ([38] for an overview), as well as their integration. These techniques are used to improve traffic conditions on motorways.

2.1. Ramp Metering

When the combined demand $d$ (veh/h) from the on-ramp and the mainstream arriving flow $q_{in}$ (veh/h) upstream of the on-ramp exceed the motorway capacity $q_{cap}$ (veh/h) downstream of the on-ramp, then a bottleneck is activated. This bottleneck generates shockwaves propagating upstream of the on-ramp, leading to a reduction in motorway throughput. The use of RM, as illustrated in Figure 1a, effectively addresses this issue. Its fundamental principle is based on regulating the inflow of vehicles from the ramp onto the motorway by stipulating a controlled ramp flow $q_r$ (veh/h) using traffic lights [39], thereby maintaining the bottleneck outflow $q_{out}$ (veh/h) near the capacity $q_{cap}$. When bottleneck flow reaches its maximum, the occupancy $o_{out}$ (veh/km) at the bottleneck is typically near the critical occupancy $o_{cr}$ (veh/km). RM alone has a limited impact on overall traffic flow and is often insufficient to alleviate congestion when mainstream demand is high.

2.2. Variable Speed Limit Control

Initially, VSL control was primarily implemented to enhance safety by smoothing shockwaves at the tail end of queues for more gradual speed drops. However, numerous studies suggest that VSL control can also relieve congestion by delaying vehicles reaching bottlenecks. As illustrated in Figure 1b, the basic idea of VSL control is to adjust the speed limits in order to regulate the upstream mainstream flow $q_{in}$ well in advance of active bottlenecks. This regulation creates a controlled outflow $q_c$ (veh/h) formed on the mainstream and establishes an acceleration area between the controlled area and the bottleneck. The acceleration area enables vehicles exiting the controlled area to speed up and pass through the bottleneck at a critical speed $v_{cr}$ (km/h). The area upstream of the acceleration area, where speed limits are actively managed, is referred to as the VSL control area. VSL control alone has a limited impact on regulating traffic flow and is often ineffective in mitigating congestion when on-ramp demand is high.

2.3. Integrated Motorway Traffic Control

When a single control method reaches its lower bound, its effectiveness is significantly diminished. To address this issue, many scholars have proposed an integrated control method, which combines two or more traffic control methods to maintain efficient operations [16]. In the specific case of the integration of RM and VSL control (Figure 1c), the key idea is to jointly manage mainstream flow $q_c$ and on-ramp inflows $q_r$ to maintain a bottleneck outflow $q_{out}$ near the capacity flow $q_{cap}$.

The advantage of this integration lies in its ability to sustain traffic management performance even when one of the individual controls reaches its operational constraints. Additionally, by jointly determining the two inflows, $q_c$ and $q_r$, it becomes possible to optimize these values according to predefined criteria, such as balancing queues [40] or minimizing traffic delay [41]. This integrated method is particularly beneficial for port motorways, where traffic conditions are highly variable. Specifically, when large ships dock, there is a sudden surge in container trucks both entering and exiting the port. By precisely managing both traffic flows, integrated control can effectively address these fluctuations and mitigate the control lags caused by container trucks.

3. Integrated Control for Port Motorways

A max-pressure-driven integrated control (IFC-MP) strategy is proposed for port motorways, combining RM and VSL control. The control system (Figure 2) is structured into three main components: the feedback control structure, the split block, and the actuation decision module.

3.1. Feedback Control Structure

The core idea of the integrated method is to jointly determine the desired mainstream flow ${\widehat{q}}_c$ (veh/h) and the desired on-ramp flow ${\widehat{q}}_r$ (veh/h) to keep the bottleneck throughput $q_{out}$ (veh/h) near the capacity flow $q_{cap}$ (veh/h). As illustrated in Figure 2, the system setup consists of a feedback control framework. A proportional–integral (PI) controller is employed to generate a reference flow ${\widehat{q}}_t$ (veh/h):

$${\widehat{q}}_t\left(k\right)={\widehat{q}}_t\left(k-1\right)+K_P\left[e_o\left(k\right)-e_o\left(k-1\right)\right]+K_I{e}_o\left(k\right)$$

(1)

where ${\widehat{q}}_t\left(k\right)$ denotes the total desired inflow to be implemented during the time interval $\left(k{T}_c,\left(k+1\right)T_c\right]$, with $T_c$ (s) as the control period of the integrated controller. This reference flow ${\widehat{q}}_t$ consists of two flows: ${\widehat{q}}_c$ (veh/h) regulated by VSL control (as shown in Figure 1b) and ${\widehat{q}}_r$ (veh/h) handled by RM (as shown in Figure 1a). Thus, ${\widehat{q}}_t$ is bounded by the sum of the mainstream capacity ($q_{cap}^m$ (veh/h)) and the on-ramp capacity ($q_{cap}^r$ (veh/h)). $K_P$ (km/h) and $K_I$ (km/h) represent the proportional and integral gains of the controller, respectively. $e_o\left(k\right)=o_{cr}-o_{out}\left(k\right)$ is the occupancy error between the critical occupancy $o_{cr}$ and the bottleneck occupancy $o_{out}\left(k\right)$ at the time $k{T}_c$.

3.2. Split Block

There are now two input flows to control the bottleneck occupancy, and [25,26] were the first to propose an allocation policy to achieve the allocation of two input streams. This policy applies RM as long as the ramp storage space is not full and switches to VSL control only when queue management is activated, i.e., ramp storage space is about to be exhausted, or when the RM lower bound has been reached. The values of $K_P$ and $K_I$ in Equation (1) for this policy depend on whether RM or VSL control is active within $T_c$. However, because traffic flow on port motorways is influenced by operational factors, this policy may lead to prolonged waiting times for vehicles on the on-ramp and reduce traffic efficiency.

