Capacity Estimation Model for Signalized Intersections under the Impact of Access Point

Highway Capacity Manual 2010 provides various factors to adjust the base saturation flow rate for the capacity analysis of signalized intersections. No factors, however, is considered for the potential change of signalized intersections capacity caused by the access point closeing to the signalized intersection. This paper presented a theoretical model to estimate the lane group capacity at signalized intersections with the consideration of the effects of access points. Two scenarios of access point locations, upstream or downstream of the signalized intersection, and impacts of six types of access traffic flow are taken into account. The proposed capacity model was validated based on VISSIM simulation. Results of extensive numerical analysis reveal the substantial impact of access point on the capacity, which has an inverse correlation with both the number of major street lanes and the distance between the intersection and access point. Moreover, among the six types of access traffic flows, the access traffic flow 1 (right-turning traffic from major street), flow 4 (left-turning traffic from access point), and flow 5 (left-turning traffic from major street) cause a more significant effect on lane group capacity than others. Some guidance on the mitigation of the negative effect is provided for practitioners.


Introduction
The access points affect traffic operations and safety by introducing conflicts and friction into the traffic stream [1]. It imposes a potential negative effect on signalized intersection capacity near signalized intersections.
Access management becomes one of the emerging themes in traffic engineering in recent years [46,47]. Access management programs can smooth vehicle flow, reduce delay, and lead to fewer crashes. Technical constraints as well as political and institutional issues (e.g. the limits of land use, the width of the median and the density of road network), however, have limited widespread implementation, particularly in the developing countries. If it is not well addressed, the access point will be a potential effect factor to the capacity of signalized intersection. The previous research on the operational effects of access points mainly focused on the delays to drivers traveling along an arterial street segment and the capacity of access point itself based on the procedures for analyzing un-signalized intersections [48][49][50].
Although much is known about the operation of signalized intersections and the access point, little or no research has been conducted on the effect of access point on signalized intersection capacity to date. Even it was not considered as one of the adjustment factors in any of the capacity manuals. But if there is an access point near the signalized intersection, the demand starvation or queue spillback problem would be periodic and predictable.
In comparison with previous studies and applications, this paper: 1. Present a theoretical model for estimating the lane group capacity at signalized intersections with the consideration of the effects of access points.

2.
Validate the proposed capacity model based on VISSIM simulation.
3. Provide practical guidance on the mitigation of the access point effect based on extensive numerical analyses.
The rest of the paper is organized as follows. Section 2 describes the framework of the computational procedure and the notation adopted in this paper. Section 3 discusses the traffic flow composition of an access point and the model of determining maximum throughput of the access point. Section 4 provides the formulations of the lane group capacity with the effect of access point. The proposed model is validated in Section 5. The effect of six types of access flow on the capacity of signalized intersection is analyzed based on numerical test in Section 6. Conclusions and recommendations are given at the end.

Model Configuration
Two scenarios of access point location are discussed in this paper as shown in Figs 1 and 2, respectively. The scenarios 1 is that the access point locates at upstream of the intersection. And the scenarios 2 is that the access point locates at downstream of the intersection. Wherever its location, the access point is a potential blockage. The paper discusses the traffic flow composition of an access point and the maximum through traffic flow rate at the access point (s 2 ), firstly. Then the calculation model of the lane group capacity with the impacts of upstream and downstream access point is established, respectively. The outline of computational procedure is shown in Fig 3. To facilitate model presentation, notations used hereafter are summarized in Table 1.

