Design and Evaluation of Actuated Four-Phase Signal Control

Transportation Engineering

pISSN 1226-7988, eISSN 1976-3808

www.springer.com/12205

TECHNICAL NOTE

Design and Evaluation of Actuated Four-Phase Signal Control

at Diamond Interchanges

Sangsoo Lee*, Choulki Lee**, and Do-Gyeong Kim***

Received October 4, 2012/Revised March 29, 2013/Accepted June 26, 2013

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Abstract

The operation of actuated four-phase control at diamond interchanges was investigated for moderate to heavy traffic volumes andfor a wide range of ramp spacing through a CORSIM simulation combined with hardware-in-the-loop simulation technology. Threemeasures of effectiveness were selected for performance comparison with three-phase control: cycle length, average delay, and totalstops. A new detection layout and phasing design for four-phase control were also developed. In addition, the theoretical relationshipbetween the overlap phase duration and U-turn volume was formulated and validated. Results showed that four-phase controlproduced longer cycle length and higher delay than three-phase control for most traffic conditions simulated. However, four-phasecontrol produced fewer stops than three-phase control. The mathematical formulation result showed that the operational efficiency ofactuated four-phase control could be reduced as the percentage of U-turn volume increased. This characteristic was validated for alltraffic volume scenarios through a simulation study, and the average delay reduction was about 5.3%. It was also shown that theperformance of actuated four-phase control could be significantly improved by applying the new detection layout and phasing designintroduced.

Keywords: actuated, four-phase control, diamond interchange, CORSIM, signal phasing

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1. Introduction

The interchange is a system of interconnecting roadways thatprovides for the movement of traffic between two or morehighways on different levels (AASHTO, 2004). Diamondinterchanges are the most commonly used interchange types inU.S. urban areas, and most diamond interchanges are operatedwith a coordinated actuated signal control to provide goodprogression along the arterial streets (Tian et al., 2007). Themajority of the interchanges are operated with an actuated signalcontrol mode, and only a few interchanges are in a pre-timedsignal control mode (Messer and Bonneson, 1997).

Numerous signal phasing strategies can be used to controltraffic demand at diamond interchanges. However, two signalphasing strategies have been recommended in terms ofoperational efficiency and safety: four-phase with two-overlapcontrol (hereafter referred to as four-phase control), and three-phase control (Venglar et al., 1998). In the three-phase control,three critical movements are controlled by a predeterminedphase sequence, whereas the four-phase control has four criticalmovements including two fixed overlap intervals.

The pre-timed signal control at diamond interchanges has beenwidely studied in terms of operational performance, signaloptimization, and design alternatives (Messer et al., 1977; Tianet al., 2004; Tian et al., 2007). Although the majority of theinterchanges adopted an actuated signal control, only a fewstudies reported the performance of actuated signal control atdiamond interchanges, especially for four-phase control.

The actuated signal control is more complex than pre-timedsignal control because many signal control variables are notpredetermined. Consequently, the operational performance isgreatly influenced by many factors including detection layout,signal control mode, and controller settings. Surprisingly, thereality for actuated four-phase control is that only two previousstudies can be found on the subject of detection layout. Though adetection layout had a big impact on the effectiveness of actuatedfour-phase control, but a few design selections were reportedfrom the previous studies, and no follow-up research has beenconducted. From an operational perspective, the performance ofactuated four-phase control at diamond interchanges has notbeen tested for a range of ramp spacing commonly found inurban areas. This is partly because there is no proper tool toemulate actuated four-phase signal control at diamond interchanges.In addition the existence of U-turn volume has a certain impact

*Professor, Division of Environmental, Civil and Transportation Engineering, Ajou University, Suwon 442-749, Korea (E-mail: sslee@ajou.ac.kr)

**Associate Professor, Division of Environmental, Civil and Transportation Engineering, Ajou University, Suwon 442-749, Korea (Corresponding Author,E-mail: cklee@ ajou.ac.kr)

***Member, Associate Professor, Dept. of Transportation Engineering, University of Seoul, Seoul 130-743, Korea (E-mail: dokkang@uos.ac.kr)

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Design and Evaluation of Actuated Four-Phase Signal Control at Diamond Interchanges

on actuated four-phase control at diamond interchanges, but littleis known about this characteristic because no paper has not yetbeen addressed this subject.