In traffic signal control, the MP strategy is widely used to balance traffic flow through a real-time segment pressure-based dynamic distributed control [42], prioritizing the flow with the highest pressure in the system. Applying this strategy to port motorways has the potential to deliver effective control outcomes, even though it has not yet been implemented in motorway traffic management. However, since port motorways are connected to on-ramps, directly adopting the classical MP strategy could lead to spillover, negatively impacting the traffic efficiency of on-ramps and adjacent road segments and further exacerbating congestion throughout the network. To address this issue, we propose a novel max-pressure-driven policy: the MP strategy assigns a higher weight to the segment with larger pressure and integrates RM and VSL control to distribute bottleneck pressure between the mainstream and the on-ramp based on these weights. Additionally, the proposed policy incorporates queue management to prevent spillover and improve overall traffic stability.

By taking the difference between upstream arrival flow $q_c$ (veh/h) and bottleneck outflow $q_{out}$ as the mainstream pressure $p_c$ (veh/h), while using the difference between on-ramp merging flow $q_r$ (veh/h) and $q_{out}$ as the on-ramp pressure $p_r$ (veh/h), the specific pressure calculations are as follows:

$$p_c\left(k\right)=q_c\left(k-1\right)-q_{out}\left(k-1\right)$$

(2)

$$p_r\left(k\right)=q_r\left(k-1\right)-q_{out}\left(k-1\right)$$

(3)

where $p_c\left(k\right)$ denotes the mainstream pressure at the time $k{T}_c$, while $p_r\left(k\right)$ denotes the on-ramp pressure at the time $k{T}_c$. $q_c\left(k-1\right)$ and $q_r\left(k-1\right)$ are the actual input flows measured by detectors during the time interval $\left(\left(k-1\right)T_c,k{T}_c\right]$, while $q_{out}\left(k-1\right)$ is the actual output flow measured by the detector during the time interval $\left(\left(k-1\right)T_c,k{T}_c\right]$.

Based on the proportion of mainstream pressure to on-ramp pressure, two reference weights $W_1$ and W₂ can be obtained, serving as a foundation for subsequent pressure-based weight allocation:

$$W_1\left(k\right)={\displaystyle \frac{\left|p_c\left(k\right)\right|}{\left|p_c\left(k\right)\right|+\left|p_r\left(k\right)\right|}}$$

(4)

$$W_2\left(k\right)={\displaystyle \frac{\left|p_r\left(k\right)\right|}{\left|p_c\left(k\right)\right|+\left|p_r\left(k\right)\right|}}$$

(5)

This policy assigns a higher weight to the segment with larger pressure between the mainstream and the on-ramp. Specifically, $W_c\left(k\right)\in \left(0,1\right)$ and $W_r\left(k\right)\in \left(0,1\right)$ represent the weights of the mainstream and the on-ramp, respectively, during the time interval $\left(k{T}_c,\left(k+1\right)T_c\right]$. The conditions are as follows: if the mainstream pressure exceeds the on-ramp pressure, that is, $p_c\ge p_r$, the mainstream weight $W_c=\max \left(W_1,W_2\right)$; if the on-ramp pressure is higher, that is, $p_c<p_r$, then $W_c=\min \left(W_1,W_2\right)$. The on-ramp weight $W_r$ is calculated as W_r = 1 − W_c.

When the on-ramp queue remains within the management threshold $\widehat{w}$ (veh), which is conservatively set below the maximum allowable queue $w_{\max }$ (veh), the on-ramp flow ${\widehat{q}}_r$ follows the flow $W_r{\widehat{q}}_t$ allocated according to the pressure-based weight. However, once the on-ramp queue exceeds the threshold, indicating the risk of spillback, queue management is activated. A proportional (P) controller with a feed-forward term based on the on-ramp demand $d$ (veh/h) is employed to compute the revised flow ${\stackrel{⌢}{q}}_r$ (veh/h), which overrides $W_r{\widehat{q}}_t$ to release additional vehicles and mitigate the spillback risk:

$${\stackrel{⌢}{q}}_r\left(k\right)=d\left(k-1\right)-{\displaystyle \frac{1}{T_c}}\left[\widehat{w}-w\left(k-1\right)\right]$$

(6)

where ${\stackrel{⌢}{q}}_r\left(k\right)$ (veh/h) denotes the revised flow resulting from queue management during the time interval $\left(k{T}_c,\left(k+1\right)T_c\right]$. $w\left(k\right)$ (veh) represents the number of vehicles in the on-ramp queue.

As queue management takes priority under potential spillback, the desired on-ramp flow ${\widehat{q}}_r$ is determined by comparing ${\stackrel{⌢}{q}}_r$ and $W_r{\widehat{q}}_t$. If ${\stackrel{⌢}{q}}_r$ is less than $W_r{\widehat{q}}_t$, the flow ${\widehat{q}}_r$ remains as $W_r{\widehat{q}}_t$. Otherwise, ${\widehat{q}}_r$ is set as ${\stackrel{⌢}{q}}_r$ to alleviate the spillback risk. To maintain consistency with the total desired inflow ${\widehat{q}}_t$, the desired mainstream flow ${\widehat{q}}_c$ is then updated accordingly as the difference between ${\widehat{q}}_t$ and ${\widehat{q}}_r$. These two cases are summarized as follows:

$${\widehat{q}}_r\left(k\right)=\left\{\begin{array}{l}{W}_r\left(k\right){\widehat{q}}_t\left(k\right),W_r\left(k\right){\widehat{q}}_t\left(k\right)>{\stackrel{⌢}{q}}_r\left(k\right) \\ {\stackrel{⌢}{q}}_r\left(k\right),W_r\left(k\right){\widehat{q}}_t\left(k\right)\le {\stackrel{⌢}{q}}_r\left(k\right)\end{array}\right.$$

(7)

$${\widehat{q}}_c\left(k\right)=\left\{\begin{array}{l}{W}_c\left(k\right){\widehat{q}}_t\left(k\right),W_r\left(k\right){\widehat{q}}_t\left(k\right)>{\stackrel{⌢}{q}}_r\left(k\right) \\ {\widehat{q}}_t\left(k\right)-{\stackrel{⌢}{q}}_r\left(k\right),W_r\left(k\right){\widehat{q}}_t\left(k\right)\le {\stackrel{⌢}{q}}_r\left(k\right)\end{array}\right.$$

(8)

where ${\widehat{q}}_r\left(k\right)$ and ${\widehat{q}}_c\left(k\right)$ are the desired mainstream flow and the desired on-ramp flow, respectively, during the time interval $\left(k{T}_c,\left(k+1\right)T_c\right]$. This mechanism ensures that the on-ramp queue is effectively managed to prevent spillback while maintaining the total desired inflow at the bottleneck and preserving the pressure-based allocation logic.

