Impact of stop-and-go waves and lane changes on discharge rate in recovery flow

Transportation Research Part B 77 (2015) 88–102

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Transportation Research Part B

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Impact of stop-and-go waves and lane changes on dischargerate in recovery flow

http://dx.doi.org/10.1016/j.trb.2015.03.0170191-2615/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +82 42 350 3634; fax: +82 42 350 3610.E-mail addresses: [email protected] (S. Oh), [email protected] (H. Yeo).

1 Tel.: +82 42 350 5674.

Simon Oh 1, Hwasoo Yeo ⇑Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Deajeon, Republic of Korea

a r t i c l e i n f o a b s t r a c t

Article history:Received 14 October 2014Received in revised form 23 March 2015Accepted 24 March 2015

Keywords:Capacity dropLane changeStop-and-go waveDischarge rateAsymmetric traffic flow theory

In an effort to uncover traffic conditions that trigger discharge rate reductions near activebottlenecks, this paper analyzed individual vehicle trajectories at a microscopic level anddocumented the findings. Based on an investigation of traffic flow involving diverse trafficsituations, a driver’s tendency to take a significant headway after passing stop-and-gowaves was identified as one of the influencing factors for discharge rate reduction.Conversely, the pattern of lane changers caused a transient increase in the discharge rateuntil the situation was relaxed after completing the lane-changing event. Although weobserved a high flow from the incoming lane changers, the events ultimately causedadverse impacts on the traffic such that the disturbances generated stop-and-go waves.Based on this observation, we regard upstream lane changes and stop-and-go waves asthe responsible factors for the decreased capacity at downstream of active bottlenecks.This empirical investigation also supports the resignation effect, the regressive effect,and the asymmetric behavioral models in differentiating acceleration and decelerationbehaviors.

� 2015 Elsevier Ltd. All rights reserved.

1. Discharge rate reduction near active bottleneck

Sudden and pronounced declines in discharge rates accompanied by the activation of bottlenecks have long beenobserved worldwide (Hall and Agyemang-Duah, 1991; Hall et al., 1992; Ringert and Urbanik, 1993; Cassidy, 1998; Chunget al., 2007) and have been the subject of traffic modeling efforts (Laval and Daganzo, 2006; Siebel et al., 2009; Leclercqet al., 2011; Srivastava and Geroliminis, 2013). Even in the absence of any physical block downstream of a bottleneck,2–16% reductions in the discharge rate are commonly observed at isolated freeway bottlenecks (Oh and Yeo, 2012). Thisphenomenon has long been a subject of interest for many transportation researchers.

One of the first studies that reported on this capacity loss was carried out by Edie and Foote (1958), who studied the out-flow from New York City’s Lincoln Tunnel. Edie and Foote observed 16% reductions in the discharge rate with the activationof a bottleneck inside the tunnel. They postulated that the capacity drop could be prevented by controlling the inflow to thetunnel. To evaluate this postulation, Edie and Foote controlled the inflow to the tunnel, and the findings from their experi-ment supported their hypothesis. Some later studies argued that the capacity drop could be an inherent result of a dis-continuity embedded in the ‘‘reverse-k’’ shape flow-density relationship (Koshi et al., 1983; Greenshields, 1935; Hall andAgyemang-Duah, 1991; Hall et al., 1992; Ringert and Urbanik, 1993; Cassidy, 1998).

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S. Oh, H. Yeo / Transportation Research Part B 77 (2015) 88–102 89

These earlier studies, however, did not fully provide a precursor state that can be monitored and signal for the capacitydrop. To understand the mechanism by which some portion of the capacity is lost, a micro-level discussion is requiredbecause the capacity drop is closely linked with other traffic phenomena such as traffic breakdowns, stop-and-go traffic,and traffic instability. Traffic breakdown refers to the transition from free flow to congestion; immediately afterward, a dropin capacity can be observed downstream of the active bottleneck. After the breakdown, stop-and-go traffic is frequentlyobserved as a repeated pattern of deceleration-acceleration inside a congestion region. It often begins around a merging loca-tion near an active bottleneck point and influences capacity drop. The traffic instability issue is also related to both trafficbreakdown and stop-and-go traffic. Capacity drop, which involves these microscopic traffic issues, is strongly related to dri-ver behavior (Saifuzzaman and Zheng, 2014).