This study investigated the operational performance ofactuated four-phase control for a wide range of ramp spacingcommonly found in urban areas. To emulate actuated four-phasesignal control, the CORSIM simulation combined with hardware-in-the-loop simulation technology was selected. The performanceof actuated four-phase control was compared with three-phasecontrol to provide relative efficiency of two frequently usedphasing strategies. Three measures of effectiveness were selectedfor this comparison: cycle length, average delay, and total stops.This study also developed a new detection layout for actuatedfour-phase signal control as well as an innovative signal phasingdesign. In addition, this study tried to formulate a mathematicalrelationship between the overlap phase duration and the U-turnvolume for four-phase signal control. This relationship wasvalidated through a simulation study, and its implications onfour-phase signal control were provided.

In the following sections, a literature review on signal controlat diamond interchanges is presented. Then the elements ofexperimental design for this study are described including signalcontroller settings, signal phasing design, and detection layout.Next, study results are discussed as well as statistical test results.Conclusions are presented in the final section.

2. Literature Review

For pre-timed signal control, Messer et al. (1977) firstlyinvestigated the selection of optimal signal phasing at diamondinterchanges extensively under a pre-timed control mode. Theyconcluded that there was no unique phasing strategy to give thebest performance for all traffic patterns and conditions, but thefour-phase control was a good strategy for the conditions studiedin general. Bonneson and Lee (2002) developed an interchangeevaluation technique to facilitate interchange-type selection orplanning level evaluation of interchange performance. Therelationship between interchange sum-of-critical-flow ratios wasdefined, which is a unique parameter that could combine thegiven traffic and geometric conditions. It was shown that tighturban diamond interchange produced less delay than the Single-point Urban Interchange (SPUI).

Tian et al. (2004) developed a mesoscopic simulation modelthat evaluated the integrated diamond interchange and rampmetering system over multiple cycles. Both three-phase andfour-phase signal operations were evaluated to validate theintegrated diamond interchange analysis methodology, but onlypre-timed signal operation was adopted. It was concluded thatthe four-phase control favored the frontage road approach,whereas the three-phase control favored arterial left-turn movementfor oversaturated ramp conditions.

A special control strategy was developed and tested fordiamond interchanges having unique traffic flow and geometriccharacteristics (Tian et al., 2007). The control strategy was

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designed to give maximum progression to the closely spacedpaired signals when the diamond interchange had tight spacingand one-way cross streets. From the simulation study results, theproposed strategy reduced the number of stops, but not theoverall delay. Abdel and Tian (2009) investigated a modifiedfour-phase signal control scheme to deal with heavy right turnvolume at one of the off-ramps at diamond interchanges. Themodified phasing scheme was compared with seven differentphasing schemes in a pre-timed signal control mode using aSimTraffic microscopic simulation model. These studies addressedparticular signal phasing strategies that could be applied tospecific traffic and geometric conditions.

Xu et al. (2010) investigated the potential difference of controldelay from pre-timed signal control between an isolatedintersection and diamond interchange using a simulation study.Then, an analytical delay model was proposed to account for theeffects of initial queue spillback at signalized diamond interchanges.It was concluded that the proposed model produced better controldelay estimates than the existing model based on simulationstudy results.

For actuated signal control, a field study was conducted toevaluate the actuated signal control at diamond interchanges(Messer and Chang, 1987). Two detection schemes and twosignal phasing strategies were evaluated for a range of rampspacing between 82 m(270-ft) and 143 m(470-ft). The resultsshowed that four-phase control produced longer cycle lengthsand higher delay than three-phase control. The study alsodeveloped several regression models for estimating cycle lengthsfor different geometric and signal control conditions.

Lum and Lee (1992) evaluated the performance of actuatedsignal operation at diamond interchanges through a simulationstudy. The study compared three-phase and four-phase signaloperation with one short ramp spacing and limited actuatedsignal settings resulting in cycle lengths of 60-120 seconds. Thestudy recommended the use of four-phase control over three-phase control in general. However, the study did not cover theentire range of traffic and geometric conditions, so the generalizationof the performance was limited.