3.3. Actuation Decision

After determining ${\widehat{q}}_r$ and ${\widehat{q}}_c$, the input control variables for the next $T_c$ can be set. Specifically, ${\widehat{q}}_r$ is regulated by RM, which determines the green-phase duration, while ${\widehat{q}}_c$ is handled by VSL control, setting the speed limits.

RM is widely recognized as an effective control method for safety concern, though there are few field tests aimed at improving traffic efficiency. ${\widehat{q}}_r$ can be converted to green-phase duration $g$ using the equation below for this conversion, and when integrated with the optimal speed limits upstream, has the potential to increase the outflow of the bottleneck downstream.

$$g\left(k\right)=\left({\widehat{q}}_r\left(k\right)/q_{r,sat}\right)T_c$$

(9)

where $g\left(k\right)\in \left[g_{\min },T_c\right]$ (s) denotes the green-phase duration within the time interval $\left(k{T}_c,\left(k+1\right)T_c\right]$, with $g_{\min }>0$ to avoid ramp closure. $q_{r,sat}$ (veh/h) represents the ramp’s saturation flow. The value of $g$ is updated every RM period $T_r$, which means it is updated every $n_r$ multiples of $T_c$, where $n_r=T_r/T_c$ is an integer.

Speed limits are typically displayed using variable message signs (VMSs), which are installed either above or along the roadside of the motorway to ensure that drivers can clearly see the latest speed limits. The number and spacing of VMS locations are crucial for enabling drivers to adjust their speeds smoothly. Firstly, the number $M$ of VMS placements depends on the speed difference $\Delta V$ between each VMS location, which can be calculated using the following equation:

$$M={\displaystyle \frac{V_{\max }-V_{\min }}{\Delta V}}$$

(10)

where $V_{\max }$ (km/h) and $V_{\min }$ (km/h) represent the maximum and minimum speed limits for the motorway, respectively. Furthermore, the spacing between VMS locations is determined by the deceleration of vehicles. Since deceleration varies across different vehicle types, the minimum deceleration $a_{\min }$ (m/s²) among all vehicle types is used to calculate the minimum spacing s_min (m), ensuring that all vehicles can adjust their speeds successfully:

$$t={\displaystyle \frac{\Delta V}{a_{\min }}}$$

(11)

$$s_{\min }=V_{\max }t+{\displaystyle \frac{1}{2}}{a}_{\min }{t}^2$$

(12)

where $t$ (s) represents the time required for vehicles to adjust. Since different vehicle types exhibit varying levels of compliance with the speed limit, the actual spacing $s$ (m) should satisfy s ≥ s_min.

Along the traffic flow direction, VMSs are sequentially installed upstream of the on-ramp, numbered from 1 to $M$. The speed limits displayed on these VMSs are denoted as $V_1,V_2,\dots ,V_M$, where $V_M$ is calculated using feedback control. Since speed limits are typically set as an integer multiple of 10, a discrete set of VSL rates $b\in \left\{b_{\min },b_{\min }+0.1.,\dots ,1\right\}$ is defined, corresponding to $V_M\in \left\{V_{\min },V_{\min }+10,\dots ,V_{\max }\right\}$. The controller for b is designated as an integral (I) controller:

$$b\left(k\right)=b\left(k-1\right)+K_R\left[{\widehat{q}}_c\left(k\right)-q_c\left(k-1\right)\right]$$

(13)

where $K_R$ (h/veh) is the integral gain. When VSL control is implemented on motorways, the change in $b$ between consecutive $T_c$ is restricted to the range $\left[-b_{\Delta ,\max },b_{\Delta ,\max }\right]$ to ensure driving safety and traffic flow stability [14]. Therefore, when the change exceeds this range, if $b\left(k\right)>b\left(k-1\right)$, then set $b\left(k\right)=b\left(k-1\right)+b_{\Delta ,\max }$; if $b\left(k\right)<b\left(k-1\right)$, then set $b\left(k\right)=b\left(k-1\right)-b_{\Delta ,\max }$. The speed limit $V_M\left(k\right)$ applied within the time interval $\left(k{T}_c,\left(k+1\right)T_c\right]$ should correspond to the final $b\left(k\right)$. The value of $V_M$ is updated every VSL control period $T_v$, meaning it is updated every $n_v$ multiples of $T_c$, where $n_v=T_v/T_c$ is an integer. Subsequently, to ensure a smooth transition of speed limits, based on the calculated results of $V_M$, the speed limit for each upstream VMS is incremented by $\Delta V$ from the speed limit of its downstream VMSs, but not exceeding the maximum allowed speed limit $V_{\max }$:

$$V_{i-1}\left(k\right)=\min \left(V_i\left(k\right)+\Delta V,V_{\max }\right),i=M,M-1,\dots ,2$$

(14)

Before VSL control is applied, all VMSs are initially set to $V_{\max }$. As a vehicle enters a new segment, it adopts the posted speed limit in that segment as its maximum speed limit.

To enhance the clarity of the proposed decision-making framework, its procedural logic is summarized in the flowchart shown in Figure 3.

