Quadrant Roadway Intersections: Tradeoffs between Control Delay Savings and Extra Travel Time

Abstract

A quadrant roadway intersection (QRI) reduces congestion relative to a four-phase intersection. (Note: this study relates to traffic systems where vehicles drive on the right-hand side of the road.) It does this by removing left-turn traffic from the main intersection, resulting in a two-phase signal. Nevertheless, there is a lack of clear understanding of the tradeoffs between savings in control delay versus extra travel time experienced by the rerouted movements. This research compared the operational performance of five QRI designs with the counterpart conventional intersection (CI) under various traffic demand scenarios via TransModeler microsimulation modeling. Three measures-of-effectiveness (MOEs) were employed: time-in-system (TIS), control delay, and intersection capacity utilization. Simulation results show that all QRI designs outperform CI design for all three MOEs under all demand scenarios. QRIs with direct left-turn design have a smaller average TIS than those with loop left-turn design, indicating that savings in control delays did not offset the extra travel times. Under a relatively low demand condition, a single QRI design can generally balance the tradeoffs between control delay and extra travel time. Under a high demand scenario, a dual or full QRI with direct left-turns is preferred, since it reroutes or partially reroutes left- and right-turn traffic to secondary intersections, thus the main intersection has a lower capacity utilization and can accommodate more through-traffic demands than CI, single QRI, and dual or full QRIs with loop left-turns.

Keywords

quadrant roadway intersection direct left-turn loop left-turn time-in-system capacity utilization microsimulation

Left-turning traffic (in traffic systems where vehicles drive on the right-hand side of the road) is more dangerous than other movements and a significant source of congestion at intersections ( 1 ). Typically, protected left-turn phases are used at signalized intersections to reduce delays and the likelihood of crashes for left-turning traffic ( 2 ). Nevertheless, implementing protected left-turn phases will increase delays to through traffic, decrease intersection capacity, and deteriorate the progression of the signal coordination. This is mainly because the addition of left-turn signal phases takes green time away from through movements and adds to the inter-phase lost time, which takes away from usable cycle time and reduces the efficiency of the intersection ( 3 ). Moreover, traffic flow may have asymmetric conditions where left-turn demand is heavier from one approach than the others; under such a condition, a protected left-turn phase may further reduce the operational efficiency of the intersection.

As traffic volumes are continuously increasing and overloading the design capacity of many intersections during peak periods, the impact of protected left-turn signals on intersection operations tends to be more significant. Therefore, instead of implementing protected left-turn phases, an alternative way is to redirect the left-turning traffic from the main intersection to sub-intersection(s) located downstream or upstream of the main intersection ( 4 – 7 ). One such design is the quadrant roadway intersection (QRI), which includes a main intersection and secondary intersections that are linked by a connector road in one or more quadrants of the intersection ( 8 ). Left-turn vehicles that would normally require a protected left-turn phase at the main intersection are instead rerouted via secondary intersections that can more easily handle the load. Figure 1 shows the geometry of a single QRI where the connection road is located in the southwest quadrant. This connection road adds two three-leg intersections to the original four-leg intersection. The location of the connection road depends on traffic demand and availability of right-of-way, and the secondary intersections are typically signalized but can also be unsignalized, depending on the traffic demand and geometric features.

In practice, intersection designs that reroute one or multiple left-turn movements using connecting roadways are not a new concept; they have been used or partially used for decades ( 4 – 7 ). However, the formalization of rerouting all left-turn movements using a standardized QRI with signal coordination did not become mature until the later 1990s, when Shin proposed rerouting left-turn movements to side roads located upstream of the intersection and utilizing these side roads as storage for left-turn queues ( 9 ). Then, during the subsequent green phase of the approaching intersection, the left turns would be completed. In comparison with the conventional intersection (CI) design, the QRI design has the potential of improving both the operational efficiency and safety performance of the intersection ( 10 ). Rerouting left-turn traffic from the main intersection allows for implementing a two-phase signal control scheme at the main intersection, which enables using a shorter cycle length. The reduced number of signal phases also means less lost time occurs during phase transition. This results in higher capacities and lower delays for through and right-turn traffic at the main intersection, thus a higher level-of-service (LOS) is expected. Moreover, rerouting left-turn traffic reduces and spreads out the number of conflict points, which reduces the crash risk at the main intersection. It is necessary to point out that the potential illegal left turns at QRIs pose an even higher risk of crashes, because other drivers on the road may not expect a vehicle to turn left at a QRI, leading to confusion and unexpected actions that can increase the likelihood of a collision. In this concern, it is essential that drivers understand the rules of navigating QRIs and always follow the traffic signs and signals.

In the U.S., the concept of QRI design was first published in 2000, and the first QRI was opened in 2012 ( 8 ). To date, there are 11 QRIs of various types in operation in the U.S. ( 11 ). Nevertheless, QRIs have some negative effects. Some require out-of-direction travel, which may add travel time to left-turning traffic. There will also be additional delay introduced to through vehicles at the secondary intersections ( 8 ). Therefore, the operational analysis of QRIs should consider the entire system instead of merely focusing on the main intersection. Moreover, each QRI design has a unique traffic flow pattern, which may redirect a specific number of left-turn vehicles to re-enter the main intersection and thus increase through-traffic volumes at the main intersection. Therefore, when determining the number and location of quadrants as well as secondary intersection signal control schemes, traffic engineers may have to balance the tradeoffs between the control delay savings from main intersection (to all traffic movements), additional control delays at the secondary intersections, and extra travel times to the rerouted left-turn movements.

