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Right-turn motorized vehicles turn right using channelized islands, which are used to improve the capacity of intersections. For ease of description, these kinds of right-turn motorized vehicles are called advance right-turn motorized vehicles (ARTMVs) in this paper. The authors analyzed four aspects of traffic conflict involving ARTMVs with other forms of traffic flow. A capacity model of ARTMVs is presented here using shockwave theory and gap acceptance theory. The proposed capacity model was validated by comparison to the results of the observations based on data collected at a single intersection with channelized islands in Kunming, the Highway Capacity Manual (HCM) model and the VISSIM simulation model. To facilitate engineering applications, the relationship describing the capacity of the ARTMVs with reference to the distance between the conflict zone and the stop line and the relationship describing the capacity of the ARTMVs with reference to the effective red time of the nonmotorized vehicles moving in the same direction were analyzed. The authors compared these results to the capacity of no advance right-turn motorized vehicles (NARTMVs). The results show that the capacity of the ARTMVs is more sensitive to the changes in the arrival rate of nonmotorized vehicles when the arrival rate of the nonmotorized vehicles is

The method of allowing right-turn motorized vehicles in the front to turn right using channelized islands is used to improve the capacity of intersections. Where channelized right-turn occurs, the ARTMVs (advance right-turn motorized vehicles) can be considered to have no effect on the capacity or delay of the intersection when they pass through the intersection [

Four aspects of traffic conflicts of the ARTMVs.

As shown in Table

Average conflict times per ARTMV under each aspect.

Site | Average conflict times per ARTMV under each aspect | |||||
---|---|---|---|---|---|---|

Intersection | Approach | Sample size | Aspect 1 | Aspect 2 | Aspect 3 | Aspect 4 |

Huancheng Bei-Beijing | East | 150 | 0.21 | 0.58 | 0.35 | 0.12 |

West | 150 | 0.23 | 0.78 | 0.33 | 0.21 | |

Huanchengdong-Chuan Jin | North | 150 | 0.34 | 0.84 | 0.20 | 0.37 |

South | 150 | 0.24 | 0.79 | 0.45 | 0.34 | |

Huanchengdong-Dong Feng Dong | East | 150 | 0.19 | 0.65 | 0.42 | 0.27 |

West | 150 | 0.34 | 0.67 | 0.32 | 0.34 | |

Huan Cheng Nan-Xichang | East | 150 | 0.11 | 0.70 | 0.36 | 0.23 |

South | 150 | 0.29 | 0.63 | 0.30 | 0.37 | |

Average | 0.25 | 0.71 | 0.34 | 0.28 |

In this paper, the shockwave theory and the gap acceptance theory are used to describe the conflicts between ARTMVs and nonmotorized vehicles moving in the same direction and a capacity model of ARTMVs is proposed. The sensitivity of the reliability (as will be described in detail in the Sensitivity Analysis section) of the proposed model was analyzed to ensure the stability and reliability of its use in engineering applications. In addition, from the data collected at typical intersections in Kunming, several model results and other factors were compared to demonstrate the rationality and validity of the proposed model. The roadmap of the paper is shown in Figure

The roadmap of the paper.

For the reader’s convenience, a list of the parameters used in the model is summarized in Table

Definition of Parameters.

Parameters | Definition |
---|---|

| The time from the start of the effective red time to the initial moment when the ARTMVs must wait to cross the conflict zone |

| The distance between the stop line and the position of the vehicle at which the moment ( |

| The width of the nonmotorized vehicle lane |

| The rate of arrival of the nonmotorized vehicles |

| The average road area occupied per nonmotorized vehicle when nonmotorized vehicles are waiting in the queue during the effective red time |

| The effective red time of nonmotorized vehicles |

| The effective green time of nonmotorized vehicles |

| The signal cycle |

| The starting wave speed of nonmotorized vehicles |

| The stopping wave speed of nonmotorized vehicles |

| The speed of the nonmotorized vehicles |

| The volume of the nonmotorized vehicles |

| The density of the nonmotorized vehicles |

| The time ARTMVs must wait before crossing the conflict zone because of spillback from the nonmotorized vehicle queue |

