Advances in Civil Engineering

Volume 2019, Article ID 2357437, 8 pages

https://doi.org/10.1155/2019/2357437

## A Method for Determining the Capacity of an Exclusive Left Lane with a Permitted Phase under Nonstrict Priority

College of Transportation, Jilin University, Changchun, Jilin 130022, China

Correspondence should be addressed to Xian-min Song; nc.ude.ulj@mxgnos

Received 11 September 2018; Accepted 19 February 2019; Published 27 March 2019

Academic Editor: Behzad Esmaeili

Copyright © 2019 Qiao-wen Bai 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

A new method has been developed for estimating the capacity of an exclusive left lane with a permitted phase under nonstrict priority. Different from maneuvers under strict priority, these left-turning vehicles were released in the form of a left-turn group. A field survey was first conducted to explore the maximum number of vehicles in a left-turn group, and the releasing process of the permitted left turns. The observations revealed that (1) the maximum number is related to the intersection geometry and (2) the releasing process includes two stages: the first left-turn group crossing at the beginning of a permitted phase and the following left-turn groups crossing using gaps provided by opposing right turns. Next, a method based on probability theory and these observation results were applied to estimate the capacity of an exclusive left lane. The procedure contains two stages and eight steps. Finally, the estimation of the left-turn capacity using the proposed model was validated by comparing the capacity from the strict priority and actual maximum volumes.

#### 1. Introduction

At a signalized intersection, permitted left turns, either from shared lanes or from exclusive lanes, will have serious impacts on intersection operations. According to traffic laws, vehicular traffic turning left and facing a permitted phase must yield the right-of-way to oncoming traffic; however, this situation is not the case in some countries, including China, Norway, and Finland. Drivers in these countries may not follow the full compliance with the official priority rules and instead fail to yield [1–3]. Left-turning vehicles always attempt to choose the shortest path where the potential conflict point is nearer to themselves than through-vehicles. Once an opposing through-vehicle accommodates a left-turning vehicle's crossing, the following left-turning vehicles will take this opportunity to finish their turning movements. As a result, through-vehicles are undoubtedly severely delayed [4]. Thus, the opposed crossing flow will also strive to maintain a small time headway to prevent being disturbed by the conflicting traffic flow. It cannot be denied that maintaining such a small time headway calls for a driver’s quick reaction; nevertheless, the nonstrict priority maneuver may improve the capacity of a left lane. In particular, when the opposing approach has a high through-flow, the nonstrict priority maneuver will result in more left turns crossing the intersection and mitigate the effect of left-turning spillover on through-vehicles in the same direction. This result explains also why traffic management officials in these countries acquiesce to the nonstrict priority behaviors of left-turning vehicles.

In addition, scholars and engineers who study autonomous vehicles should also focus on the nonstrict priority behaviors of left-turning vehicles, especially for mixed traffic flow with human-driving and autonomous vehicles. At an intersection with permitted left-turning phase, through autonomous vehicles must pay close attention to opposed left-turning vehicles by human-driving and then decide whether it can cross the intersection. According to the capacity model under nonstrict priority, the significant factors will be obtained as well. Then, it can provide reference on optimizing the coordination strategy of the autonomous vehicles, to improve the capacity of the intersection with a permitted left-turning phase.

Many scholars have conducted studies on intersection capacity under a permitted phase. Existing methods can be categorized into two aspects: traditional method for two traffic flows with strict priority and platoon method for two flows with the same priority.

##### 1.1. Traditional Methods

The traditional methods used to compute the capacity of a permitted left-turn lane mostly follow a strict priority [5]. The procedure of the *Highway Capacity Manual* [6] uses eight adjustment factors to estimate the left-turn saturation flow rate. In addition, the operations of the permitted left-turning stream are divided into three periods: (1) before the first left-turning vehicle arrives; (2) left turns are obstructed by opposing through-flow; (3) left turns find the acceptable gaps and finish their turning movements after clearance of the opposing queue. Similarly, the *Canadian Capacity Guide for Signalized Intersection* [7] also utilizes the saturation adjustment factor that is relevant to the green splits and the weight of through- and left-turning flows. In contrast, the SIDRA model [8] and the Levinson method [9] adjust the capacity by reducing lost green times caused by lane blockages. The SIDRA model is a gap-acceptance-based model, and the iterative technique is used to determine the capacity. Levinson’s model is not so complicated, and it assumes that the capacity is affected by blockages of left-turning vehicles in the same direction and the opposing direction. These models are classical models, but they are limited to left-turning vehicles under the assumption of full compliance with the right-of-way.

##### 1.2. Platoon Method

The platoon method was first proposed by Wang [10] to calculate the capacity of an unsignalized intersection. His observation showed that drivers preferred to cross through the intersection alternately via a platoon of vehicles, especially during a peak hour. In fact, these studied intersections operate under a nonstrict priority. Meng et al. [11] performed an extended study of an unsignalized intersection with dual lanes. In his analysis, conflicts between left turns and oncoming flows were simplified to be those between two through-flows with large critical gap and follow-up times. Subsequently, Li and Song [12] improved the capacity model, taking into account the influence of nonmotorized vehicles and pedestrians. These works certainly improved the capacity under nonstrict priority. However, they oversimplified the intersection operation and neglected the characteristics of left-turning traffic streams. In addition, driver maneuvers during a permitted phase are different from those at an unsignalized intersection.

According to Bai’s empirical study on permitted left-turning maneuvers, left-turning vehicles would release in the form of a left-turn group under nonstrict priority. In his study, a left-turn group is comprised of all the vehicles turning at the same time without interruption by through-vehicles (saturation flow) or all those turning without interruption and with a time headway of no more than four seconds (unsaturation flow), as shown in Figure 1. He proposed that once the leading left-turning vehicle obtains a gap, the following vehicles will strive to maintain a small interval and cross through the intersection. Moreover, the following drivers prefer to begin their turning movement before the vehicle ahead to preempt the potential conflict point with opposing through-vehicles. The left-turning vehicle will not stop and wait for another chance to cross the intersection until the time its wheel may touch the centerline if the vehicle continues its turning movement. The phenomenon also indicates that the number of vehicles a left-turn group can accommodate is related to the intersection geometry.