With this concern, this research compares the operational performance of various QRI configurations under different traffic control schemes and traffic demand scenarios to identify the applicability of various QRI designs. The remainder of this paper first includes a systematic review of the operational, safety, and design considerations for QRIs. Then, there is a description of operational performance modeling methodologies. After that, the results of QRI operation performance were presented. Finally, discussions on the applicability of QRI and recommendations were made.

State-of-the-Practice

Traffic Operations

In practice, the most critical element of operating a QRI is to coordinate the main and secondary signals. For instance, at a single quadrant intersection, the main intersection operates as a simple two-phase signal, and the secondary intersections operate under a three-phase signal scheme with the through movement as the coordinated phase to the main intersection ( 8 ). Although the number of QRIs is limited, there is evidence showing the QRI is a promising design for the intersection of two high-volume multi-lane roadways. Reese et al. presented an observational comparison of traffic operations before and after the implementation of a QRI in North Carolina ( 12 ). Since the QRI was introduced, the total network delay on the major road has decreased by 46% during peak periods, which indicates that the QRI design is a viable alternative for improving traffic operations at congested intersections.

When considering operational performance assessment methodology, Sangster and Rakha pointed out that a QRI includes a high level of rerouting of vehicles, which some of the performance assessment methodologies do not account for ( 13 ). The research investigated the applicability of three methodologies for assessing the performance of QRIs. Results show that the critical sum method could not provide reliable assessment of operational performances. The Highway Capacity Manual 6th Edition (HCM) incremental queue accumulation delay estimation method can provide indicative delay assessment results, but it did not account for the extra travel time incurred by the rerouted traffic. In comparison, a microsimulation method was recommended to compare the operational performance between alternative designs. Reid and Hummer indicated that a QRI design is a system of multiple intersections; therefore, operational analysis needs to consider the operations of each intersection and the relationship between them ( 11 ). Their research summarized three categories of traffic operations analysis tools for QRIs: planning-level analysis tools such as critical lane volume and CAP-X, the HCM method, and microsimulation analysis.

Several microsimulation-based studies have been conducted during the past two decades to assess the operational performance of QRIs. Based on CORSIM microsimulation modeling, Reid found that the single quadrant intersection reduced average system travel time at a study intersection from 66.9 s to 58.2 s and reduced average intersection control delay from 35.8 s to 24.4 s, respectively ( 8 ). The improvements to main intersection through-movement are particularly significant, where the travel time and intersection control delay reduced from 86.6 s to 66.5 s and from 41.2 s to 13.5 s, respectively. Other research by Reid and Hummer compared travel times between seven alternative intersection (AI) designs using CORSIM microsimulation ( 14 ). Results show that AI designs always had a lower system average travel time than the conventional design, and the QRI design consistently produced the lowest travel times. Nevertheless, the QRI design also produced the highest distance traveled at each intersection.

Hughes et el. tested the operational performance of a single QRI under various geometric configurations and volume scenarios using VISSIM microsimulation ( 15 ). Results show that, under moderate and balanced through-traffic conditions, a QRI performs comparably to a CI. However, the QRI usually has higher throughput and lower travel times when the major road has heavy through and moderate left-turn traffic volumes, and in scenarios with heavy through and left-turn traffic on the minor road. Naghawi et al. evaluated the effect of three AI designs (median U-turn, superstreet, and QRI) using Synchro modeling ( 16 ). Results showed that all three AIs outperformed the CI design with regard to control delay, but only the single-QRI design improved the main intersection LOS from F to B. The single-QRI design increased average travel speed by 52% with a decrease in control delay by 34%. A similarly Synchro-based study by Hadidi et al. found that the single-QRI design, although it did not improve the LOS of the study heavily congested intersection, reduced the intersection delay by 75.6% ( 17 ).

Traffic Safety Performance

Methodologies for AI safety performance assessment mainly include the following four categories: 1) empirical crash data-based analysis, 2) deterministic approach based on the number of conflict points and speed variations, 3) driver behavior studies through driving simulator experiment or stated and revealed preference surveys, and 4) surrogate safety assessment based on microsimulation ( 18 , 19 ).

By removing left-turn movements from the main intersection, the total number of potential vehicle-vehicle conflict points for a single QRI reduces from 32 to 28. Furthermore, these conflicts are now divided across three intersections, resulting in less overall complexity at any given intersection. Additionally, some of the crossing conflict points are converted to safer diverging and merging conflict types. The reduction in conflict points and changes in conflict types are usually considered as indicators of reduced risk and severity of crashes ( 8 , 11 , 15 , 20 ). Driver behavior studies based on driving simulators or surveys have the potential to investigate driver perceptions and behavioral adaptations to AI designs, but no such studies have been conducted for QRIs to date. The Federal Highway Administration (FHWA) surrogate safety assessment model (SSAM) is commonly used to assess the safety performance of various roadway configurations ( 21 , 22 ). However, a major drawback of SSAM is that vehicle trajectories are generated in a simulation environment that is assumed to be collision-free. Furthermore, no SSAM-based research has been conducted for QRIs to date.

