Journal of Advanced Transportation

Volume 2019, Article ID 8151582, 11 pages

https://doi.org/10.1155/2019/8151582

## Modified Traffic Flow Model with Connected Vehicle Microscopic Data for Proactive Variable Speed Limit Control

^{1}Transportation Department, Fuzhou University, Fuzhou, Fujian, China^{2}Department of Civil Engineering, Ryerson University, Toronto, Ontario, Canada

Correspondence should be addressed to Jie Fang; nc.ude.uzf@eijgnaf

Received 16 February 2019; Revised 16 April 2019; Accepted 22 May 2019; Published 10 June 2019

Guest Editor: Md. A. S. Kamal

Copyright © 2019 Jie Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

Urban freeways provide efficient and convenient traffic service for road users and play a significant role in accelerating the development of regional economy [1]. With the rapid economic development, the great increase in car-ownership has aggravated the traffic congestion. Thus, traffic mobility and safety have become major challenges in freeway operations. Due to the restriction of urban space and the high cost of infrastructure construction, the problems may not be solved simply by expanding road facilities. To ease traffic congestion, some traffic control measures have been adopted, such as Route Guidance [2, 3], Ramp Metering [4, 5], and Variable Speed Limits (VSL). Among these measures, VSL control draws widely attentions. It determines a dynamic speed limit according to the current traffic flow states, climatic, road environments, etc. The main benefits of VSL control are as follows: (1) improves traffic operations through regulating the mainstream traffic flow and delaying the forthcoming traffic breakdown for potential capacity gain and higher level of service, (2) mitigates the speed differences between individual vehicle for fewer traffic collisions, and (3) reduces the vehicle stop frequencies for vehicle emission and air pollution [6–8].

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 [9]. This newly available data source may better capture the details of traffic flow dynamics in the VSL controlled environment. Thus, in this paper, a VSL control strategy based on a modified METANET model utilizing the microscopic traffic data was proposed. In the modified model, the microscopic data are used in the prediction model as a supplement to predict the evolution of the traffic dynamics. By analyzing higher resolution data, such as the individual acceleration rate and headway at second-by-second level, the responding and evolving of the traffic flow to the control measure can be modeled more accurately, thus improves the prediction accuracy. The modified model with proposed control strategy was implemented in a simulated freeway to validate their feasibility and control performance.

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.

#### 2. Literature Review

The studies of VSL control in Europe and North America, traced back to 1990s, have provided valuable state-of-the-art and practical experiences [10]. Various VSL control strategies have been proposed and can be grouped into three categories: rule-based VSL control strategies, feedback controller-based VSL control strategies, and model-based VSL control strategies.

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. [11] proposed a real-time conflict prediction model and showed that the precursors of conflict could be decided in an objective manner to replace the subjective classification mode used in the analysis. In 2006, Lee et al. [12] proposed a VSL strategy that reduced the speed limit when the potential conflict exceeded a preset threshold*.* The optimal speed limit was selected based on several thresholds associated with safety. The results suggested that the number of potential conflicts were decreased, but travel time was increased.

In 2011, Carlson et al. [13] designed a simple local feedback controller Mainstream Traffic Flow Control (MTFC) to improve traffic-flow efficiency. The control strategy was evaluated using simulation and the performance of the controller was shown to approach the optimal control effect. In 2013, the same group of authors [14] proposed two simple feedback controllers that relied on readily available real-time measurements for local MTFC via VSL. The results showed that the feedback controllers had satisfactory control effects. Recently, Iordanidou et al. [15, 16] proposed an extended feedback-based VSL control strategy, considering multiple-bottleneck locations, and obtained good results.

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 [17]. In model experiment, future traffic conditions (e.g., congestion) are foreseen before they even occur, and VSL strategies are deployed to reduce traffic volume in the expected congestion area, see, for example, Khondaker et al. [18]*. *The framework uses a model to predict future traffic states. The MPC-based VSL control strategies consider future traffic conditions and quantitatively evaluate the impact of VSL control on traffic-flow dynamics to keep traffic flow at high efficiency, especially during congested periods. In 2005, Zhang et al. [19] used MPC to design a roadway controller that reduced traffic congestion. In 2009, Zegeye et al. [20] used MPC to evaluate the impact of dynamic speed limit control and the results showed a reduction in total time spent. In 2010, Ghods et al. [21] solved the problem of real-time optimal control of traffic flow in a freeway network with a promising approach by casting the underlying dynamic control problem in an MPC framework. Hadiuzzaman et al. proposed a modified Cell Transmission Model (CTM) based on Daganzo’s original model [22] and used MPC to alter the speed limit dynamically [23, 24]. In 2017, Han et al*.* [25] developed a fast MPC based approach for VSL coordination to resolve freeway jam waves. This MPC approach is based on a more accurate discrete first-order model that keeps the linearity property of the classical discrete first-order model and takes capacity drop into consideration. The simulation results demonstrated that the proposed control strategy resolved the jam wave with a real-time feasible computation speed [26].