There have been numerous studies that attempted to explain traffic phenomena related to capacity drop. To address themechanism of traffic breakdown and traffic instability, Kerner and Rehborn (1996a, 1996b) introduced the concept of‘‘spontaneous breakdown’’ caused by drivers overreacting to deceleration under unstable traffic conditions and argued thatit was one of the contributing factors of capacity drop. However, Daganzo et al. (1999) and Ahn and Cassidy (2007) con-tended that the spontaneous breakdown theory for both formation and growth of oscillation was limited to minor casesand that traffic breakdown was primarily triggered by lane-changing events. More recently, Zheng et al. (2011a) demon-strated the capabilities of wavelet transform in analyzing bottleneck traffic. By identifying the origins of oscillations througha wavelet transform on NGSIM data (in case of US 101 – uphill segment), Zheng et al. (2011b) found that approximately 34%of a traffic wave was triggered by lane changing while the remainder (66%) was generated by traffic instability. Moreover,detailed studies on driving behavior convinced that the instability can be one of the major factors inducing traffic oscillations(Chen et al., 2012a). As for the primary factor for stop-and-go wave generation, it appeared that both traffic instability andlane-changing maneuvers influenced this wave generation.

Daganzo (2002) explained traffic breakdown by using a behavior theory with two different behaviors. He sought toexplain this traffic phenomenon by assuming that drivers fall into two distinct classes—rabbits (aggressive drivers withhigher free-flow speed) and slugs (timid drivers with lower free-flow speed). Daganzo proposed that the rabbits and slugswould remain separated while the traffic was freely flowing and that the rabbits would change their lanes to the slugs’ lanewhen a queue began to form in their lane. This migration of rabbits to the slugs’ lane could trigger the onset of congestion aswell as capacity drop. Chung (2004) also reported evidence of lane changing contributing to capacity drop from differenttypes of bottlenecks. Chung found a strong link between a capacity drop and the number of vehicles in the vicinity of abottleneck. His findings indicated that although the sequence of events leading to a capacity drop may have differed amongbottlenecks, the number of vehicles in the vicinity of the bottleneck triggering the capacity drop were reproducible at eachsite. These findings were further confirmed by Cassidy and Rudjanakanoknad (2005) and Chung et al. (2007). Laval andDaganzo (2006) explained capacity drop with a hybrid model that created a void between an incoming vehicle from anadjunct lane and the leading vehicle in the existing lane. The hybrid model suggested that the void was caused by theacceleration performance limitation and maximum speed capability of the lane changer. The authors ascribed the causeof the capacity drop to this void, which was an additional headway to the normal headway. For validation, Laval et al.(2005) compared the travel times, the number of lane-changing maneuvers, and the capacity drop observed from empiricaldata with the results of a simulation based on the hybrid model. The results showed a positive relationship between thenumber of lane changes and the capacity drop and a mitigation effect of on-ramp metering on lane changes and the shoulderlane’s queue. Their study reported consistency between the simulation and the empirical data. Laval and Leclercq (2008) andLeclercq et al. (2011) subsequently adopted and extended the theory. Leclercq et al. (2011) proposed an analytical model ofthe capacity drop at merges with an extension of the Newell–Daganzo model. This model incorporated the merging mecha-nism described in the hybrid model in Laval and Daganzo (2006). The theory explains the impact of slow lane changers onthe reduction of traffic efficiency for active bottlenecks in merging areas, particularly for outer lanes.

We should also consider other explanations for the reduction in discharge rate. Newell (1962) used two distinct driverbehaviors in acceleration and deceleration that assumed that the spacing in the acceleration state was larger than that inthe deceleration state. Daganzo et al. (1999) explained transition curves by using a simple Markovian model for trafficbehavior caused by disturbances with the flow-density plane. They demonstrated the potential explanatory power of asym-metric traffic theory. As for this theory, Yeo (2008) and Yeo and Skabardonis (2009a) developed an asymmetric drivingbehavior theory consisting of five phases that considered changes in gap acceptance among drivers with respect to the pas-sage of kinematic waves. The drivers changed their gap acceptance pattern from aggressively short spacing in the decelera-tion state (D-state) to a less aggressive pattern with larger spacing in the acceleration state (A-state), as shown in Fig. 1.Furthermore, Laval and Leclercq (2010) incorporated different driver characteristics (aggressive and timid branches) andproposed a parsimonious theory that extended Newell’s car-following model to explain traffic oscillations. Through a sim-ulation study, Laval and Leclercq concluded that two different drivers’ behaviors in reaction to a deceleration wave canexplain traffic oscillations, thus explaining capacity drop from the driver’s behavioral perspective. The asymmetric behav-ioral model was enhanced by Chen et al. (2012a) capturing the non-equilibrium behavior. Using the model, the authorsrevealed the feature of hysteresis in Chen et al. (2012b). Treiber et al. (2006) empirically observed two distinct behaviorsfrom Dutch A9 and compared time gaps in two speed regimes by using single-vehicle data. Based on observations showinga larger time gap in the free-flow speed regime than in the congested regime, the authors ascribed the capacity drop to aresignation effect by providing a theoretical explanation of human aspects related to driving behavior. In addition, the drivertendency of decreased accelerations and increased time gaps after passing congested traffic (resignation effect) resulted in a

(a) Speed-Spacing plane (b) Flow-Density plane

D

Spacing, S

Speed, V

A

QC

QD

D

Density, K

Flow, Q

A

Fig. 1. Capacity drop description from the asymmetric perspective.