Because of the limited number of QRIs in operation in the U.S., there are insufficient empirical crash data to quantitatively describe the safety benefits of a QRI. Reese et al. performed a preliminary crash analysis of crashes that occurred in the 3 years before the construction of a QRI in North Carolina and 2 years after the opening of the QRI ( 12 ). They found that, despite significant changes in development in the study area, the overall traffic safety was not degraded. Although there was an 8.9% increase in the crash rate at some road segments and intersections, this increase was relatively insignificant considering the 18% increase in traffic volumes in the area ( 11 , 12 ). Nevertheless, Reese et al. found that there were complaints about the new patterns and observed illegal left turns, and suggested adding more signs and markings or using physical barriers to reduce the safety hazards caused by these turns. An Ohio case study showed that the number and severity of crashes at the main intersection and one of the secondary T-intersections was reduced, while a significant number of crashes occurred at the other secondary T-intersection, resulting in a higher total number of crashes than in the CI ( 11 ). A similar trend was observed in a Virginia case study, where total crashes increased by 25%, but injury crashes and injuries were reduced by 130% and 230%, respectively ( 11 ). These results are generally opposed to the expected safety benefits from a reduced number of conflict points, but they make sense when considering the combined effects of induced traffic volumes and driver confusion with unconventional left-turn patterns.

Applicability and Design Considerations

The QRI is typically considered as a spot treatment to alleviate congestion at a particular intersection ( 15 ). Ideally, a QRI would be considered at locations with one or more pathways that can be used as connection road(s), or where such pathways could easily be developed. Also, QRIs are particularly suitable for skewed intersections, as they allow for a shorter connection road with a smoother curve on the connector and eliminate sharp left-turn angles. With regard to traffic flow patterns, previous studies have found that QRIs are appropriate for intersections with heavy through volumes and low-to-moderate major road left-turn volumes, particularly if only one of the four left-turn movements at the main intersection is heavy ( 11 , 15 ).

For QRI design, it has been a consensus that the spacing of the secondary intersections from the main intersection is one of the most influential geometric elements of a QRI, which should be a trade-off between left-turn travel distance versus available storage for the left-turn movement ( 15 , 18 , 23 ). Moreover, the design of QRIs should take into account human factors and driver expectations, such as drivers desiring to make a left turn not expecting the prohibition of direct left turns at the main intersection, nor do they expect out-of-direction travel. Therefore, the intersection spacing should provide adequate sight distance and signing to allow drivers to safely change to the right-turn lane if necessary for completing their left-turn movement ( 11 , 15 , 23 ). In reality, the optimal spacing should be determined according to the dominant traffic conditions, prevailing speeds, and, typically, a sensitivity test should be conducted using microsimulation modeling to explore the most suitable distance for each set of traffic conditions ( 18 ). Reid and Hummer recommended, in general, an optimal signal spacing of 500 ft to accommodate left-turn volumes and storage capacity needs ( 11 ). Although the research clarified that the spacing may be site-specific according to actual geometry and traffic conditions, it emphasized that a spacing larger than 800 ft tends to impose substantial greater travel time and delays for any rerouted traffic subject to out-of-direction travel.

Another key design element is the location of the connection road, which is primarily determined by the left-turn volume at the intersection ( 11 , 15 ). Specifically, for a single QRI, the connection road is usually placed to allow the highest volume of left-turn traffic to receive the most direct path. For a dual-quadrant design, the two connection roads are recommended to be placed on diagonal quadrants to avoid the need for four-phase signals at the secondary intersections. A three- or four-quadrant design is also possible, although the operational efficiency of a three- or four-quadrant design tends to be affected by the signal timing scheme of the secondary intersection. For example, if a four-phase or long-cycle signal is applied at the secondary intersection, then the operational benefits of the QRI would be lost ( 15 ).

Methodology

Because of unavailability of empirical data, the operational performance of QRI designs could be assessed through the following methods: 1) Planning-level analysis tools such as the FHWA CAP-X tool, 2) macroscopic analysis such as the HCM method, and 3) microscopic simulation modeling (11, 24 –28). While planning-level analysis usually only provides a high-level operational assessment such as LOS, macroscopic analysis can provide a more detailed analysis of performance during peak hours, but it does not consider the interactions between signals ( 11 ). In current practice, microsimulation is still widely considered as the most powerful tool to assess AI designs; therefore, this research employs microsimulation to test the operational performance of QRI design variations, types of control, and different demand levels.

Left-Turn Treatments

This research proposes five QRI configurations (illustrated in Figure 2) to cover typical QRI designs:

1) single quadrant intersection (SQR) (Note that all four lefts use the southeast connector as per the pattern shown)

2) dual quadrant intersection with direct left-turns from major street (DQR_D)

3) dual quadrant intersection with loop left-turns from major street (DQR_L)

4) full quadrant intersection with direct left-turns (FQR_D)

5) full quadrant intersection with loop left-turns (FQR_L)

The left-turn treatments and secondary intersection signal phasing diagrams for each QRI design are specified below. For all QRI designs, this research assumed a two critical movements (CM) phasing scheme at the main intersection.

Single Quadrant Configuration

Figure 3 shows how all four of the left-turn movements are rerouted over the connection road located at the southeast quadrant of the main intersection. These four left-turn patterns are typically named: “loop” (through-right-right-through), “direct left-turn” (also known as “corner cut” or “left-left”), “jughandle” (right-left-through), and “reverse jughandle” (through-left-right), corresponding to the rerouted eastbound, westbound, northbound, and southbound left-turn movements, respectively ( 29 ). A three-CM phasing scheme was applied to the secondary intersections, as illustrated in Figure 4.