Actuated signal control was evaluated at diamond interchangescombined with advanced features built in a modern signalcontroller (Koonce et al., 1999; Engelbrecht and Barnes, 2003).A hardware-in-the loop simulation was used to emulate theadvanced features built in a traffic signal controller, such asconditional service mode and separate intersection control mode.Lee and Messer (2003) compared the performance of two three-phase phasing strategies for actuated signal control at diamondinterchanges. In this study, the effect of different barrier locationson signal performance was evaluated using a hardware-in-the-loop simulation technology. Lee et al. (2006) assessed theperformance of actuated signal control at diamond interchangesunder oversaturated traffic conditions using a hardware-in-the-loop simulation. The study characterized the performance ofactuated signal control under congested traffic conditions, and itproduced several regression models for performance estimation

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purpose.

As shown above, most prior studies focused on comparing theperformance of pre-timed signal control at diamond interchanges.Only a few studies have investigated the performance of actuatedsignal control at diamond interchanges for narrow ramp spacing,especially for four-phase control. In addition, there was notechnical paper to deal with detector layout of four-phase controlexcept one reference from Messer and Chang (1987). Thisresearch effort was initiated to characterize the performance ofactuated four-phase control for wide range of ramp spacing byapplying a new detection layout and an innovative phasingdesign.

3. Experimental Design

A diamond interchange has eight conflicting movements: fourexternal inbound movements and four internal outboundmovements. The movements and identifying numbers definedare listed in Fig. 1. The four-phase control sequentially serves thetraffic demand of each external movement in a clockwisemanner. The two overlap phases are available between thearterial movement and frontage road movement due to thephysical separation of the two ramp terminals (i.e., A(φ1 + φ2)and B(φ5 + φ6)). In three-phase lag-lag control, traffic demandsof both frontage roads are served simultaneously. Then, twoarterial through movements and two internal left-turn movementsare served. The ring structures of the two phasing strategies areillustrated in Fig. 2.

To emulate actuated four-phase signal control at diamondinterchanges, the microscopic CORSIM simulation combinedwith hardware-in-the-loop simulation technology developed byTexas Transportation Institute (TTI) was used (Engelbrecht andBarnes, 2003). A 15-minute simulation period was used throughoutthe study. To examine the variability of the study, the simulation

Fig. 1. Diamond Interchange Movements

Fig. 2. Ring Structures of Two Phasing Strategies

was repeated five times with different sets of random seednumbers for each volume scenario. Since the hardware-in-the-loop simulation runs in real-time, the number of replications waslimited to five. Several experimental elements are summarized in

Fig. 3. Study Interchange Configuration and Detection Layout

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Design and Evaluation of Actuated Four-Phase Signal Control at Diamond Interchanges

Table 1. Four Traffic Volume Scenarios

Approach Volume (vph)

1245

A: Heavy EB & SB2201150*1300*430B: Heavy EB & WB360950*750320C: Heavy NB & SB3805501100*310D: Heavy All Throughs3101000*1200*360Note: Xc: Critical volume-to-capacity ratio of the interchange. *: Heavy movements.

Scenario

64501000*800950*

83007001000*1050*

Xc

0.820.770.770.83

the following section.

3.1 Study Diamond Interchange and Detector Design

The geometry of the study interchange is illustrated in Fig. 3.Arterial approaches have two through lanes in each direction.Two frontage roads have a three-lane approach. A single-laneleft-turn bay is provided to serve left-turn traffic. The arrowindicates the assigned traffic movements of each lane. A widerange of ramp spacing was considered in this study: 79 m(260-ft), 122 m(400-ft), 183 m(600-ft), and 244 m(800-ft). This rangecould encompass most signalized diamond interchanges found inurban areas. The free-flow speed was fixed at 48 kph (30 mph)for all approaches.

Regarding a detection layout, a previous study concluded thatthe multi-point detection was more effective than single-pointdetection in four-phase control (Messer and Chang, 1987). Inaddition, an optimal detection layout was investigated using asimulation study (Prabhakar et al., 1994). The study recommendedplacing two detectors on frontage roads with 30 m(100-ft)setback distance of advance detector for four-phase control. Theuser guide for PASSER III also recommended a detection layoutwith two detectors on each frontage road (Venglar et al., 1998).The detection layout developed for four-phase control in thisstudy is also shown in Fig. 3.

It was a multi-point detection system on two frontage roads,and the setback distance should be carefully selected to obtainefficient operation of four-phase control. A procedure determiningthe setback distance of an advance detector was also developed.It was a function of the overlap phase duration and dischargeheadway, and a detailed discussion of this procedure waspresented in the later section.