| The time during which the shockwave propagates backward from the stop line to the perpendicular line S |

| The time required for the queue of nonmotorized vehicles before the perpendicular line S to dissipate |

| The queue of nonmotorized vehicles by the end of the effective red time |

| The time required for the nonmotorized vehicle queue before the perpendicular line S to completely dissipate |

| The headway of the nonmotorized vehicles |

| The saturation headway of the ARTMVs |

| The minimum headway of the nonmotorized vehicles |

| The critical gap in the flow of the nonmotorized vehicles |

| The probability density of |

| The time it takes for a nonmotorized vehicle to pass through the conflict zone during a signal cycle, assuming that the vehicle does not stop |

| The number of ARTMVs that can pass through the conflict zone in a signal cycle |

| The capacity of the ARTMVs |

| The observed capacity of the ARTMVs |

| The calculated capacity of the ARTMVs |

The four aspects of the traffic conflicts of the ARTMVs are listed in the Introduction. The following paragraphs discuss each of these traffic conflicts.

The conflicts that occur between the ARTMVs and the motorized vehicles passing straight through an intersection are mainly visible in the shared through and right lanes. They can be categorized into the following two situations:

The conflicts that occur between ARTMVs and nonmotorized vehicles moving in the same direction can also be categorized into the following two situations:

Nonmotorized vehicle queue overflows into the conflict zone.

In most cases, both the ARTMVs and the pedestrians crossing the right-turn lane are unsignalized. ARTMVs usually cross the conflict zone only after following strict rules to ensure the safety of pedestrians. When the volume of ARTMVs and the volume of pedestrians are both low, the probability of a collision occurring between the two is also small. As the volume of both groups increases, the risk to pedestrians increases, and it also becomes more difficult for ARTMVs to pass through the intersection. Severe cases can cause interference to both nonmotorized vehicles and straight-through motorized vehicles moving in the same direction.

When the nonmotorized vehicles on the left are waiting during the effective red time, they do not affect the ARTMVs, and they can cross the conflict zone during saturated flow. When the nonmotorized vehicles on the left cross the intersection while the light is green, the nonmotorized vehicles affect the movement of the ARTMVs, especially when many nonmotorized vehicles are waiting for a green time. At this time, the nonmotorized vehicles pass through the conflict zone at a high density, and only after this do the ARTMVs take advantage of the gap before the subsequent arrivals of nonmotorized vehicles in order to cross the conflict zone. If the ARTMVs wait too long, a queue forms, affecting pedestrians, nonmotorized vehicles, and straight-through motorized vehicles moving in the same direction.

In summary, when the ARTMVs pass through an intersection, they cross the four conflict zones. Therefore, the capacity of the ARTMVs should be the minimum value of the four aspects of the traffic conflicts listed earlier. As described in the Introduction, for most of the ARTMV flows, the most severe traffic conflicts occur with nonmotorized vehicles moving in the same direction. To be specific, this aspect of traffic conflict has the greatest influence on the capacity of the ARTMVs. Therefore, this paper mainly studies the capacity of ARTMVs under the influence of nonmotorized vehicles moving in the same direction.

The previous analysis of the conflicts between the ARTMVs and the nonmotorized vehicles moving in the same direction shows that spillback from the nonmotorized vehicle queue had a pronounced impact on the capacity of the ARTMVs crossing the intersection. Hence, one of the keys to calculating the capacity of the ARTMVs is determining whether the nonmotorized vehicles overflow into the conflict zone. This paper takes a two-phase signalized intersection as an example to analyze the influence of an overflow of the nonmotorized vehicle queue.

According to the observations that were made by the authors, when the opening into the crossing of the ARTMVs was less than 2.5 m after nonmotorized vehicles queue overflowed, the ARTMVs were not able to complete their trip through the conflict zone. This moment was considered the initial moment when the ARTMVs needed to wait to cross the conflict zone, denoted as

Diagram of the crossing process of the ARTMVs.

