# Control Strategy Optimization for Two-Lane Highway Lane-Closure Work Zones

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Problem Statement

#### 3.1. Control Strategy 1: Flagger Control

#### 3.2. Control Strategy 2: Pre-Timed Control (Proposed by Schonfeld)

_{i}(i = 1, 2) denotes the optimal green time for direction i; Q

_{i}(i = 1, 2) denotes the number of arrival vehicles per hour (i.e., hourly flow rate) for direction i; P

_{i}(i = 1, 2) denotes the discharge rate for direction i; and r

_{i}(i = 1, 2) is the average travel time in the remaining lane adjacent to the work zone for direction i. Note that r

_{i}is also the clearance (i.e., all red) time for direction i.

_{i}can be obtained from 3600 s (one hour) divided by the H

_{i}(average headway for vehicles running at the remaining lane adjacent to work zone area) as follows:

_{i}(i = 1, 2) can be calculated from the work zone length divided by the average travel speed at the only open lane adjacent to the work zone area. Note that even though the average speeds for both directions at the open lane are the same, the clearance time of the lane-closure direction is larger due to the extra lane shifting time from the closed lane to the adjacent lane, and then from the adjacent lane back.

#### 3.3. Control Strategy 3: Pre-Timed Control (Proposed by Webster)

_{op}denotes optimal cycle length; Y is the sum of critical phase flow ratios; and L

_{op}is the total lost time within the cycle. Because there is no typical start-up lost time for two-lane work zones, the start-up lost time for intersections in HCM, 2 s, was adopted. The total lost time can be obtained then by:

_{op}into C

_{op}and expanding Y, the optimal cycle length of strategy 3 used in the paper is expressed as follows:

_{i}represents the saturation flow rate and can be calculated by Washburn’s model [34]. With Equation (7), the optimal minimum delay cycle length for the two-lane highway work zone can be obtained. Then, the green time for each direction can be calculated following Webster’s original model in Reference [35].

#### 3.4. Control Strategy 4: Actuated Control

## 4. Mathematical Model Development

_{2}+ r

_{1}+ r

_{2}) and (G

_{1}+ r

_{1}+ r

_{2}), respectively, while the discharging times (namely, green time) for directions 1 and 2 are G

_{1}and G

_{2}. The maximum queuing length is the hourly flow rate multiplied by the maximum queuing time. Assuming the queues are discharged within one cycle, G

_{1}and G

_{2}can be formulated as

_{1}and G

_{2}can be obtained, as shown in Equations (1) and (2).

_{1,1}and Y

_{1,2}, respectively), and deterministic stopped delay time in mean vehicle delay (d

_{1,1}and d

_{1,2}) can be calculated by Equations (10) and (11):

_{i}is the average travel time in the remaining lane adjacent to the work zone for direction i.

_{i}denotes the volume-to-capacity ratio, m is the vehicle arrival adjustment factor accounting for the randomness in vehicle arrival rates, k is controller setting adjustment factor, and I is upstream filtering/metering adjustment factor. In HCM 2010, k is 0.5 for pre-timed control, and I = 1.0 for isolated signals. These two values are also used in this study.