A 30 m(100-ft) long inductive loop detector was placed in twoarterial approaches and interior left-turn bays based on therecommendation of the user guide for PASSER III when theapproaching speed was 48 kph (30 mph). A six-foot longinductive detector was placed on the interior through lanes, andthe detectors were operated with non-locking memory. Thefrontage roads had two six-foot long inductive loop detectors oneach lane. The advance detector was operated as a vehicledetector when the green phase was terminated. When a call wasdetected during the green phase, the green phase was held untilthe detector gapped out. Once the gap-out occurred, the detectorwas turned off until the green phase was terminated. All loopdetectors were operated under the presence mode.

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3.2 Traffic Volume Scenarios

Four traffic volume scenarios encompassing a wide range oftraffic patterns were developed for this study. The traffic volumescenarios are listed in Table 1.

The traffic demand from the left-side intersection was heavyfor scenario A. Heavy arterial and frontage road traffic demandswere given in scenarios B and C, respectively. All approacheshad heavy movements in scenario D. The maximum left-turnvolume at the ramp terminal was set to 400 vph, but the rangewas 300-350 vph for most cases except for the right-sideintersection of scenario A. It was assumed that U-turn trafficfrom the frontage roads was 20 percent of the left-turn volume.The right-turn volume from the four external approaches wasassumed to be 20 percent of the through volume.

3.3 Signal Controller Settings

The controller settings include minimum green time andmaximum green time. Currently, no optimum guideline existsthat produces minimum delay operation for actuated four-phasecontrol at diamond interchanges. Bonneson and Lee (2000)studied the optimum actuated controller settings for diamondinterchanges. However, the scope of the study was limited tobasic three-phase control, which had two barriers before andafter the frontage road phases. The user guide for PASSER IIIrecommends that the phase split times obtained from PASSERIII can be used as a maximum green time, provided that thevolume-to-capacity ratios are not greater than 0.85.

The maximum green time was decided using optimum phasesplits from PASSER III optimization outputs with an inflationfactor of 1.8. Five-second minimum green time was assigned toeach phase. No recall mode was used and yellow and redclearance intervals were 3.5 and 1.5 seconds, respectively, for allphases.

3.4 Design and Implementation of Signal Phasing

A NEMA-based Eagle EPAC 300 diamond interchange controllerprovides several built-in phasing strategies through the diamondcontrol mode (Eagle Traffic Control Systems, 1996). Both three-phase and four-phase control can also be implemented using astandard eight-phase NEMA ring structure under “Full FunctionEPAC Mode”. A similar concept was described in a paper byNelson et al. (2000). In this study, the ring structure of four-phasecontrol shown in Fig. 2 was implemented under “Full FunctionEPAC Mode” as shown in Fig. 4.

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Fig. 4. Four-Phase Signal Phasing Implemented

It was a lead-lead phasing sequence, and the traffic demand onfrontage roads was served by two phases: a phase with a variableduration (i.e., φ4) and a phase with a fixed duration (i.e., φ3). Thefixed duration was typically set as the travel time for the rampspacing. This phasing feature provided the so-called an internal“phase overlap”.

Minimum values of yellow and red clearance times for a phasedefined in the EPAC 300 controller are 3.0 and 0 seconds,respectively. Although two frontage phases (i.e., φ3 and φ4) arethe same phase, the controller recognizes them as two differentphases. Therefore, independent controller settings are requiredfor the two phases. This fact must be considered during the splitcalculation of maximum green time between the two frontagephases. From Fig. 4, the following relationships are required forfrontage road phases to provide good progression on the arterialmovements.

Y4+g3+(Y+AR)3≤(Y+AR)5+l1,6+TTBY8+g7+(Y+AR)7≤(Y+AR)1+l1,2+TTAwhere:

AR=gi=l1,i=TTA(B)=

Red clearance interval, sec

Effective green time for movement i, secStart-up lost time for movement i, sec

Travel time for a ramp spacing in A (or B) direction,sec

Yi= Yellow interval for movement i, sec

(1)

frontage roads. The advance detector and stopline detector areassigned to the variable phase (i.e., φ4 or φ8) and the fixed phase,respectively. If the setback distance is less than optimal setbackdistance, the cycle length increases because the variable phase isalways called. Consequently, the portion of fixed phase is likelyto become waste time unless heavy traffic demand exists. Whenthe setback distance is greater than the optimal setback distance,the probability of early gap-out is greatly increased. Therefore,there is an optimal setback distance of the advance detector infour-phase control.