4. Simulation Results Analysis and Discussion

In this section, we present simulation experiments designed to verify the effectiveness of the proposed control strategy. The effectiveness of the control strategy in alleviating traffic congestion is evaluated based on traffic flow characteristics. The improvement in traffic efficiency is assessed using total time spent (TTS), while the reduction in environmental pollution is measured by total pollutant emissions (TPEs).

Based on these evaluation metrics, the performance of IFC-MP is compared with that of a no-control baseline and other control strategies with similar feedback control structures. These include RM with queue management (PI-ALINEA/Q) [43], VSL control (MTFC-VSL) [44], and integrated control that activates VSL control only when RM reaches its lower bound (integrated-FB) [25].

4.1. Simulation Experimental Design

In this experiment, we extracted the Guoju section of the Chuanshan Port Motorway in Ningbo City from the open-source website OpenStreetMap (www.openstreetmap.org) as the research scenario. MATLAB R2022b and SUMO v1.18.0 were then employed for co-simulation (Figure 4), ultimately generating comprehensive traffic state information for the entire emulated control process.

The starting point of the Guoju section is the Ningbo Yuandong Terminal. The motorway has a total length of 3.2 km and comprises three lanes. An on-ramp, located 1.6 km from the terminal, is 0.63 km long and consists of one lane. Field observations indicate that container trucks account for approximately 60% of the traffic on this section, with half of these trucks carrying a twenty-foot equivalent unit (TEU) and the other half carrying a forty-foot equivalent unit (FEU). Moreover, since the on-ramp connects to the network of the Meishan Container Terminal, the vehicle composition for both mainstream and on-ramp demand is set to 40% cars, 30% TEU-carrying container trucks, and 30% FEU-carrying container trucks.

To manage the flow of these vehicles, RM is implemented by installing traffic signals on the on-ramp. In fact, some areas in China have already installed physical traffic signals, with the default assumption that drivers must strictly adhere to the signals. For VSL control, the speed-factor parameter in SUMO is used to regulate vehicle adherence to speed limits. A value of 1 means full compliance, while values greater or less than 1 indicate traveling above or below the limit, respectively. According to references [45,46] and general motorway regulations, heavier and larger vehicles are subject to lower speed limits. To ensure all vehicles’ full compliance, the speed factor for cars is set to 1, while it decreases to 0.9 and 0.8 for TEU-carrying and FEU-carrying container trucks, respectively, based on their size and weight. Additionally, considering driver behavior differences across vehicle types, we adjusted the sigma and speed dev parameters. Sigma reflects driver behavior randomness, while speed dev indicates speed fluctuations. Similarly, as vehicle size and weight increase, these parameters decrease, indicating more stable driver behavior and smaller speed fluctuations. The specific settings are shown in

Table 1. Parameters for different vehicle types.

Vehicle Type		Length (m)	Accelerate (m/s2)	Decelerate (m/s2)	Sigma	Speed Factor	Speed Dev
Car		5.0	2.6	4.5	0.5	1.0	0.1
Container Truck	carry TEU	10.0	1.0	2.0	0.3	0.9	0.05
	carry FEU	16.0	0.3	1.0	0.1	0.8	0.03

.

$V_{\max }$ and $V_{\min }$ of this motorway are 120 km/h and 60 km/h, respectively, corresponding to $b_{\min }=0.4$. The maximum speed variation constraints in both time and space are 20 km/h, corresponding to $b_{\Delta ,\max }=0.2$ and $\Delta V=20$ km/h. Based on the data in Table 1 and Equations (11)–(13), it can be concluded that $M=3$ and $s_{\min }=170$ m. In this experiment, we have chosen $s=400$ m, which is greater than $s_{\min }$. To collect data once per $T_c$, various types of detectors are installed along the section (Figure 5): loop detectors gather $q_{out}$, $q_c$, $q_r$, and $d$; segment detectors collect $o_{out}$ and $w$. Here, occupancy represents the average occupancy per lane, and $w$ corresponds to the halting vehicles at the last second of the period.

In this experiment, $o_{cr}$ is set to 20 veh/km, and $q_{cap}$ is approximately 3100 veh/h, as estimated based on the motorway design capacity. Based on this value, two sets of trapezoidal demand scenarios (shown in Figure 6) are developed to simulate different congestion patterns, following the demand variation method in [43] and flow levels referenced in [17,24].

Considering the on-ramp length of 630 m and a safety gap of 2.5 m, $w_{\max }$ is approximately 51 veh based on the vehicle lengths and composition ratios. Due to the limited acceleration performance of container trucks, $\widehat{w}$ is conservatively set to 25 veh, which is half of the theoretical value to mitigate the risk of spillback. For control period settings, we refer to recommendations from the literature [47,48,49]: $T_r$ is set to 30 s with $g_{\min }$ equal to 3 s and $T_v$ to 120 s. Of these, $T_c$ takes the smaller value, which is $T_c=30$ s.

4.2. Traffic Flow Characteristics Analysis Under Different Strategies

The no-control case serves as the baseline experiment for quantifying the efficiency improvements achieved through various control strategies. Figure 7 and Figure 8 presents the speed time–space diagrams under scenario 1 and scenario 2, respectively, where the intensity of red indicates the degree of congestion. Figure 9 illustrates the occupancy, flow, and speed in the bottleneck area under different scenarios, highlighting the effectiveness of the proposed control strategy in improving traffic stability and alleviating congestion. As shown in these figures, the demand at the bottleneck exceeds the capacity (approximately 3100 veh/h), resulting in congestion. Consequently, this congestion forces the bottleneck occupancy to reach 50 veh/km, reduces the bottleneck speed to 20 km/h, and limits the bottleneck throughput to 2800 veh/h, representing an approximately 10% reduction relative to the capacity. In the absence of any strategies, congestion propagates upstream; in both scenarios, it spreads approximately 1.6 km upstream and persists for about 60 min.