Dual Quadrant Configurations

To investigate the tradeoffs between signal control delay and extra travel time, this research proposed two dual quadrant configurations. The DQR_D configuration keeps signals for all secondary intersections, where major street left-turn movements proceed the intersection through the direct left-turn pattern to avoid entering the main intersection and eliminates extra travel distances. The minor street left-turn movements have a reverse jughandle pattern, as shown in Figure 5. A three-CM phasing scheme was applied to the secondary intersections, as illustrated in Figure 6. For major road secondary intersections, right-turn movements from the connector (i.e., Phase 8 in Figure 6b and Phase 4 in Figure 6d) may adopt a concurrent phasing scheme with major street left-turn traffic (i.e., Phase 1 in Figure 6b and Phase 5 in Figure 6d, respectively). This will help to reduce the number of CMs at the major road secondary intersection from three to two, thus potentially reducing control delays to major street through movements.

For the dual quadrant intersection with loop left-turns from major street (DQR_L) configuration, major street left-turn movements need to proceed through the intersection using the loop pattern, and minor street left-turn movements have a reverse jughandle pattern, as shown in Figure 7. Figure 8 illustrates the signal phasing diagrams for DQR_L. A three-CM phasing scheme was applied to the secondary intersections on the minor road. For the secondary intersections on the major road, a two-CM phasing scheme was adopted. A continuous green scheme could be applied to one direction of each major road secondary intersection (i.e., Phase 6 in Figure 8b, and Phase 2 in Figure 8d) unless a signalized pedestrian crossing of the major road is presented at the intersection; the other direction operates under a right-in, right-out (RIRO) operational strategy. Moreover, depending on arterial through-traffic volume and right-turn traffic demand form the connector, major road secondary intersections might be treated as unsignalized to eliminate control delays to major street traffic.

Full Quadrant Configurations

Moreover, this research proposed two full quadrant configurations to further investigate the tradeoffs between control delay and extra travel time. The first configuration keeps signals for all secondary intersections to allow all left-turn movements proceed through the direct left-turn pattern, so no left-turn movement will enter the main intersection, as shown in Figure 9. A three-CM phasing scheme was applied to the secondary intersections, as illustrated in Figure 10.

The FQR_L configuration redirects all left-turn movements to proceed the intersection through the loop pattern, as shown in Figure 11. A two-CM phasing scheme was applied to all secondary intersections to reduce control delays at the secondary intersections, as shown in Figure 12. Note that the secondary intersections might be treated as unsignalized, depending on the demands of the arterial through traffic and connector right-turn traffic.

Traffic Volume Conversion

Most microsimulation packages employ intersection-level turning traffic volumes rather than an origin-destination (O-D) matrix as input. Since each QRI design will result in a unique traffic flow rerouting pattern, traffic volume conversions are needed to accommodate such microsimulation models or to serve analytical models. Figure 13 depicts the conversion of a CI turning traffic volumes into turning traffic volumes for various QRI configurations. Depending on QRI configuration, the rerouted traffic could either decrease or increase the volumes entering the main intersection.

Measures of Effectiveness

The latest edition of HCM recommends control delay as an intuitive measure for determining signalized intersection LOS and uses capacity as a planning-level analysis of design sufficiency ( 26 ). For AI designs with secondary intersections, the HCM method employs “experienced travel time” (ETT), which consists of control delay at each intersection and “extra distance travel time” caused by rerouting, for determining LOS.

To investigate the tradeoffs between savings in control delay and extra travel time, this research employs three measures-of-effectiveness (MOEs) to provide information about the treatments at the intersection and system levels. Movement-based time-in-system (TIS), which is similar to the ETT concept in the HCM method, was employed as the primary MOE for assessing the system performance of each QRI design. Moreover, average control delay and intersection capacity utilization (ICU) at the main intersection were employed as indirect MOEs for investigating the effects of the rerouted traffic on the operations of the main intersection ( 30 ).

Microsimulation Model Development

Microsimulation modeling was performed with the Caliper TransModeler 5.0 software. The research started with the development, calibration, and validation of the baseline model. Based on the calibrated baseline model, the proposed five QRI designs were developed. When converting the baseline model to a QRI model, this research kept the original number of turning lanes for each movement. The Trafficware Synchro 11 software was employed to optimize the cycle lengths, splits, and offsets for each QRI model according to its converted turning traffic volumes. Moreover, average control delay and ICU at the main intersection were also estimated via Synchro software.

Baseline Model

The baseline model was developed based on the Oleander Drive and College Road intersection in Wilmington, North Carolina, U.S. The geometric layout of this site is shown in Figure 14.

Data Collection and Extraction

Field data was collected through a remote-controlled drone during a weekday PM peak period. This research distinguished the field collected data into three categories: 1) simulation input data, such as intersection geometry elements, peak hour O-D traffic arrival rates and vehicle composition, and signal control information; 2) model calibration parameters describing driver behavior and vehicle characteristics and the green time allocated to each phase during the data collection period; 3) traffic performance measures for model validation, such as movement-based TIS.