In this paper, a simple method using the relation between theoverlap phase duration and discharge headway was developed todetermine the optimal setback distance. The proper value ofdischarge headway at diamond interchanges might be estimatedusing a model developed by Messer and Bonneson (1997). Then,the optimal setback distance of advance detector could beestimated as follows:(OLi–l1,i)Lv

------------------+LbDs=-----------hdiswhere:

Ds=

hdis=Lb=Lv=OLi =

Optimal setback distance of advance detector, ftDischarge headway, secBuffer length (e.g., 40 ft), ft

Average length of queued vehicle (e.g., 25 ft), ft Overlap phase duration for the frontage road phasei, sec

(2)

Using Eq. (2), the setback distances for four ramp spacingswere calculated as 36 m(120-ft), 45 m(150-ft), 58 m(190-ft), and67 m(220-ft), respectively, and they were applied for four-phasecontrol in this study.

4.2 Average Cycle Length

The average cycle lengths derived for actuated control for eachvolume scenario are shown in Fig. 5. Several observations can bemade from the results. Firstly, the average cycle lengths of four-phase operation generally increased as ramp spacing increased,except for scenario D. This trend was because the duration of thefixed phase increased in four-phase control as the ramp spacingincreased. Three-phase operation showed a relatively stabletrend in cycle lengths for the range of ramp spacings. Four-phasecontrol produced longer cycle lengths than three-phase control ingeneral. In addition, the difference in cycle length between thetwo phasing strategies increased as ramp spacing increased.Secondly, four-phase operation produced similar cycle lengthto three-phase operation when traffic demand from all approacheswas heavy. This was because the capacity gain increased as theramp spacing increased in four-phase control. The maximumdifference of cycle lengths was identified as 16 percent at 79m(260-ft) spacing for scenario D. With short ramp spacing, thecapacity gain of four-phase control was limited since theclosely spaced interchange provided only short overlap phaseduration.

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The maximum green time for the fixed phase (i.e., φ3) wasdetermined by applying Eq. (1). Then, the remaining maximumgreen time was assigned to the maximum green time of thevariable phase (i.e., φ4).

4. Study Results

A simulation study was completed with four different rampspacings for all traffic volume scenarios. Three measures ofeffectiveness were selected for performance comparison with three-phase control: cycle length, average delay, and total stops. Theaverage delay was a volume-weighted average delay computedfrom all movements as recommended in HCM (TRB, 2010). Thetotal stops were obtained by adding stops from all approaches. 4.1 Setback Distance of the Advance Detector

As shown in Fig. 3, two loop detectors were placed on the

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Design and Evaluation of Actuated Four-Phase Signal Control at Diamond Interchanges

Fig. 5. Average Cycle Lengths Simulated: (a) Scenario A, (b) Scenario B, (c) Scenario C, (d) Scenario D

Thirdly, it was observed that the cycle length of four-phasecontrol was positively sensitive to the left-turn volume of arterialapproaches. This fact was deduced from the ring structure shown inFig. 4. The left-turn volume of arterial approaches is served byinterior left-turn phases (i.e., φ1 or φ5). The length of the left-turnphase is affected by the amount of left-turning vehicles. In thissituation, the cycle lengths should increase even if there is no trafficdemand from the frontage roads, because a simultaneous gap-out isrequired for the frontage road phase and interior left-turn phase. Fourthly, the results showed that cycle lengths of four-phasecontrol were almost identical at long ramp spacing regardless oftraffic patterns. The cycle lengths from 183 m(600-ft) to 244m(800-ft) ramp spacings were about 80 seconds and 90 seconds,respectively, for all volume scenarios. Thus, it can be inferredthat actuated four-phase control at diamond interchanges withlong ramp spacing in urban areas has no difficulty to serve trafficdemand unless it is quite oversaturated.

4.3 Average Delay

The results of average delay are shown in Fig. 6. Three-phasecontrol produced less delay than four-phase control in general.This trend was also consistent with the observations from thecycle length results. However, four-phase control providedcomparable delay performance when the traffic demand of thetwo ramp terminals was significantly unbalanced. For scenarioA, the two external movements (i.e., φ6 and φ8) of the right-sideintersection had low traffic volume. Therefore, the ring structureof four-phase control became similar to three-phase control,except for phase order and the existence of fixed phase, as shown

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in Fig. 2. The delay difference was reduced compared to othervolume scenarios.