When applying PI-ALINEA/Q, the integral and proportional gains are determined through repeated experiments conducted around the empirical values provided in [26]. In scenario 1, the proportional and integral gains are set to 290 km/h and 120 km/h, respectively. As shown in Figure 7b, compared to the no-control case, the red congestion area significantly decreases after the application of PI-ALINEA/Q. However, since this strategy cannot regulate the upstream arrival flow, brief congestion still occurs when the mainstream flow surges. This congestion persists for approximately 20 min of congestion at the bottleneck, starting at 60 min, during which the bottleneck speed drops from 60 km/h to 30 km/h. In scenario 2, the controller’s proportional and integral gains are set to 300 km/h and 120 km/h. Since the impact of the mainstream on the bottleneck in this scenario is lower than that in scenario 1, PI-ALINEA/Q demonstrates better control performance under such conditions. Although no significant congestion occurs, the on-ramp queue reaches the setpoint of 25 veh during 30–60 min (Figure 10b), forcing the release of a portion of the flow, which still leads to intermittent congestion at the bottleneck. These results illustrate that while PI-ALINEA/Q plays a significant regulatory role, it has limitations meaning that additional upstream control measures are required to optimize overall traffic operations when mainstream demand is excessively high.

When applying MTFC-VSL, the gains of its controller are determined with reference to the empirical values reported in [25,50], and they are further refined through repeated experiments. In scenario 1, the primary controller uses proportional and integral gains of 25 km/h and 50 km/h, respectively, while the secondary (VSL rate) controller uses an integral gain of 0.0015 h/veh. In scenario 2, the proportional and integral gains are set to 30 km/h and 50 km/h, and the integral gain of the secondary controller remains the same as in scenario 1. As shown in Figure 7c and Figure 8c, compared to the deep red area observed between 0.8 and 3 km in the no-control case, the application of this strategy results in light red areas around 1–2 km and at the bottleneck. As shown in Figure 7c and Figure 8c, compared to the deep red area observed between 0.8 and 3 km without control, the application of this strategy results in light red areas at around 1–2 km and at the bottleneck. This improvement occurs because VSL control can form controlled flow upstream of the on-ramp, thereby increasing the bottleneck speed to approximately 30–60 km/h. As the minimum speed limit is 60 km/h, the flow regulation capability of MTFC-VSL is limited. Once the speed limit reaches its lower bound, continued increases in either mainstream demand or on-ramp demand may lead to renewed congestion. For example, in scenario 2 at 50 min, the speed limit reaches the lower bound (see Figure 10b), causing congestion at the bottleneck to persist for more than 30 min, with the bottleneck speed dropping to as low as 20 km/h. Therefore, if the on-ramp demand is excessively high and on-ramp vehicles merge into the motorway without restriction, the congestion could become even more severe.

For the application of integrated control, integrated-FB activates VSL control only when RM reaches its lower bound. The PI-ALINEA/Q gains are used for RM, while the MTFC-VSL gains are applied for VSL control. As shown in Figure 10, when the queue reaches the setpoint of 25 veh, the speed limit continues to play a role in regulating the flow. This regulatory mechanism compensates for the limitation of PI-ALINEA/Q, which cannot adjust the upstream arrival flow. As shown in Figure 9, the occupancy under this strategy is more stable than that of PI-ALINEA/Q and MTFC-VSL, remaining around 20 veh/km. Although there are small fluctuations, the amplitude does not exceed 10 veh/km. However, this strategy demonstrates a delay in achieving full control effectiveness on the port motorway due to the poor deceleration performance of container trucks, a phenomenon that is especially noticeable in Scenario 1. Specifically, RM reaches its lower bound and activates VSL control at 60 min, but brief congestion still occurs and the bottleneck speed quickly drops to around 30 km/h. This forces the VSL control to apply a lower speed limit to further delay upstream vehicles from reaching the bottleneck, with congestion only being alleviated at 65 min. Although this strategy addresses some of the limitations of both RM and VSL control, as shown in Figure 7d and Figure 8d, traffic flow distribution remains uneven and intermittent brief congestion persists.

The IFC-MP strategy allocates weights based on upstream and on-ramp pressure, ensuring that the side experiencing higher pressure is given a higher weight. The gains of its controller are obtained through repeated experiments. In scenario 1, the controller gains are set to $K_P=10$ km/h, $K_I=20$ km/h, and $K_R=0.0015$ h/veh. Due to the high mainstream demand, the upstream weight (Figure 11a) is relatively high, predominantly ranging between 0.8 and 0.9. In scenario 2, the controller gains are set to $K_P=10$ km/h, $K_I=15$ km/h, and $K_R=0.0015$ h/veh. With the increased on-ramp demand in this scenario, the on-ramp weight (Figure 11b) rises accordingly, remaining around 0.3 for most of the time. As illustrated in Figure 7e and Figure 8e, the speed distribution under this strategy is overall more balanced compared to the other strategies. In the range of 1–3 km, the speed generally remains around 60 km/h, and no significant congestion is observed. Since the mainstream demand in scenario 2 is lower than that in scenario 1, the speed in the 0–1 km section is higher, reaching approximately 70 km/h. In both scenarios, the bottleneck occupancy consistently stays around 20 veh/km, and the bottleneck throughput becomes more stable, at approximately 3000 veh/h, representing an improvement of about 7% compared to the no-control case. However, as shown in Figure 11, regardless of whether the on-ramp flow is saturated, it remains relatively small compared to the mainstream demand, resulting in the on-ramp typically being assigned a lower weight, with a maximum value not exceeding 0.5. This leads to the phenomenon observed in Figure 10, where the on-ramp queue is significantly shorter than under other strategies, typically not exceeding 20 veh, and the speed limit remains at the lower bound of 60 km/h for an extended period. Such a situation may cause insufficient utilization of the on-ramp space and prolong the travel time on the main road.