These data were extracted from the drone videos using a third-party data processing software named DataFromSky (DFS), which enables tracking individual vehicle trajectories and designating detectors anywhere in the video to collect data at a point such as the timestamp and instantaneous speed of each vehicle passing the detector. Peak hour upstream traffic flow arrival rates (presented in Figure 14) and microscopic driver behavior data such as saturation headways, speeds, and so forth were extracted. Being limited by the drone camera range, this research extracted the TIS data for the Eastbound Through (EBT) traffic for model validation purposes. Locations of the data collection sensors placed at the DFS software are illustrated in Figure 14.

Base Model Calibration and Validation

Since the baseline model was developed exactly following the intersection aerial map, it allows for matching the data collection sensor locations in TransModeler to those used for field data collection.

From a calibration perspective, a previous study revealed that a principal parameter for signalized intersections is the saturation discharge flow rate, which is derived from saturation headway ( 31 ). Moreover, the model calibration process includes calibrating the initial queue, signal timings, vehicle compositions, and so forth; TransModeler employs a “headway buffer” to model a vehicle’s appropriate acceleration or deceleration in response to the vehicle in front of it, and this research calibrated the headway buffer through an iterative trial-and-error process until the simulated saturation headways match field observations. The initial queue calibration was achieved by running a 15 min warm-up simulation; similarly, a trial-and-error process was used to adjust the traffic demands in the warm-up period until the simulated maximum queue matched field observation. The signal timing parameters were adjusted to ensure that the signal controller outputs in the simulation model (i.e., the distribution of cycle lengths and green times) matched those achieved in the split monitor reports.

Figure 15a compared the simulated saturation headways with field observations, indicating that the baseline model is generally well calibrated. With the calibrated model, this research conducted 10 simulation runs, and compared the simulated TIS for EBT movement with field observations shown in Figure 15b. The results indicate that, although there are some visible differences between field data and TransModeler simulation results, the calibrated model generally performs better than the uncalibrated model with regard to proximity to field observations, with an absolute deviation of 3.7% for the calibrated model compared with an absolute deviation of 32.1% for the uncalibrated model.

QRI Models and Simulation Scenarios

Based on the calibrated baseline simulation model, this research developed QRI models to represent the proposed five QRI configurations. According to the FHWA QR Informational Guide, the spacing between signals was determined as approximately 600 ft ( 11 ).

The simulation experiment included four factors: intersection type, main intersection phasing scheme, secondary intersection phasing scheme, and traffic demand scenarios. The first three factors created six scenarios (as discussed in the left turn treatment scenarios section). Four traffic demand scenarios were tested: base demand collected by drone (Volume-to-Capacity, v/c ratio approximately 0.75 to represent an undersaturated condition); demand increase by 20% to represent peak hour operations; heavy major street left turn traffic scenario (Eastbound Left-turn, EBL and Westbound Left-turn, WBL increase by 20%), and heavy major street through-traffic scenario (EBT and Westbound Through, WBT increase by 20%). A total of 24 simulation scenarios were determined (as shown in Figure 16); for each scenario, 10 simulation runs with various random seeds were conducted to minimize the stochastic errors of microsimulation.

Traffic data collection sensors were added to each TransModeler simulation to collect traffic flow and travel time data. To cover the entire QRI system, and in an attempt to capture the vehicle queues upstream of the secondary intersections, the data collection sensors were placed at approximately 1,400 ft. upstream and downstream from the main intersection. Figure 17 illustrates the locations of data collection sensors at the FQR_D model. For each movement, the travel distance from the upstream sensor to the downstream sensor is defined as the distance-in-system (DIS) for this movement. For all six TransModeler models, each data collection sensor was placed at the same location to ensure the DIS for each movement is consistent between models. The DISs for each intersection configuration are presented in Table 1.

Table 1.

Comparison of Distance-in-System (DIS) between Conventional Intersection (CI) Model and Quadrant Roadway Intersection Models

Movement	DIS* (ft) by movement
Movement	CI	SQR	DQR_D	DQR_L	FQR_D	FQR_L
EBL	2,820	5,350 ^a	2,720 ^b	5,350 ^a	2,720 ^b	5,350 ^a
EBT	2,920	2,920	2,920	2,920	2,920	2,920
EBR	2,740	2,740	2,740	2,740	2,680	2,680
WBL	2,780	2,650 ^b	2,650^b	5,380 ^a	2,650^b	5,380 ^a
WBT	2,920	2,920	2,920	2,920	2,920	2,920
WBR	2,750	2,750	2,750	2,750	2,640	2,640
SBL	2,800	4,000 ^c	4,000 ^c	4,000 ^c	2,700 ^b	5,420 ^a
SBT	2,700	2,700	2,700	2,700	2,700	2,700
SBR	2,760	2,760	2,660	2,660	2,660	2,660
NBL	2,820	4,060 ^d	4,070 ^c	4,070 ^c	2,730^b	5,420 ^a
NBT	2,700	2,700	2,700	2,700	2,700	2,700
NBR	2,720	2,600	2,600	2,600	2,600	2,600

Note: DQR_D = dual quadrant intersection with direct left-turns from major street; DQR_L = dual quadrant intersection with loop left-turns from major street; EBL = Eastbound Left-turn; EBR = Eastbound Righ-turn; EBT = Eastbound Through; FQR_D = full quadrant intersection with direct left-turns; FQR_L = full quadrant intersection with loop left-turns; NBL = Northbound Left-turn; NBR = Northbound Right-turn; NBT = Northbound Through; SBL = Southbound Left-turn; SBR = Southbound Right-turn; SBT = Southbound Through; SQR = single quadrant intersection; WBL = Westbound Left-turn; WBR = Westbound Right-turn; WBT = Westbound Through.