As a macroscopic modeling tool, the METANET model, developed by Papageorgiou et al. [10], and its extensions are widely used. One of the pioneering MPC-based VSL control strategies was proposed by Hegyi [27] and Hegyi et al. [28, 29]. The authors modified the METANET model, for example, by proposing a revised the desired speed term. The new desired speed is the minimum of the targeted speed based on the current traffic conditions and the displayed speed limit. The MPC framework was adopted to determine the optimal speed limit. Hence, Hegyi et al. [29] proposed an extended METANET model with modeling of dynamic speed limits and mainstream origins. The results showed that the VSL can prevent traffic breakdown and maintain a higher outflow. In 2010, Carlsonet al. [30] incorporated VSL in the METANET model as an additional control component leading to an extended optimal control formulation. The results showed that traffic-flow efficiency was substantially improved when VSL control measures were used. In 2012, Hadiuzzaman et al. [23] replaced the fundamental diagram with the VSL control variable in the relaxation term of the METANET model, the proposed traffic dynamics with the control strategy were implemented in a freeway corridor using the MPC framework. The analysis was carried out in VISSIM and the results showed that VSL was mostly effective during congestion periods in terms of mobility. In 2014, Sun et al. [31] proposed a new extension of METANET model in which traffic state variables were modeled and predicted. In addition, VSL values were optimized using MPC. Yu et al. [32] proposed an extended METANET model, in which the desired speed term was modified to minimize the total crash risk. The results showed that traffic safety improved and speed homogeneity was enhanced. The MPC based VSL control have been proven effective in the preceding researches.

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.

#### 3. Methodology

##### 3.1. Model Formulation

###### 3.1.1. Macroscopic METANET Model

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 [27]*.*

According to the conservation equation of fluid motion,

where = average inflow from onramp at position (veh) and = average outflow of the off-ramp at position (veh).

If the number of lanes of segment is and the length of segment is , (1) becomes

After adjustment, the conservation equation of vehicles is obtained as

where = density of segment at time (veh/km/ln); = traffic flow of segment at time (veh/h); = on-ramp flow of segment at time (veh/h) and = off-ramp flow of segment at time (veh/h).

The outflow of segment is equal to the density multiplied by the average speed and the number of lanes of that segment. That is,

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 ahead, a certain time and spacing are required for the vehicle to adjust according to the observation of the downstream traffic-flow state. If the adjustment time is , then

Applying Taylor series expansion to each side of (5), then

In previous researches, was set to be an average value of based on the empirical data [10, 27], while is the sensitivity of adjusting towards the anticipated speed, considering segment density. Defining , (6) becomes

where

Based on (8), (7) can be written as

After discretizing and rearranging (9), one obtains

where = desired speed of segment (km/h), = a parameter with negative value, sensitivity of adjusting towards the anticipated speed of segment at time , = driver adjustment delay coefficient of segment , = positive compensation coefficient to avoid the error brought by too-small , = free-flow speed of segment (km/h), = model parameter of segment, and = critical density (veh/km/ln).

In the basic METANET model, , , and are treated as constant model parameter. Thus, (10) becomes

###### 3.1.2. Proposed Macroscopic METANET Model with Microscopic Connected Vehicle Data

The term in (6) indicates the lag of speed adjustments. In the basic METANET model, is assumed to an empirical averaged value of , and was replaced as a constant system parameter. In other words, the distance required for speed adjustment was set to be half of the headway, by simply assuming averaged vehicle headway as the ideal situation. However, this assumption is not always consistent with field implementation. Although this assumption is relatively accurate under high density, under low density circumstances the large averaged headway will cause significant model mismatches, as illustrated in Figure 1.