Among the tested strategies, PI-ALINEA/Q effectively reduces congestion compared to the no-control case but struggles to prevent brief congestion under high mainstream demand. MTFC-VSL improves upstream flow regulation through speed control, yet its performance is limited once the minimum speed limit is reached. Integrated-FB enhances stability by combining RM and VSL but exhibits delayed control effectiveness due to truck deceleration characteristics. Overall, IFC-MP outperforms all other strategies, achieving the most balanced traffic conditions and delivering the highest improvement in bottleneck throughput and congestion alleviation.

4.3. Total Time Spent Analysis Under Different Strategies

Total time spent (TTS) refers to the sum of total travel times (TTTs) for all vehicles on the port motorway and total waiting times (TWTs) for all vehicles on the on-ramp serving as a key indicator for evaluating improvements in overall traffic efficiency. Both TTT and TWT are extracted from SUMO, which defines a vehicle’s waiting time as the duration (in seconds) during which its speed remains below 0.1 m/s since it last exceeded this threshold. Essentially, the waiting time of a vehicle resets to 0 every time it resumes movement. The resulting TTS values for all scenarios are summarized in

Table 2. Summary of TTS for simulated scenarios.

Scenario	Strategy	TTT	TWT	TTS
		(veh h)	(veh h)	(veh h)
Scenario 1	No-Control	456.8	0	456.8
	PI-ALINEA/Q	333.0	15.6	348.6 (−23.7%)
	MTFC-VSL	337.3	0	337.3 (−26.2%)
	Integrated-FB	323.4	20.5	343.9 (−24.7%)
	IFC-MP	328.9	4.0	332.9 (−27.1%)
Scenario 2	No-Control	452.5	0	452.5
	PI-ALINEA/Q	325.8	30.6	356.4 (−21.2%)
	MTFC-VSL	334.6	0	334.6 (−26.1%)
	Integrated-FB	321.6	30.9	352.5 (−22.1%)
	IFC-MP	323.0	10.5	333.5 (−26.3%)

, serving as a benchmark for evaluating the effectiveness of different control strategies.

In the no-control case, the TTS reaches 456.8 veh h and 452.5 veh h in scenario 1 and scenario 2, respectively. As shown in Figure 12, the TTS rises rapidly once the bottleneck is activated, with the congestion spreading upstream and causing the travel time within the network to increase progressively.

When PI-ALINEA/Q is applied, the TTS reduces to 348.6 veh h in scenario 1, and 356.4 veh·h in scenario 2, representing improvements of 23.7% and 21.2%, respectively, compared to the no-control case. Restricting vehicle merging onto the mainline reduces the travel time of mainline vehicles but simultaneously increases the waiting time for on-ramp vehicles. Under the high on-ramp demand scenario, more vehicles accumulate while waiting to merge, resulting in a TWT reaching 30.6 veh h.

For the MTFC-VSL application, the TTS is 337.3 veh h in scenario 1 and 334.6 veh h in scenario 2, corresponding to reductions of 26.2% and 26.1%, respectively, compared to the no-control case. Although it achieves improvements in TTS compared to the no-control case and PI-ALINEA/Q, its TTT is 1–3% higher than that under PI-ALINEA/Q. This is because the imposed speed limits constrain the upstream vehicle speeds, thereby increasing overall travel time.

The TTS for integrated-FB is 343.9 veh·h in scenario 1 and 352.5 veh·h in scenario 2, reflecting improvements of 24.7% and 22.1%, respectively, compared to the no-control case. As shown in Figure 12, the fluctuations in time spent per minute are similar to those observed under PI-ALINEA/Q. This is because integrated-FB primarily relies on PI-ALINEA/Q, with VSL control being activated for only a short duration, approximately 20 min in scenario 1 and less than 30 min in total in scenario 2, as illustrated in Figure 10. Although there is a delay in the activation of VSL control, its involvement provides supplementary regulation, resulting in a 1–3% improvement in TTT compared to PI-ALINEA/Q and a 3–4% improvement compared to MTFC-VSL.

In contrast, the implementation of IFC-MP significantly smooths the time spent per-minute compared to other strategies, with the peak not exceeding 4 veh·h. The TTS in scenario 1 is 332.9 veh·h and in scenario 2 is 333.5 veh·h, representing reductions of 27.1% and 26.3%, respectively, compared to the no-control case. With VSL control continuously in effect and adjusting the speed limit based on feedback pressure, the waiting time for on-ramp vehicles is reduced, resulting in a 4–5% improvement compared to PI-ALINEA. Additionally, IFC-MP avoids the delayed activation of VSL control, which mitigates the lag in control effectiveness, leading to an improvement of about 3–4% compared to integrated-FB. Although IFC-MP performs similarly to MTFC-VSL in terms of TTS, it alleviates some of the bottleneck pressure by simultaneously restricting on-ramp vehicles from merging onto the mainline. This prevents upstream vehicles from being constrained by the lower speed limit for extended periods, resulting in a 3–4% improvement in TTT compared to MTFC-VSL.

4.4. Total Pollutant Emissions Analysis Under Different Strategies

Total pollutant emissions (TPEs) consist of CO, CO₂, NO_x, and HC, which are the primary harmful components in vehicle exhaust. Since the default HBEFA (Handbook of Emission Factors for Road Transport) model embedded in SUMO can provide emission factors for various pollutants based on the vehicle type, speed, and acceleration, and has been validated in practical applications, it met the requirements for evaluating pollutant emissions from multiple vehicle types in this experiment. Therefore, we used this model to collect pollutant emission under different control strategies. The resulting TPE values for all scenarios are presented in

Table 3. Summary of TPE for simulated scenarios.