Italic = DIS of right-turning traffic that utilize the main intersection.

DISs were rounded to the nearest 10 ft.

loop left-turn; ^bdirect left-turn; ^c reverse jughandle left-turn; ^djughandle left-turn.

For QRI model validation, since no traffic operational data from field for QRI designs, only O-D volumes were available for validating the QRI models ( 11 ). The Geoffrey E. Havers (GEH) statistical test (shown in Equation 1) was employed to determine the validity of the simulation outputs. Typically, a GEH result less than 5.0 is considered as acceptable, while a recent research recommended an amended GEH threshold of 0.85 for microsimulation model validation ( 32 ). GEH results for each QRI model are listed in Table 2; results indicate that all the QRI models generated acceptable traffic volume outputs.

GEH = \sqrt{\frac{2 {(o - i)}^{2}}{o + i}}

(1)

where

$o$ = output traffic volume from the simulation model (vehicles per hour [vph]), and

$i$ = input traffic volume (vph).

Table 2.

Geoffrey E. Havers (GEH) Statistical Test Results for Quadrant Roadway Intersection (QRI) Models

Movement	Input demand (vph)	Simulation output (vph)*					GEH test result
Movement	Input demand (vph)	SQR	DQR_D	DQR_L	FQR_D	FQR_L	SQR	DQR_D	DQR_L	FQR_D	FQR_L
EBL	309	305	304	308	305	308	0.23	0.29	0.06	0.23	0.06
EBT	652	644	652	651	645	647	0.31	0.00	0.04	0.27	0.20
EBR	192	191	192	190	191	189	0.07	0.00	0.14	0.07	0.22
WBL	384	382	380	382	372	379	0.10	0.20	0.10	0.62	0.26
WBT	694	691	690	690	687	685	0.11	0.15	0.15	0.27	0.34
WBR	70	69	70	69	69	68	0.12	0.00	0.12	0.12	0.24
SBL	117	115	115	113	116	117	0.19	0.19	0.37	0.09	0.00
SBT	1420	1,414	1,412	1,403	1,407	1,407	0.16	0.21	0.45	0.35	0.35
SBR	272	273	271	271	271	270	0.06	0.06	0.06	0.06	0.12
NBL	75	73	73	74	74	73	0.23	0.23	0.12	0.12	0.23
NBT	1,134	1,106	1,125	1,129	1,132	1,128	0.84	0.27	0.15	0.06	0.18
NBR	61	57	61	62	61	60	0.52	0.00	0.13	0.00	0.13
Total	5,380	5,320	5,345	5,342	5,330	5,331	0.82	0.48	0.52	0.68	0.67

Note: DQR_D = dual quadrant intersection with direct left-turns from major street; DQR_L = dual quadrant intersection with loop left-turns from major street; EBL = Eastbound Left-turn; EBR = Eastbound Right-turn; EBT = Eastbound Through; FQR_D = full quadrant intersection with direct left-turns; FQR_L = full quadrant intersection with loop left-turns; NBL = Northbound Left-turn; NBR = Northbound Right-turn; NBT = Northbound Through; SBL = Southbound Left-turn; SBR = Southbound Right-turn; SBT = Southbound Through; SQR = single quadrant intersection; vph = vehicles per hour; WBL = Westbound Left-turn; WBR = Westbound Right-turn; WBT = Westbound Through.

The simulation outputs collected at the downstream of the intersection are generally lower than the actual traffic passing the stopbar, because at the end of the simulation there are vehicles left in the system.

Simulation Modeling Results

For planning purposes, Figure 18 presents the overall performance of the main intersection. It was found that QRI designs have considerably lower control delays than the CI design under all demand scenarios, as shown in Figure 18a. Among the five QRI designs, the DQR_D design results in the lowest average control delay at the main intersection under all demand scenarios.

Figure 18b compares the main intersection’s capacity utilization under baseline conditions. Results show that the CI design has the highest ICU, with existing traffic demands occupying 84% of the intersection capacity. In comparison, the main intersections at both DQR_D and FQR_D utilize about 60% of their intersection capacity, indicating that the main intersection has the potential to accommodate an additional 40% of through-traffic demands, particularly if the traffic signals at the secondary intersections are coordinated with the main intersection signal. The ICU for the SQR design is 0.74, meaning the SQR design can still accommodate about 26% more traffic. The ICUs for the DQR_L and FQR_L designs are both around 0.8, with the DQR_L design rerouting only two left-turn movements back to the main intersection, resulting in a slightly lower ICU (2%) than the FQR_L design.

Table 3 shows the simulated TIS from each model under various demand scenarios. For each movement, the average TIS of all vehicles that passed through both upstream and downstream sensors were presented. Moreover, a volume-weighted average TIS was employed to assess the overall performance of the entire system.

Table 3.