Model Formulation
Maximum throughput of the access point Adjustment for access traffic flow (1). As illustrated in Fig 5(a), the access traffic flow (1) (right turn vehicles) often slow the following through vehicles when they enter into the access connection from the major street. So it will make the through traffic flow rate decrease, which can be illustrated as Eq 2. The proportion of right-turns and the decrease of saturation flow rate cause by right-turns are considered. The factor, 0.15, is based on the right turn adjustment formulation in HCM2010 [6].
Adjustment for access traffic flow (2). As Fig 5(b) illustrated, the access traffic flow (2) is allowed to enter the outside lane of the major street when an accepted gap occurs. It will cause   (2) is somewhat similar with the operation of traffic-actuated intersections [51]. Along the same lines as the capacity estimating model of traffic-actuated intersections, the adjustment factor for the access traffic flow (2) is calculated by Eq 3.
Adjustment for access traffic flow (3). The impact of access traffic flow (3) is that a part of time in which the conflict zone is occupied by it. So the proportion of time which is used by the through traffic should be determined. The operation principal of through traffic and the access traffic flow (3) at the conflict zone is similar to that of access traffic flow (2). The  difference is, in this case, all lanes of the through traffic are impacted by access traffic flow (3), as illustrated in Fig 5(c).
Adjustment for access traffic flow (4). As Fig 5(d) illustrated, the access traffic flow (4) has to cross the through traffic and merge into the inside lane of the opposing through traffic. If the median of the street is not wide enough, the through traffic of the major street is blocked by the access traffic flow (4) when it is waiting for the gap acceptance of the opposing through traffic. It can be illustrated by Eq 13, in which the average number of waiting vehicles is calculated based on the average queue length formulation at un-signalized intersections [52], as shown in Eq 14. The number of blocked lanes is related with the width of the median, as Eq 15 illustrated. Adjustment for access traffic flow (5). As Fig 5(e) illustrated, the access traffic flow (5) cannot across opposing through traffic until accepted gap occurs. During the waiting time, it will impact the following through traffic flow. So the waiting time of left turn vehicles should be taken into consideration, which can be specified as Eq 16. The probability of no waiting vehicle can be calculated based on the queue length probability model at un-signalized intersections [52], as shown in Eq 17.
Adjustment for access traffic flow (6). As Fig 5(f) illustrated, the access traffic flow (6) is allowed to enter the inside lane of the major street when an accepted gap occurs, so that it will cause the time loss of the following through traffic, which is similar to that of access traffic flow (2). Along the same lines as the adjustment factor estimating model of access traffic flow (2), the adjustment factor for the access traffic flow (6) is calculated by Eq 18.
Capacity with the impact of upstream access point The upstream access point would cause a negative effect on approach capacity by the potential impact of upstream blockage. For example, when the input volume of the approach is limited by the upstream access point, the lane group capacity couldn't be larger than the through traffic flow rate of the access point. The influence extent is related to the effective green time (g e ) and the maximum queue clearance time (T m ), which can be divided into two different situations, as shown in Fig 6. As illustrated in Fig 6(a), when the effective green time is shorter than the maximum queue clearance time (g e ≦ T m ), the flow rate of the lane group is equal to the ideal saturation flow rate (s 1 ), during all effective green time and the upstream access point has no effect on the lane group capacity. The capacity of a given lane group may be stated as shown in Eq 23.
; ðg e T m Þ ð 23Þ As illustrated in Fig 6(b), when the effective green time is longer than the maximum queue clearance time (g e > T m ), the flow rate of the lane group is equal to the ideal saturation flow rate (s 1 ) during the maximum queue clearance time, and it is equal to the ideal arrival rate of the approach (s 2 ) during the rest of the effective green time. The capacity of a given lane group may be stated as shown in Eq 24.
For a given signal timing, the maximum queue clearance time is computed using Eq 25. If the distance between an access point and stop line is long enough, the queue length of the arrival vehicles would not overflow to the access point, then the maximum queue clearance time is equal to the time for clearing the maximum arrival vehicles during the effective red time. Contrarily, if it does cause queue blockages to the access point, the maximum queue clearance time is equal to the time for clearing the stopped vehicles between the access point and stop line.

Model Validation
In this section, the proposed capacity model is validated based on VISSIM simulation. Table 2 summarized the data inputs. Totally, 72 scenarios were tested. Model validation results are shown in Table 3. As Table 4 illustrated, the paired samples T-test shows that there was no significant difference between the capacity calculated by the proposed model and that obtained by the simulations (t = 1.100, P = 0.275 > 0.05). Consequently, the accuracy of the proposed capacity estimation models is acceptable.

Sensitivity Analysis
In this section, the effect of six types of access flow on the capacity of signalized intersection is evaluated based on numerical analysis. Cycle length was set to 120 s in all cases.    point situation (the right column), respectively, and the number of major street lanes increases from bottom to top. For each sub-picture, the horizontal axe represents distance between stop line and access point, and the vertical coordinate is the lane group capacity of the intersection.
The following observations could be made from Fig 8. 1. Overall, capacity increases with the distance between stop line and access point. This increase has an asymptotic shape towards the capacity of ideal condition.
2. If the distance between the intersection and access point is long enough, the effect of access traffic flow could be ignored. For example, when the cycle length equals to 120 s and the green time ratio equals to 0.27, the access point locating more than 100 m upstream of the intersection or 90 m downstream of the intersection has no effect to the intersection capacity.
3. The column sub-pictures show an inverse correlation between the number of major street lanes and the negative impact of access points on the capacity. The negative impact of access points fade away, but could not be eliminated, with the increase of the number of lanes on major street.
4. The access traffic flow 1 (right-turning traffic from major street), flow 4 (left-turning traffic from access point), and flow 5 (left-turning traffic from major street) cause a significant effect on lane group capacity. Therefore, auxiliary turning lanes should be used to reduce the severity and duration of conflict between turning vehicles and through traffic, if the land use is permitted.

Conclusions
A theoretical model for estimating the lane group capacity with the consideration of the effects of access points is developed. From extensive numerical analysis, the following conclusions can be drawn: 1. The access point reduces the capacity of the lane group when it is close to the signalized intersection. The influence extent is mainly related to the signal timing, the number of lanes, the distance between the intersection and access point, and the types of access flows.
2. The access flows have no effect on lane group capacity if only the effective green time is shorter than the maximum queue clearance time in the case of upstream access point, or the effective green time is shorter than the time shock wave backing up to the stop line in the case of downstream access point.
3. Overall, the larger the number of major street lanes or the longer distance between the intersection and access point the less the negative impact of access point on the capacity generates. If the distance between the intersection and access point is long enough, the effect of access traffic flow could be ignored. For example, when the cycle length equals to 120 s and the green time ratio equals to 0.27, the access point locating more than 100 m upstream of the intersection or 90 m downstream of the intersection has no effect to the intersection capacity.
4. The access traffic flow 1 (right-turning traffic from major street), flow 4 (left-turning traffic from access point), and flow 5 (left-turning traffic from major street) have a significant effect on lane group capacity. Auxiliary turning lanes could be used to reduce those effects if the land use is permitted.
Some factors in the model, such as critical time headways, move-up time, minimum arrival headway, proportion of free vehicles, are closely related with the driver behavior [55][56][57][58] and local traffic condition [59,60]. For application in the practice, they should be calibrated for local traffic condition.
Supporting Information S1 Table. Lane group capacity under the impact of access traffic flows.