Four-phase control produced large delay for scenario D at shortspacing because of growing queues on all external approaches.With three-phase control, the probability of queue spillback wasvery high at this short ramp spacing. Since no queue spillbackwas observed in this study, three-phase control produced lessdelay. Therefore, four-phase control is still a good alternative forthese geometric and traffic conditions, since the performance ofthree-phase control will be diminished significantly if queuespillback occurs.

The delay difference between the two phasing strategies generallyincreased as the ramp spacing became wider. This trend wasprobably related to the cycle length results. From the delaymodel in HCM, the uniform delay increases as the cycle lengthincreases. The uniform delay component is a major contributorto control delay when the level of traffic volume is belowcapacity. Therefore, the trends of delay performance in Fig. 6were similar to those of cycle lengths in Fig. 5.

Efficient use of the overlap phase had a great influence on thedelay performance of four-phase control. If the traffic demandfrom frontage roads is heavy enough to prevent demand starvationduring overlap phase duration, then the performance of four-phase control will be greatly improved. This fact was supportedby the delay trends found in scenarios C and D in Fig. 6. Therelative performance of four-phase control was greatly improvedin scenario C compared to scenario B. In scenario C, four-phasecontrol produced less delay than three-phase control for up to122 m(400-ft) spacing.

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Sangsoo Lee, Choulki Lee, and Do-Gyeong Kim

Fig. 6. Average Delay Simulated: (a) Scenario A, (b) Scenario B, (c) Scenario C, (d) Scenario D

Fig. 7. Total Stops Simulated: (a) Scenario A, (b) Scenario B, (c) Scenario C, (d) Scenario D

4.4 Total Stops

The results of total stops are shown in Fig. 7. It was clear thatfour-phase control produced fewer stops than three-phase controlfor most scenarios. Considering the principle of four-phasecontrol strategy, these trends were quite reasonable. From Fig. 5and Fig. 7, the average cycle length and total stops results showed a

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Design and Evaluation of Actuated Four-Phase Signal Control at Diamond Interchanges

similar performance trends in three-phase control. However, theperformance trends between average cycle lengths and total stopswere not consistent for all volume scenarios in four-phase control.For example, the cycle lengths of volume scenario D in Fig. 5showed parabola-shape pattern, but the total stops in Fig. 7 hadcontinuously decreasing-shape pattern. From these analysis results,the total stops were largely affected by the progression of traffic flowin four-phase control. Therefore, many factors will be considered toimprove the performance of total stops in four-phase control such asramp spacing, level of traffic volume, and travel speed.

In general, three-phase control produced fewer stops at wideramp spacing simulated in this study. Therefore, the stopdifference between three-phase and four-phase control wasreduced as the ramp spacing increased. The maximum stopdifference between the two phasing strategies was observed at79m(260-ft) ramp spacing for all scenarios.

4.5 Statistical Test

A statistical test was performed to identify the factors affectingthe performance of actuated signal operation. Three experimentalfactors were identified: phasing strategy (P), ramp spacing (S),and traffic pattern (T). A three-factor analysis of variance (ANOVA)with multiple observations was conducted using StatisticalAnalysis Software (SAS Institute, 2009).

The statistical analysis was completed using the simulationoutputs of delay and stops. ANOVA test results of delay arelisted in Table 2. All three factors were statistically significantat a significance level of five percent, and all interactionsbetween factors were found to be statistically significant. Inaddition, ANOVA test results for stops also showed that allthree factors were statistically significant at a significance levelof five percent (p-value=.0001). Therefore, it was concludedthat the performance of actuated signal control could beaffected by the three factors: phasing strategy, traffic pattern,and ramp spacing. It was also identified that traffic pattern andsignal phasing had higher impact than ramp spacing from bothdelay and stop test results.