## 5. Simulation Model Development

#### 5.1. Field Data Description

#### 5.2. Simulation Model Development

## 6. Result Analysis

#### 6.1. Simulation Performance with Field Data

#### 6.2. Impact of Control Strategies on Stopped Delay

#### 6.3. Impact of Control Strategies on Queue Length

#### 6.4. Impact of Control Strategies on Throughput

## 7. Discussion

#### 7.1. The performance of Control Strategies under Different Volume Conditions

- Under Low volume

- Under Moderate volume

- Under High volume

#### 7.2. The Performance of Mathematical Stopped Delay Estimation

## 8. Conclusions and Suggestions

- Flagger control after gap-out distance optimization is recommended due to the good performance of average delay, queue length, and throughput, especially under low- or high-volume conditions;
- Because optimal gap-out distance exists for flagger control, simulation can be employed to come up with the optimal value. A mark can be placed at the optimal gap-out distance ahead of the stop bar. When no vehicles run between the stop bar and the mark, flaggers can switch the paddle to the stop side;
- Actuated control, one of the most commonly used intersection control strategies, is a little bit worse than flagger control but outperforms pre-timed control. Under moderate-volume conditions, actuated control could be a good alternative for work zone areas due to its small queue length and large vehicle throughput;
- Although both of the pre-timed control strategies perform worst for two-lane work zones, they may still be used, as no additional devices (such as loop detectors) are required except for signal lights. After modification, Webster’s pre-timed control strategy is recommended for its better performance relative to Schonfeld’s method;
- Speed limit, as well as the average speed at work zone areas, can influence the performance of control strategies. With safety as the prerequisite, the average vehicle speed can be increased in the remaining lane. This is one general method to lower the stopped delay and queue length and to improve the vehicle throughput. In addition, the average speed needs to be controlled, and the speed limit should be determined carefully, although higher speed can reduce the vehicle delay. This is because higher speed means higher accident risk on one hand and because higher speeds will not result in significant delay reductions on the other hand.
- After calibration, the mathematical model can be used to describe the stopped delays under most of the work zone control strategies, except for under the flagger control method with low traffic volume conditions.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Configuration of a typical work zone and an intersection: (

**a**) work zone on a two-lane highway; and (

**b**) a two-phase intersection.

**Figure 3.**Speed and headway on the two-lane highway work zone: (

**a**) speed distribution; and (

**b**) headway distribution.

**Figure 4.**Calculation result of the simulation model: (

**a**) stopped delay based on different gap-out distance; and (

**b**) percentage error (PE) of stopped delay.

**Figure 7.**Average stopped delay for different control strategies and volume: (

**a**) under low volume; (

**b**) under moderate volume; and (

**c**) under high volume.

**Figure 9.**Queue length for different control strategies: (

**a**) under low volume; (

**b**) under moderate volume; and (

**c**) under high volume.

**Figure 10.**Difference between vehicle input and throughput: (

**a**) under low volume; (

**b**) under moderate volume; and (

**c**) under high volume.

**Figure 11.**Radar maps of control performance under different volumes: (

**a**) pre-timed control (Webster); (

**b**) pre-timed control (Schonfeld); (

**c**) flagger control; and (

**d**) actuated control.

**Figure 12.**Mathematical and simulation delay estimations: (

**a**) under moderate volume; (

**b**) under low volume; and (

**c**) under high volume.

Direction | Traffic Demand (veh/h) | Truck Percentage (%) | Speed Limit (Km/h) | Average Speed in Work Zone Area (Km/h) | Average Stopped Delay (s/veh) | Lane Changing Time (s) |
---|---|---|---|---|---|---|

1 | 261 | 5.0 | 79.6 | 35.1 | 38.6 | 2.4/2.2 |

2 | 328 | 8.7 | 79.6 | 40.6 | 32.9 | - |

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**MDPI and ACS Style**

Hua, X.; Wang, Y.; Yu, W.; Zhu, W.; Wang, W.
Control Strategy Optimization for Two-Lane Highway Lane-Closure Work Zones. *Sustainability* **2019**, *11*, 4567.
https://doi.org/10.3390/su11174567

**AMA Style**

Hua X, Wang Y, Yu W, Zhu W, Wang W.
Control Strategy Optimization for Two-Lane Highway Lane-Closure Work Zones. *Sustainability*. 2019; 11(17):4567.
https://doi.org/10.3390/su11174567

**Chicago/Turabian Style**

Hua, Xuedong, YinHai Wang, Weijie Yu, Wenbo Zhu, and Wei Wang.
2019. "Control Strategy Optimization for Two-Lane Highway Lane-Closure Work Zones" *Sustainability* 11, no. 17: 4567.
https://doi.org/10.3390/su11174567