Movement-Based Average Time-in-System (TIS) for Various Traffic Demand Scenarios

Movement (free-flow travel time [s])^*	Average TIS (s) by movement
Movement (free-flow travel time [s])^*	CI	SQR	DQR_D	DQR_L	FQR_D	FQR_L
(a) Base demand scenario
EBL [55.5]	114.7	170.9	83.3	176.6	102.6	173.1
EBT [44.2]	105.3	70.0	69.1	68.0	71.0	69.5
EBR [54.3]	67.4	72.8	68.2	67.3	78.4	80.4
WBL [54.9]	144.5	92.3	84.0	187.9	84.7	195.7
WBT [44.2]	104.2	66.1	68.6	81.0	69.3	69.4
WBR [54.5]	72.3	60.9	67.1	63.1	78.2	77.1
SBL [55.2]	153.5	118.2	131.7	135.2	95.8	190.0
SBT [40.9]	91.1	62.6	65.6	79.8	63.6	82.0
SBR [54.6]	83.5	62.6	72.5	70.9	75.9	70.7
NBL [55.5]	148.0	129.8	136.5	138.2	104.8	181.9
NBT [40.9]	85.2	66.7	63.5	65.7	60.6	63.4
NBR [54.0]	81.7	65.6	62.2	72.4	72.3	78.2
Weight avg. TIS	98.8	75.5 (−23.6%)	71.1 (−28.0%)	89.2 (−9.7%)	71.0 (−28.1%)	90.7 (−8.2%)
(b) High demand scenario
EBL	128.4	197.6	90.8	233.5	103.7	346.5
EBT	118.9	75.8	72.4	81.3	73.2	85.2
EBR	71.2	79.3	85.6	72.8	86.0	88.9
WBL	493.6	100.3	91.5	332.7	89.1	354.7
WBT	193.5	71.6	72.8	247.7	70.2	117.8
WBR	151.2	66.3	75.7	95.1	80.9	80.1
SBL	232.6	192.6	146.5	200.8	102.3	242.3
SBT	172.6	138.3	72.2	158.6	85.9	146.2
SBR	165.7	128.7	75.7	117.0	80.6	82.2
NBL	206.8	150.1	157.3	185.1	107.3	430.7
NBT	145.8	77.5	67	98.4	66.2	94.9
NBR	146.9	70.9	67.1	91.8	75.6	77.2
Weight avg. TIS	175.5	106.4 (−39.4%)	77.0 (−56.1%)	157.0 (−10.5%)	79.6 (−54.6%)	148.2 (−15.6%)
(c) High major street left-turn movement scenario
EBL	122.2	171.9	88.6	183.7	101.4	193.9
EBT	103.3	72.5	71.1	69.7	73.5	71.1
EBR	65.9	75.3	72.5	66.3	80.8	82.8
WBL	313.5	93.4	92.4	209.9	86.9	278.8
WBT	106.9	66.8	71.1	77.5	69.4	72.8
WBR	71.5	60.3	66.7	65.5	77.0	72.1
SBL	145.8	118.5	139.6	145.2	89.5	214.5
SBT	91.2	61.5	64.0	107.5	67.4	115.4
SBR	83.0	62.4	71.7	81.7	78.6	72.2
NBL	146.2	137.2	133.6	137.2	102.4	200.6
NBT	84.8	65.3	62.6	67.6	62.7	68.8
NBR	81.1	64.6	64.6	76.4	66.4	77.1
Weight avg. TIS	112.0	76.9 (−31.3%)	72.6 (−35.2%)	101.8 (−9.1%)	73.4 (−34.5%)	111.9 (−0.1%)
(d) High major street through movement scenario
EBL	113.5	171.7	85.8	177.3	106.9	178.5
EBT	114.4	68.5	67.8	70.2	72.3	70.4
EBR	65.3	74.3	69.1	66.4	81.0	79.5
WBL	132.5	93.6	88.1	247.1	87.8	216.5
WBT	186.7	66.9	68.9	171.3	70.8	73.5
WBR	132.9	60.8	67.1	68.9	77.6	78.0
SBL	146.7	119.7	133.9	139.4	90.9	189.9
SBT	90.9	66.5	64.5	90.3	69.1	93.9
SBR	83.6	66.7	72.6	72.5	76.2	69.8
NBL	140.8	128.3	133.1	135.1	114.3	188.1
NBT	85.1	66.3	63.6	67.3	63.5	65.6
NBR	82.0	65.8	62.6	77.7	75.5	73.1
Weight avg. TIS	111.3	76.3 (−31.4%)	71.1 (−36.1%)	108.7 (−2.3%)	73.9 (−33.6%)	95.4 (−14.3%)

Italic = the absolute deviation in weighted average TIS compared with the CI design.

Note: CI = conventional intersection; DQR_D = dual quadrant intersection with direct left-turns from major street; DQR_L = dual quadrant intersection with loop left-turns from major street; EBL = Eastbound Left-turn; EBR = Eastbound Right-turn; EBT = Eastbound Through; FQR_D = full quadrant intersection with direct left-turns; FQR_L = full quadrant intersection with loop left-turns; NBL = Northbound Left-turn; NBR = Northbound Right-turn; NBT = Northbound Through; SBL = Southbound Left-turn; SBR = Southbound Right-turn; SBT = Southbound Through; SQR = single quadrant intersection; WBL = Westbound Left-turn; WBR = Westbound Right-turn; WBT = Westbound Through; weight avg. TIS = sum of movement average TIS multiples by movement demand divided by intersection total demand.

Numbers in square brackets (top-left box) are free-flow travel time by movement; a 12.8 s acceleration-deceleration delay was added to left- and right-turn movements per Highway Capacity Manual acceleration–deceleration delay approach ( 26 ).