In this paper, the authors used shockwave theory to describe the phenomenon of spillback among nonmotorized vehicle queues. The shockwave theory was proposed by Lighthill-Whitham-Richards (LWR) [

Time-space diagram of the shockwave (the starting wave).

The authors used the signal cycle as the analytical period to analyze the impact of the spillback on the nonmotorized vehicle queue. In each signal cycle, the time ARTMVs must wait before crossing the conflict zone because of spillback from the nonmotorized vehicle queue is denoted by

Time-space diagram of the shockwave (the stopping wave).

Due to the density of the subsequent nonmotorized vehicles during a period of moderate flow, the authors used the Greenshields model to describe this process, which can be formulated as follows [

Substituting Equation (

As a result of the nonmotorized vehicles with states of high density during the initial green time, the authors used the Greenberg model to describe this process [

Substituting Equation (

The queue of nonmotorized vehicles

Nonmotorized vehicles did not stop when passing through the conflict zone. These vehicles were usually moving in a state of relatively low density and high speed. Therefore, it could be assumed that the headway of the nonmotorized vehicles followed a negative exponential distribution, and the authors used gap acceptance theory to calculate the capacity of ARTMVs when the nonmotorized vehicles continuously crossed the conflict zone [

This conflict zone could be considered an X-intersection intersected by two one-way traffic flows, as shown in Figure

The X-intersection intersected by two one-way traffic flows.

The headway of the nonmotorized vehicles is denoted by

The ARTMV lane was thought to meet the needs of the ARTMV queue in this paper. The probability density of

For any

Let

Because the ARTMV lane meets the ARTMV queue, the reduction factor of the length of the ARTMV lane for the capacity can be considered equal to 1. By substituting the probability density function of a negative exponential distribution

In a signal cycle, the ARTMVs volume passing through the conflict zone is

Reliability is generally defined as the probability that the system of interest has the ability to perform an intended function or goal. It can be formulated as the determination of the (supply) capacity of the system to meet certain (demand) requirements [

The model shows that the capacity of ARTMVs is affected by the arrival distribution of nonmotorized vehicles, the arrival rate of nonmotorized vehicles, and signal timing parameters. To fully evaluate the influence of nonmotorized vehicles on ARTMVs, the authors selected the arrival rate of nonmotorized vehicles as the disturbance variable to analyze the sensitivity of the reliability of the model, and it was assumed that other factors were unchanged. During analysis, the arrival rate of the nonmotorized vehicles derived from other influence factors was determined. According to the capacity model of ARTMVs deduced earlier, the sensitivity of the reliability analysis model under the influence of the arrival rate of the nonmotorized vehicles could then be written as follows:

The influence of the different arrival rates of nonmotorized vehicles on the capacity of the ARTMVs can be analyzed using Equation (

To verify the capacity model of the ARTMVs, the Huancheng Bei-Beijing intersection (one of many signalized intersections with channelized islands used for ARTMVs in Kunming, China) was chosen as the model validation site, as shown in Figures

(a) Video camera location; (b) screen shot; (c) geometry of the Huanchengbei-Beijin intersection.

Illustration of the signal timing of the Huancheng Bei-Beijing intersection.

The video was reviewed using a Corel VideoStudio Pro X4 and the traffic parameters of the model were obtained frame by frame. The video system was set to 25 frames per second. Because about 90% of the nonmotorized vehicles were electric bicycles, the model parameters were different from those of nonelectric bicycles, as shown in Table

Parameters of the Model.