4.6Formulation of Relationship between Overlap Phase

and U-turn Volume

The four-phase control is characterized by the existence of the

Table 2. ANOVA Test Result for Average Delay

Sum of

Mean SquareF Value

Squares

P1162.760162.76068.67T3949.810316.603133.57P*T382.36727.45511.58S354.98718.3297.73P*S322.3237.4413.14T*S9234.78526.08711.01P*T*S9166.19818.4667.79Error64151.7002.370Note: P: Phasing strategy, T: Traffic pattern, S: Ramp spacingSource

DF

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two unique overlap phases. A mathematical relationship betweenoverlap phase duration and U-turn volume is formulated forfour-phase control. To simplify the formulation process, it isassumed that reasonably good traffic platoons will be maintainedfor a given traffic flow. The generalized condition for overlapphase duration will be characterized and discussed.

From the fundamental relationship of signal phase time infour-phase control, the following relationships should exist: G2+G4+G6+G8=C+ΦG1+G5where

Gi=Phase time for movement i, sec, i = 1, 2, 4, 5, 6, 8C= Cycle length, sec

Φ= total overlap duration (from both directions), sec

Assuming there is no U-turn volume from frontage roads, thefollowing statement holds based on the given assumptions: G1=G6

and

G5=G2

(4)

=C–Φ

(exterior)(interior)

(3)

Then, a necessary condition for overlap phase duration can bestated from Eq. (3) and Eq. (4) as:

G4+G8=2Φ (5)Therefore, the total duration of overlap phases should be equalto half of the total duration of the frontage road phases if there isno U-turn volume. Assuming that U-turn volume is proportionalto the total volume of the frontage roads, the following relationshipexists:

G1=G6+αG8G5=G2+αG4where:

α=fraction of U-turn volume to total volume of frontage

roads, 0 ≤ a ≤ 1.

The necessary conditions for overlap phase duration can bederived from Eq. (3) and Eq. (6) as: G2+G4+G6+G8 =C+ΦG2+αG4+G6+αG8=C–Φ

Finally, Eq. (7) is reduced to the following equation: Φ=(G4+G8)

(1–)----------α-----2

(6)

(7)

, 0≤α≤1(8)

p-value.0001.0001.0001.0002.0313.0001.0001

In Eq. (8), the total overlap phase duration can be described asa function of the percentage of U-turn volume and phaseduration of the frontage roads. The condition illustrated in Eq.(5) can be easily recovered from Eq. (8). From Eq. (8), the lengthof overlap phase duration can be reduced when there is U-turndemand volume from frontage roads. That is, the operationalefficiency of actuated four-phase control will be reduced as thepercentage of U-turn volume increases.

A simulation test was performed to validate the relationshipderived in Eq. (8). For this, the traffic volume scenario in Table 1

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Table 3. Performance Difference by U-Turn Volume(Unit: Percent)VolumeCycle Average Total ScenarioLengthDelayaStopsA-2.4-3.1-1.4B-2.1-6.9-4.3

Four-Phase

C-6.1-1.2-1.1D-3.4-10.0-1.0

aNote: : Percent difference of average delay (i.e., [100(d0%−d20%)/d20%])Control Type

was modified to generate new traffic volume scenario. In thenew scenario, U-turn volume was reduced to zero and it wasadded to the left-turn traffic volume, making the total volume inTable 1 unchanged. Using this new volume scenario, a simulationstudy was performed for the same experimental condition at244m(800-ft) ramp spacing. Then, the percentage difference ofperformance was calculated, and the results are listed in Table 3. As deduced from Eq. (8), the performance of actuated four-phase control was improved for all scenarios when the U-turnvolume was reduced. In terms of delay, large improvement wasfound for the scenarios B and D. Especially large delaydifference was found between scenarios B and C in spite of thesame critical volume-to-capacity ratio of the interchange (Xc). Infour-phase signal control, the U-turn volume is served by theinternal left-turn phase, as shown in Fig. 4. In this situation, theU-turn volume will experience more frequent cycle failureswhen the traffic volume in arterial is high and the traffic volumein frontage road is low. Therefore, the delay of scenario B wasmore sensitive than scenario C. The average value of delayimprovement was about 5.3%.

4.7 Performance Comparison with a Previous Study

The results of this paper were compared with previous study toevaluate the relative performance improvement gained from thenew detection layout and phasing design for actuated four-phasecontrol. One previous study result (Messer and Chang, 1987)was a good reference for this purpose. As mentioned before, afield study was conducted to evaluate actuated three-phase andfour-phase control, and several regression models for estimatingcycle lengths were developed. Therefore a comparison was madeusing the cycle length outputs from both studies.