Scenario	Strategy	TCOE	TCO2E	TNOXE	THCE	TPE
		(kg)	(kg)	(kg)	(kg)	(kg)
Scenario 1	No-Control	55.0	3571.0	1.4	0.3	3627.7
	PI-ALINEA/Q	33.7	3265.8	1.2	0.2	3300.9 (−9.0%)
	MTFC-VSL	31.6	3215.3	1.2	0.2	3248.3 (−10.5%)
	Integrated-FB	34.0	3282.9	1.2	0.2	3318.3 (−8.5%)
	IFC-MP	30.6	3200.5	1.2	0.2	3232.5 (−10.9%)
Scenario 2	No-Control	56.3	3539.2	1.4	0.3	3597.2
	PI-ALINEA/Q	36.6	3252.4	1.2	0.2	3290.4 (−8.5%)
	MTFC-VSL	33.1	3165.5	1.2	0.2	3200.0 (−11.0%)
	Integrated-FB	38.2	3274.9	1.2	0.2	3341.5 (−7.9%)
	IFC-MP	33.3	3169.8	1.2	0.2	3204.5 (−10.9%)

as a reference of the achievable performance.

In the no-control case, the TPE is 3627.7 kg in scenario 1 and 3597.2 kg in scenario 2. As shown in Figure 12 and Figure 13, TPE increases along with rising TTS. This is because congestion leads to prolonged idling, causing incomplete fuel combustion and higher pollutant emissions.

When PI-ALINEA/Q is applied, TPE is reduced to 3300.9 kg in scenario 1 and 3290.4 kg in scenario 2, representing improvements of 9.0% and 8.5%, respectively, compared to the no-control case. With MTFC-VSL control, the TPE further reduced to 3248.3 kg in scenario 1 and 3200.0 kg in scenario 2, improving by 10.5% and 11.0%. The higher pollutant emissions associated with PI-ALINEA/Q compared to MTFC-VSL are due to the fact that when on-ramp vehicles are restricted from merging onto the mainline, they are forced to stop and wait. This results in frequent acceleration and deceleration, which typically leads to higher emissions compared to the smoother deceleration pattern promoted by MTFC-VSL.

The emissions reduction effect of integrated-FB is similar to that of PI-ALINEA/Q, but slightly worse. In scenario 1 and scenario 2, the TPEs are 3318.3 kg and 3341.5 kg, corresponding to improvements of 8.5% and 7.9% over the no-control case. The slightly higher emissions under integrated-FB can be explained by its control logic. Before the RM reaches its lower bound, integrated-FB operates similarly to PI-ALINEA/Q and does not reduce the frequent acceleration and deceleration of on-ramp vehicles. Once the lower bound is reached, VSL control is activated, imposing speed restrictions on upstream mainstream vehicles. Compared to PI-ALINEA/Q, which only regulates ramp inflow, the additional speed control on the upstream under integrated-FB slightly increases overall emissions.

Under the IFC-MP strategy, the pollutant emissions per minute become more stable, with the peak not exceeding 40 kg, as shown in Figure 13. The TPE decreases to 3232.5 kg in scenario 1 and 3204.5 kg in scenario 2, respectively, representing a 10.9% improvement compared to the no-control case. Although Figure 10 indicates that IFC-MP may lead to some underutilization of on-ramp capacity, it effectively reduces the frequent acceleration and deceleration behaviors of ramp vehicles, which are prevalent under PI-ALINEA/Q and integrated-FB. Consequently, IFC-MP achieves a 2–3% greater improvement in pollutant emissions than these two strategies. Moreover, compared to MTFC-VSL, IFC-MP achieves slightly better TPE optimization in scenario 1, with a 0.4% improvement, but performs slightly worse in scenario 2. This indicates that its emission optimization effect is sensitive to on-ramp demand. When on-ramp demand is low, restricting on-ramp inflow optimizes emissions more effectively than imposing upstream speed limits. However, under a high ramp demand, IFC-MP leads to slightly higher emissions than MTFC-VSL, mainly reflected in CO and CO₂, which are more sensitive to prolonged idling and frequent acceleration and deceleration.

4.5. Performance Evaluation and Analysis Under Different Compliance Levels

In the previous analysis, we assumed that all vehicles fully comply with the speed limits. However, references [51,52] indicate that drivers do not always fully adhere to speed limits, often exceeding them by 10 km/h or more, especially container truck drivers, who strive to complete deliveries or pickups within a specific time frame. To observe the sensitivity of IFC-MP to compliance levels, we conducted a stability analysis by adjusting the speed factor values to represent three compliance levels. High compliance assumes all vehicles fully adhere to the speed limits, medium compliance allows a 10% speed overage, and low compliance involves a severe 20% speed overage. The specific parameter settings are shown in

Table 4. Speed factor settings under different compliance levels.

Compliance Levels	Car	TEU-Carrying Container Trucks	FEU-Carrying Container Trucks
High compliance	1.0	0.9	0.8
Medium compliance	1.1	1.0	0.9
Low compliance	1.2	1.1	1.0

.

Figure 14 shows the variations in bottleneck occupancy, flow, and speed under different compliance levels.

In both scenario 1 and scenario 2, the curves under high-compliance conditions exhibit greater smoothness. Bottleneck occupancy fluctuates minimally and bottleneck flow remains stable between 20 and 80 min, while the bottleneck speed maintains around 60 km/h even at its minimum. This stability is attributed to the strict adherence of high-compliance drivers to speed limits, which minimizes external disturbances and enables IFC-MP to move closer to an ideal control state. In contrast, under medium and low compliance levels, more pronounced fluctuations are observed. Particularly under low compliance, the bottleneck speed in scenario 2 fluctuates frequently between 40 km/h and 60 km/h during 30–80 min. Such instability is mainly due to the speeding behavior, which causes upstream vehicles to arrive at the bottleneck earlier and forces the IFC-MP strategy to continuously adjust to the rapidly changing traffic conditions.

Figure 15 and

Table 5. Summary of TTS under different compliance levels.