Bold = the shortest TIS for each movement among six intersection designs.

Simulation results show that, for all tested scenarios, QRI designs outperform the CI design with regard to weighted average TIS, particularly under the high demand scenario where the maximum improvement in TIS reaches approximately 55% when using a DQR_D or FQR_D design. This is consistent with previous research finding that a QRI has a higher capacity and a lower delay than the counterpart CI. Among the five QRI designs, DQR_D design always has the shortest weighted average TIS under all demand scenarios. In general, loop left-turn designs have a substantial higher TIS than direct left-turn designs, particularly under high demand scenarios. This indicates savings in control delay may not offset the extra travel time; moreover, loop left-turn designs have to redirect the left-turn traffic back to the main intersection, which results in additional control delay to both left-turn and through movements.

When considering movement-based TIS, it was found that, under a relatively low demand level, CI design tends to benefit right-turn movement since it reduces the probability of encountering traffic signals. In comparison, a direct left-turn design benefits left-turn movements, although left-turn movements must turn left twice at two secondary intersections. Moreover, a direct left-turn design can also benefit through movements, since it reroutes or partially reroutes left- and right-turn traffic to secondary intersections, which reduces the traffic flow entering the main intersection. SQR design can generally balance the tradeoffs between control delay and extra travel time (e.g., under the baseline demand scenario, four movements have the shortest TIS, three movements have the second shortest TIS, and three movements have a TIS that is not far from the shortest TIS), and it tends to be a reasonable choice under a relatively low demand condition, particularly when left-turn demands are not high, or only one direction has a high LT demand, while, under a high demand scenario, DQR_D or FQR_D design is preferred.

Conclusions

A QRI design has long been known to reduce congestion at the main intersection relative to a CI by moving left turns to secondary intersections, thus allowing a two-phase signal at the main intersection. However, reducing congestion at the main intersection does not necessarily reduce overall travel time in the system relative to the CI system when secondary intersections are involved. Thus, when deploying a QRI, a major question that was not answered before this research is whether the delay savings at the main intersection will offset the out-of-direction travel time and additional control delay at the secondary intersections.

Based on microsimulation, this research investigated the operational performance of various QRI designs under different traffic demand scenarios. Three MOEs were employed for performance assessment: movement-based and system average TIS, main intersection control delay, and main intersection ICU. The major findings of this research include:

All QRI designs outperform the CI design with regard to volume-weighted average TIS and control delay at the main intersection, particularly under the high demand scenario.

Among the five QRI designs, the DQR_D design has the smallest weighted average TIS and main intersection control delay under all demand scenarios.

In general, loop left-turn designs have a higher weighted average TIS than direct left-turn designs, indicating that savings in control delay may not offset the extra travel time.

Under a relatively low demand level, the CI design tends to benefit the right-turn movement since it has only one signal, thus reducing the probability of encountering red indications at traffic signals.

SQR design can generally balance the tradeoffs between control delay and extra travel time, which could be a reasonable choice under relatively low demand conditions, especially when left-turn demands are not high, or when only one direction has high left turn demand.

Under a high demand scenario, a DQR_D or an FQR_D design is preferred, as it reroutes or partially reroutes left- and right-turn traffic to secondary intersections, allowing the main intersection to accommodate more through-traffic demands.

The CI design has the highest ICU. Among the tested five QRI designs, ICUs for the loop left-turn designs are approximately 20% higher than the direct left-turn designs, indicating that the direct-left option is likely a better choice than loop options.

The findings from this research are based on the geometry and traffic volumes collected at a single real-world CI. Future work should cover a variety of geometric conditions, traffic flow scenarios, and left-turn phasing treatments to develop practice-ready, volume-based guidelines for selecting QRI configurations. When field implementations of different QRIs take place, real-world data will become available, and more reliable operational performance and safety analyses should be carried out. Additionally, future work should further investigate strategies for optimizing signal coordination between system intersections based on the various O-D pairs through the system to minimize control delay and the number of stops in the entire QRI system. In addition to the proposed left-turn phasing treatments, an option is to allow left-turns only from the QRI connectors. This will allow all secondary intersections to operate a two-phase signal. Future work could further investigate whether coordination with a lead or lag left turn has more influence than the need for three phases at some secondary intersections.

Because QRIs reduce TIS and increase overall capacity, future research could also focus on their potential to support walkable mixed-use development. QRIs are sometimes faulted when secondary intersections introduce additional crossings for pedestrians. Nevertheless, if a grid system already exists in an area, existing intersections could be transformed into secondary intersections. Under such conditions, the impact of QRIs on pedestrians will be lessened. Additionally, QRIs can support higher surrounding densities than CIs, and traffic-calming designs may be able to achieve safer speeds for pedestrians without negatively affecting overall TIS relative to the baseline CI option.

Footnotes

Acknowledgements

The authors thank Professor George List of NC State University for his constructive comments on TIS and microsimulation model calibration, and Gyounghoon Chun of NC State University for helping with field data collection and extraction for base model calibration.

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: G. Yang, M. Brown, C. Cunningham; data collection: G. Yang; analysis and interpretation of results: G. Yang, C. Cunningham, M. Brown; draft manuscript preparation: G. Yang, M. Brown, C. Cunningham. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Data Accessibility Statement

Some or all data, models, or codes that support the findings of this study are available from the corresponding author on reasonable request.

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