^{1}

^{1}

^{2}

^{1}

^{2}

Most previous prediction based Variable Speed Limit (VSL) control strategies focused on improving traffic mobility based on the macroscopic traffic data. Nowadays, the emerging technologies provide access to the microscopic traffic flow data, which better captures the details of traffic flow dynamics in the VSL controlled environment. Thus, in this paper, the microscopic traffic flow data were utilized as a supplement to predict the evolutions of traffic flow parameters. The proposed VSL control algorithm adopts the Model Predictive Control (MPC) framework, which employs a modified version of the classic traffic flow model METANET to take advantage of the microscopic data in traffic flow predictions. The microscopic traffic simulation software VISSIM was used to establish an experimental simulation platform and perform real time traffic responsive control based on field data. The proposed control strategy was evaluated against the no-VSL control and macroscopic-based VSL controlled scenario. The results show that utilizing the proposed modified METANET model reduced the error in speed prediction accuracy and improved system mobility performance.

Urban freeways provide efficient and convenient traffic service for road users and play a significant role in accelerating the development of regional economy [

The MPC control framework has recently been widely adopted in proactive freeway control simulations implementing VSL. The essential core of the MPC framework is the included traffic state prediction model for process control. For this approach, the performance of VSL control strategy depends heavily on the accurate prediction of traffic-flow parameters, which will be used for quantitatively determining the dynamic speed limits. To adapt the limitation of the traditional data collection methods, existing VSL control methods adopt macroscopic traffic flow data that can be easily collected, such as speed, volume, and density. Enabled by the fast-emerging technologies, such as internet of vehicles, the real-time microscopic traffic data, such as the acceleration rate, can be collected by the in-vehicle or roadside sensors [

The next sections present a brief literature review of existing VSL control strategies, followed by the descriptions of the basic and modified METANET models. The following sections present the model validation through an application of the proposed control strategy using VISSIM simulation and the conclusions.

The studies of VSL control in Europe and North America, traced back to 1990s, have provided valuable state-of-the-art and practical experiences [

The rule-based control strategies use real-time traffic measurements as a basis for real-time control. The decision tree strategy can be categorized as rule-based control strategy, which is the earliest to be developed for VSL control. It uses an algorithm that defines an indicator, such as density, as a criterion for determining whether to start the VSL control. Decision tree-based strategies are straightforward for field implementation. Lee et al. [

In 2011, Carlson et al. [

The Model Predictive Control- (MPC-) based VSL control strategy is a model-based VSL control strategy, of which the model has predictive function. The limitation of the rule-based control strategies is that traffic conditions may have already broken down before VSL is deployed. Thus, Model Predictive Control (MPC) has emerged as a new approach to address this limitation. The MPC is a valuable, widely used framework for VSL control of freeways [

As a macroscopic modeling tool, the METANET model, developed by Papageorgiou et al. [

However, most previous VSL control strategies predicted traffic-flow states using collected macroscopic traffic data to determine the VSL control signal. Due to lack of microscopic traffic flow data, the prediction accuracy maybe compromised in certain circumstances, such as low density (free flow). With the development of new sensoring and communication technologies, microscopic traffic data can be collected and incorporated into the formulation of the basic METANET model for better modeling the responding and evolving of the traffic flow under VSL controlled environment. Thus, in this paper, a modified METNET model incorporating microscopic traffic data will be proposed to establish an MPC based proactive VSL control strategy that further improves the prediction accuracy and freeway operation efficiency.

In this paper the authors adopted the MPC framework that incorporates the METANET model and its extensions, which are valuable tools widely used to make accurate prediction of traffic-flow variables. The METANET model is deterministic, discrete-time, discrete-space, and macroscopic, making it very suitable for model-based traffic control [

According to the conservation equation of fluid motion,

where

If the number of lanes of segment

After adjustment, the conservation equation of vehicles is obtained as

where

The outflow of segment

When adjusting towards the desired speed, there will a brief delay related to the drivers’ reaction time and vehicle acceleration capability. In other words, to reach the desired speed at position

Applying Taylor series expansion to each side of (

In previous researches,

where

Based on (

After discretizing and rearranging (

where

In the basic METANET model,

The term

Variation of density corresponding actual and basic METANET predicted speeds: (a) actual density and (b) actual speed and basic METANET predictions.

As noted in Figure

In the basic METANET model, since the actual individual vehicle status is unknown, the vehicle is assumed to be equally distributed along the road segment (by taking the segment averaged headway). Thus, the distance required for speed adjustment

where ^{2}).

The mathematical interpretation of established sigmoid model (

Interpretation of the term

As demonstrated in Figure

Comparison of speeds of basic and modified METANET models: (a) actual and predicted speeds and (b) percentile prediction error of basic and modified METANET model.