Scenario	Compliance Levels	TTT	TWT	TTS
		(veh h)	(veh h)	(veh h)
Scenario 1	High compliance	328.9	4.0	332.9
	Medium compliance	314.2	5.7	319.9
	Low compliance	308.1	10.9	319.0
Scenario 2	High compliance	323.0	10.5	333.5
	Medium compliance	308.8	19.5	328.3
	Low compliance	301.6	19.9	321.5

show the TTS under different compliance levels. It can be observed that although TTS decreases as compliance levels decrease, the reduction is not significant. This is because while speeding behavior shortens TTT, TWT increases with the reduction in compliance. In scenario 1, the TWT for high compliance is 4.0 h, while for low compliance, it rises to 10.9 h; in scenario 2, the TWT for high compliance is 10.5 h, and for low compliance, it increases to 19.9 h. This is because when upstream vehicles deviate significantly from the speed limits, the actual bottleneck flow exceeds the feedback value, forcing the control system to continuously adjust by restricting the on-ramp vehicle flow into the mainline, leading to an increase in TWT.

Figure 16 and

Table 6. Summary of TPE under different compliance levels.

Scenario	Driver Compliance	TCOE	TCO2E	TNOXE	THCE	TPE
		(kg)	(kg)	(kg)	(kg)	(kg)
Scenario 1	High compliance	30.6	3200.5	1.2	0.2	3232.5
	Medium compliance	32.7	3199.7	1.2	0.2	3233.8
	Low compliance	34.5	3224.2	1.2	0.2	3260.1
Scenario 2	High compliance	33.3	3169.8	1.2	0.2	3204.5
	Medium compliance	41.0	3294.0	1.2	0.3	3336.5
	Low compliance	40.7	3266.1	1.2	0.3	3308.3

show the TPE under different compliance levels. It can be observed that TPE increases as compliance decreases, particularly in scenario 2, where this trend is more pronounced. Under medium compliance, TPE is 3336.5 kg, while under low compliance, it increases to 3308.3 kg, exceeding high compliance by 3–4%. This change is attributed to the tendency of vehicles to travel at higher speeds under medium and low compliance. When sudden braking occurs, it often leads to incomplete fuel combustion, thereby increasing TPE emissions.

The stability analysis reveals that the IFC-MP operates more smoothly under high compliance, with minimal fluctuations in bottleneck occupancy, flow, and speed. However, under medium and low compliance, greater fluctuations occur due to speeding, which causes upstream vehicles to reach the bottleneck earlier, necessitating more frequent adjustments from the control system. While the effect of different compliance levels on TTS is relatively small, TWT increases notably with lower compliance as the system adapts to changing traffic conditions. Additionally, TPE rises as compliance decreases, driven by higher speeds and more frequent braking. Despite these variations, the IFC-MP remains stable and effective in controlling bottleneck flow, density, and speed.

5. Conclusions

In conclusion, this study proposes a novel max-pressure-driven integrated ramp metering and variable speed limit control (IFC-MP) method that continuously adjusts the RM and VSL control weights through pressure feedback, with higher pressure corresponding to a larger weight. By simultaneously applying both controls according to their respective weights, rather than activating VSL control only after RM reaches its lower bound. The proposed method achieves a more flexible response to fluctuations in mainstream and on-ramp demands on port motorways compared to traditional integrated approaches. Moreover, a queue management mechanism is incorporated to release a portion of on-ramp flow once the queue exceeds the threshold, thereby preventing overflow.

Micro-simulation experiments were conducted on the Guoju section of the Chuanshan Port Motorway in Ningbo City. RM was implemented via traffic lights, and VSL control was applied using variable message signs. The results showed that the IFC-MP strategy achieved a more uniform speed distribution, with bottleneck throughput improving by about 7%, and the minimum bottleneck speed maintained above 60 km/h. TTS was reduced by 26–27% compared to the no-control scenario, and by 4–5% compared to PI-ALINEA/Q, with IFC-MP further optimizing TTT by 3–4% over MTFC-VSL. Regarding TPE, IFC-MP reduced emissions by approximately 11% compared to no-control and 2–3% compared to integrated-FB. This improvement resulted from the simultaneous activation of RM and VSL control, which minimized frequent acceleration and deceleration, reducing CO and CO₂ emissions.

The above analysis assumed full compliance with RM and VSL control. However, compliance of speed limits may vary in practical applications. Stability analysis showed that under high compliance, IFC-MP operated smoothly with minimal fluctuations in key metrics, whereas under medium and lower compliance, frequent adjustments of on-ramp merging flow were needed, thus diminishing the improvements in TWT and TPE. These differences are more pronounced under high-ramp-demand scenarios but are less significant under high-mainstream-demand scenarios.

These findings enhance the theoretical understanding of max-pressure control by showing its effectiveness in coordinating ramp metering and speed limits under varying traffic conditions. From a policy perspective, the IFC-MP method offers a practical tool for easing congestion and reducing emissions on freight-intensive port motorways. It delivers improved traffic and environmental outcomes while remaining stable across different compliance levels.

However, the IFC-MP method also has certain limitations. Observations across different scenarios reveal that queues under IFC-MP are generally shorter. While this helps reduce TWT, it may lead to underutilization of on-ramp resources or cause the mainstream to adopt lower speed limits, thereby increasing TTT. In addition, the variability of the evaluation scenarios in this research is limited, and pollutant emissions were estimated using the HBEFA model embedded in SUMO. These limitations may affect the generalizability of this method under more complex and dynamic traffic conditions. In future research, we plan to expand the validation by including a broader range of traffic scenarios, such as incidents, varying weather conditions, and diverse compositions of container trucks. More precise evaluation models can also be developed based on the traffic flow characteristics of port motorways, thereby enabling a more comprehensive assessment of the robustness and applicability of the proposed method. In addition, practical deployment aspects will be further explored, including the required infrastructure such as on-ramp traffic lights and variable message signs, as well as the coordination of transport authorities to support integrated control in actual port environments.