The regression models in the reference covered for the rangeof total interchange critical volume from 1100 to 2600. Since thetotal interchange critical volumes in Table 1 lied in this range,cycle lengths were interpolated for all traffic volume scenarios inTable 1 by applying the regression models (i.e., study 1). Then,they were compared with the cycle length results listed in Fig. 5(i.e., study 2). Since the experimental conditions of the twostudies were not identical, a direct comparison of the cyclelengths might lead to biased interpretations of the performance.However, the difference of cycle length between three-phase andfour-phase control for each study could give unbiased interpretations,because they were obtained under the same experimentalconditions. Therefore the cycle length difference (i.e., C4φ-C3φ)was calculated from both studies, and used for performance

Fig. 8. Comparison of Cycle Length Difference for Two Studies

comparison.

The results are illustrated in Fig. 8. It can be seen that theperformance trends of the two studies were almost identical, butthe magnitude of cycle length difference was greatly reduced forall traffic volume scenarios. On average, the cycle lengthdifference was 23.8 seconds for study 1 and 6.0 seconds forstudy 2. From Fig. 8, it was concluded that the performance ofactuated four-phase control was significantly improved byapplying the new detection layout and phasing design.

5. Conclusions

The performance of actuated four-phase control was investigatedfor moderate to heavy traffic volumes and for a wide range oframp spacing. To improve the operational efficiency of four-phase signal control, a new detection layout and signal phasingdesign were developed. In addition, a mathematical relationshipbetween the overlap phase duration and U-turn volume wasformulated for four-phase signal control. From the analysisresults, the following conclusions were drawn.

The cycle lengths of four-phase control generally increased asramp spacing increased. This was because the duration of fixedphase was positively correlated with the length of ramp spacing.It was found that the cycle lengths of the four-phase operationwere positively sensitive to the left-turn volume of arterialapproach. In general, four-phase control produced longer cyclelengths than three-phase control.

The average delay of four-phase control was greatly affectedby the availability of overlap phase duration or efficient use ofoverlap phase duration. In general, four-phase control producedgreater delay than three-phase control. However, four-phasecontrol could produce better or comparable delay performancewhen the traffic demand of the two ramp terminals wassignificantly unbalanced, or the traffic demand of frontage roadswas heavy enough to prevent demand starvation during overlapphase duration.

In terms of stops, four-phase control produced fewer stops thanthree-phase control for most scenarios. The performance trendsbetween average cycle lengths and total stops were not

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Design and Evaluation of Actuated Four-Phase Signal Control at Diamond Interchanges

consistent for all volume scenarios in four-phase control becausetotal stops were largely affected by the progression of trafficflow. Therefore, many factors will be considered to reduce totalstops in four-phase control such as ramp spacing, level of trafficvolume, and travel speed.

From the mathematical formulation, it was shown that theoperational efficiency of actuated four-phase control could bereduced as the percentage of U-turn volume increased. Thischaracteristic was validated for all traffic volume patternsthrough a simulation study, and the average delay reduction wasabout 5.3%. It was also shown that the performance of actuatedfour-phase control could be significantly improved by applyingthe new detection layout and phasing design. This result alsoimplies that there is more efficient detection layout andexperimental design for actuated four-phase control.

It is deemed necessary to conduct additional research toinvestigate the performance difference among various detectionlayouts for actuated four-phase control. It is also necessary toperform the sensitivity analysis on the different combinations offraction values to quantify the effect of U-turn volume existence.

Acknowledgements

This work was supported by the National Research Foundationof Korea grant funded by the Korea government (MEST) (NRF-2010-0029450).

Notations

The following symbols are used in this paper:

AR=Red clearance interval, secC=Cycle length, sec

Ds=Optimal setback distance of advance detector, ftgi=Effective green time for movement i, sec

Gi=Phase time for movement i, sec, i = 1, 2, 4, 5, 6, 8hdis=Discharge headway, sec

l1,i=start-up lost time for movement i, secLb=Buffer length, ft

Lv=Average length of queued vehicle, ft

OLi=Overlap phase duration for the frontage road phase

i, sec

TTA(B)=Travel time for a ramp spacing in A (or B) direction,

sec

Y=Yellow interval, sec

α=Fraction of U-turn volume to total volume of frontage

roads, 0 ≤ α ≤ 1

φi=Signal phase for a movement i

Φ= Total overlap duration (from both directions), sec

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