Then, the density and volume of segment

In the MPC-based VSL control strategy proposed in this paper, (

The constraints of the METANET model by Cao et al. [

To guarantee drivers’ safety, the optimal speed limit must be lower than the maximum speed:

To maintain operating efficiency, the optimal speed limit must be higher than the minimum speed:

For safe operation, the difference in the speed limits of two consecutive time steps should be less than the maximum difference:

Not all vehicle drivers are able to drive at the speed limit. Therefore, to ensure that the speed limit is more suitable for actual traffic conditions, the difference between the optimal speed limit and the speed detected downstream should be less than the maximum difference:

To calibrate the proposed model modification, the parameters of the basic and modified METANET (

The other 50 days of data were used for model validation. These data and the optimal parameters were used in the prediction model to predict traffic-flow state. As shown in Figure

In this paper, an MPC framework is used to solve the problem of optimal speed limit for implementing proactive VSL control. In MPC, the time horizon is

MPC-based control framework.

As shown in Figure

Schematic diagram of the METANET model.

The objective function of VSL optimization was set as the weighted sum of total time spent (TTS) and total travel distance (TTD), in order to improve the mobility of the network, as suggested by Cao et al. [

To evaluate and analyze the MPC-based VSL control strategy using the modified METANET model, an urban freeway corridor is selected as the experimental simulation site. The selected freeway is about 9 km long with three lanes in each direction. For modeling, the corridor is further divided into 13 segments including five on-ramps (

Schematic diagram of expressway segments.

The traffic data were collected on-site using loop detectors installed in each segment, and the experiment was conducted for a peak-hour period of two and a half hour. The VISSIM simulation software was selected to establish the network simulation platform. The authors chose 10 random simulation seeds in the experiment, and the all simulation results in this paper are based on the average of the 10 different scenarios. The simulation resolution is 5 per second in this paper, since a higher resolution will lead to high computational load. Using MATLAB, the MPC-based VSL control strategy that includes the modified METANET model was implemented on the simulated site. The simulation platform was calibrated by minimizing the difference between actual and predicted traffic state variables.

In the experiment, three different control scenarios were evaluated in the simulation platform: (1) no control, (2) VSL control based on the basic METANET model, and (3) VSL control based on the modified METANET model.

The basic demand profile of the experiment site is shown in Figure

Volume variation at different segments without control.

The evaluation results of the objective function for No-VSL, basic METANET-VSL, and modified METANET-VSL controls (using an interval of 20 s) are shown in Table

Comparison of the objective function for no VSL, basic and modified METANET-VSL controls.

Time | Objective Function | ||
---|---|---|---|

No VSL | Basic METANET | Modified METANET | |

6:30-6:50 | 392.3 | 381.1 | 381.1 |

6:50-7:10 | 610.0 | 798.6 | 806.5 |

7:10-7:30 | 2739.6 | 2539.9 | 2505.5 |

7:30-7:50 | 5527.7 | 2932.8 | 3465.9 |

7:50-8:10 | 8613.2 | 2589.7 | 2515.2 |

8:10-8:30 | 9445.6 | 2617.7 | 1049.4 |

8:30-8:50 | 3779.2 | 736.5 | 624.9 |

| |||

Total | 31107.6 | 12596.3 | 11348.5 |

Comparison of the objective function for No VSL, basic, and modified METANET-VSL controls.

For segment densities, a comparison of no-VSL and basic and modified METANET-VSL controls is shown in Figure _{7} and such. It can be observed that both the severity and duration of the congestion has been significantly reduced by the deployed VSL control strategy, especially in the two identified bottlenecks (segment

Comparison of segment densities of No-VSL, basic, and modified METANET-VSL controls: (a) no-VSL control; (b) basic METANET model; (c) modified METANET model.

By capturing the variations of the speed dynamics, the METANET-model activated the VSL to prevent capacity drop and relieve traffic congestion. Taking Segment

Comparison between limit speed and actual speed under modified METANET control.

This paper proposed a modified METANET model that utilizes the microscopic traffic-flow data. A MPC framework-based control strategy incorporates the proposed modified model was established to capture the variations of traffic flow dynamics, which enables the VSL control to prevent dramatic decline of link speed beforehand and gains improvement on the freeway mobility performance.

The proposed formulation of the anticipation term in the modified METANET model is more reasonable and comprehensive. The proposed modification takes in the microscopic traffic-flow data, such as individual vehicle headway and accelerations, to better interpreted the progress of drivers adjusting toward the anticipated speed. The proposed modified model can produce more accurate prediction results, which provides a more reliable basis for achieving further improvement in VSL control applications. The modified METANET model has reduced the prediction error by up to 14.9% and 14.1% for the low and high-density ranges, respectively.

As a result, traffic mobility was substantially improved along with the reduced prediction error. The VISSIM software was used to establish a field data based experimental simulation platform for model validations. To evaluate the control benefits, the traffic-flow states of the modified METANET-based VSL control strategy were compared with those of the No-VSL control and basic METANET-based VSL controlled scenario. The modified METANET model has achieved substantial improvements in terms of mobility performance. The simulation results demonstrated that the modified METANET model reduced segment density, increased segment speed, and shortened the congestion period, indicates the improved freeway mobility. More initiatives to aid the speed prediction of the model should continue to be explored in the future.

The data used to support the findings of this study may be released upon application to the authors, who can be contacted at

The authors declare that they have no conflicts of interest.