Parameters | Values | Sample size | Parameters | Values | Sample size |
---|---|---|---|---|---|

| 2.6 | 217 | | 0 | — |

| 2 | 246 | | 2.8 | 243 |

| 4.6 | — | | 7.35 | 262 |

| 129 | — | | 10 | 271 |

| 48 | — | | 0.32 | 216 |

| 2.36 | 169 | | 0.45 | 243 |

| 21.1 | — | | 0.03 | 234 |

| 3.8 | — |

In this example, when

The proposed model was analyzed using data from the survey. First, the capacity of the ARTMVs was calculated using the proposed model. The results of the proposed model were compared to those of the observed results, the HCM 2010 model (the HCM 2010 model is applicable to the situation in which the flow rate of nonmotorized vehicles is

Comparison between the Observed and Calculated Capacities of the ARTMVs.

| | | Relative error | ||||
---|---|---|---|---|---|---|---|

Proposed model | VISSIM | HCM 2010 | Proposed model | VISSIM | HCM 2010 | ||

113.3 | 1366.7 | 1296.0 | 1264.6 | 1298.8 | 5.2% | 7.5% | 5.0% |

260.0 | 1273.3 | 1179.7 | 1109.9 | 1223.6 | 7.4% | 12.8% | 3.9% |

353.3 | 1146.7 | 1106.5 | 1012.6 | 1175.7 | 3.5% | 11.7% | 2.5% |

473.3 | 973.3 | 1014.8 | 890.4 | 1114.2 | 4.3% | 8.5% | 14.5% |

633.3 | 920.0 | 898.4 | 736.0 | 1032.1 | 2.4% | 20.0% | 12.2% |

946.7 | 806.7 | 681.5 | 479.9 | 871.5 | 15.5% | 40.5% | 8.0% |

1053.3 | 500.0 | 570.8 | 411.8 | 816.8 | 14.2% | 17.6% | 63.4% |

1226.7 | 453.3 | 433.1 | 327.6 | 727.9 | 4.5% | 27.7% | 60.6% |

1360.0 | 406.7 | 352.6 | 288.5 | 659.5 | 13.3% | 29.1% | 62.2% |

1446.7 | 360.0 | 309.2 | 276.6 | 615.0 | 14.1% | 23.2% | 70.8% |

1513.3 | 360.0 | 279.7 | 275.2 | 580.9 | 22.3% | 23.5% | 61.3% |

1640.0 | 260.0 | 231.5 | 292.7 | 515.9 | 11.0% | 12.6% | 98.4% |

1693.3 | 240.0 | 213.9 | 308.4 | 488.5 | 10.9% | 28.5% | 103.6% |

MAPE | 9.9% | 20.3% | 43.6% |

The capacity of ARTMVs under different models.

(a) Capacity of the ARTMVs when the nonmotorized vehicles queue did and did not overflow; (b) difference between the capacity of the ARTMVs when the queue of nonmotorized vehicles overflowed and when it did not.

In this paper, two important factors were selected for further analysis; these two factors were the distance between the conflict zone and the stop line and the effective red time of the nonmotorized vehicles. The authors also compared the results of the capacity of the NARTMVs and provided a theoretical basis for the reasonable traffic control of right-turn motorized vehicles.

It was assumed that, when comparing the capacity of the ARTMVs and the capacity of the NARTMVs, the effects of pedestrians and other vehicle flows (except for nonmotorized vehicles moving in the same direction) on right-turn vehicles could be ignored, and the NARTMVs and the nonmotorized vehicles were both controlled by the signal. In this situation, the capacity of the NARTMVs was as follows:

The influence of the change in the distance between the conflict zone and the stop line on the capacity of the right-turn vehicles is described as follows. Figure

Influence of the changes in the distance between the conflict zone and the stop line on the capacity of the right-turn vehicles.

According to Figure

The influence of the change of the effective red time on the capacity of the right-turn vehicles is described as follows. Figure

Influence of change in the duration of the effective red time on the capacity of the right-turn vehicles.

According to Figure

Capacity sensitivities for different arrival rates of the nonmotorized vehicles.

As shown in Figure

This paper presents a capacity model of ARTMVs at signalized intersections with mixed traffic conditions using different traffic theories. The proposed capacity model was validated by the data collected at a single intersection with channelized islands in Kunming. This capacity model can be used to analyze the traffic characteristics of right-turn motorized vehicles turning right using channelized islands and nonmotorized vehicles, and to provide theoretical support for traffic management. Based on the results of the analysis, the following conclusions can be reached.

The survey and analytical data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China [Grant no. 61364019].