90 S. Oh, H. Yeo / Transportation Research Part B 77 (2015) 88–102

flow reduction at the bottleneck downstream (Treiber and Kesting, 2013). There is a theoretical connection between theresignation effect, regressive effect, and asymmetric behavioral model (Previous theories 1, PT1) in explaining capacity dropwith varying driving behaviors according to the traffic state. In congested traffic where an incessant series of kinematicwaves pass through, a driver decelerates before a stop-and-go wave and then accelerates after passing the wave to recoverspeed. In a bottleneck area, a driver’s behavior before and after a stop-and-go wave changes from an aggressive pattern withshort spacing (D-state) in the upstream area to a less aggressive pattern with large spacing (A-state) in the downstream area(Fig. 1(a)); this can be supported by the theories mentioned above. Thus, we can surmise that the flow after passing a stop-and-go wave will be low. This low flow can be assigned as one of the possible reasons for the reduction in discharge rate,resulting in a flow gap between the D-curve and the A-curve (QC–QD) in Fig. 1(b).

Based on this background, this paper conducted a microscopic analysis to investigate traffic conditions that triggerdischarge rate reductions near active bottlenecks. We estimated time headways by classifying the influencing factors on dis-charge rates into several groups (normal traffic, wave passing traffic, and lane-changing related traffic), followed by discus-sions of the impact of stop-and-go and lane-changing traffic on recovery flow (discharge rate).

2. Study site and data

2.1. NGSIM data of US 101

The study site of US 101 consisted of five freeway lanes with an auxiliary lane between the on- and off-ramps. A bottle-neck activated between Stations 717,489 and 717,488 during peak hours in the weaving section, and the traffic at Station717,488 sustained free-flow speeds of approximately 90–120 km/h (Fig. 2).

In addition to this information, Fig. 3 provides the detailed vehicle trajectories for lanes-1 and 2 extracted from video data(Next Generation SIMulation, 2006) between 07:50 and 08:00 (morning peak) on June 15th, 2005. There was a 148 m dis-tance gap between the spatial range of NGSIM data (640 m) and the Station 717,488 location (788 m), and the available tra-jectory data of our study area was ‘‘recovery flow’’ from the congested traffic of the weaving area. We observed vehicles with

0

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140

2:24 4:48 7:12 9:36 12:00 14:24

Spee

d (k

m/h

r )

Time

Vd (Station 717488)Vu (Station 717489)

Fig. 2. Speed (Vu, Vd) at US 101 (15th June, 2005).

(a) lane-1

640m

(NG

SIM

ava

ilabl

e )

Traf

fic d

irect

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m21

3m25

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Station: 717489AbsPM: 11.88


148

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788m

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ne-1

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-2la

ne-3

lane

-4la

ne-5

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Congested(D-state)

time, t

space, s

08:0007:50

100mStudy area of discharge rate: 60~80 (km/hr)

Congested area: 0~50 (km/hr)

(b) lane-2

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(NG

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1m

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Study area

lane

-1la

ne-2

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-3la

ne-4

lane

-5

Recovery(A-state)

Congested(D-state)

time, t

space, s

08:0007:50

100mStudy area of discharge rate: 60~80 (km/hr)

Congested area: 0~50 (km/hr)

Fig. 3. NGSIM trajectory data from US 101 (lane-1–2, 07:50–08:00).


average speeds of 66.8 km/h recovering from lower speeds of 34.6 km/h in the congested state as distributed in Fig. 4. Speeddifferences can exist between the VDS (Vehicle Detection System) speed and NGSIM because of (i) the spatial distance gapand (ii) the different speed measurement (Time-mean speed in VDS-speed and point speed in NGSIM-speed). In general,capacity drop is estimated at the downstream location which state is completely free-flow. Because of the spatial rangeof NGSIM (US101), the ‘‘Study area’’ is recovering area. Analyzing the recovery flow, we can infer the mechanism of reductionin discharge rate. And, this discharge rate analysis is limited to the 10 min, since the tail of the queue propagates from furtherdownstream and forms congested traffic both upstream and downstream (after approximately 08:00). A series of kinematicwaves showing both growth and dissipation generated upstream of the active bottleneck is also graphically shown in Fig. 3.

2.2. Individual lane properties

The vehicle trajectory data from the outer lanes are not included in the discharge rate analysis in Sections 4 for severalreasons. First, we can generally observe a high rate of capacity drop in the inner lanes, meaning that the capacity drop oflanes 1 and 2 is more responsible for the capacity drop of the entire freeway than the outer lanes in a multi-lane freeway(Oh and Yeo, 2012). Moreover, a correlation coefficient analysis of discharge rates using NGSIM data (US 101) between‘‘the aggregated cumulative flow (lane1 + 2 + 3 + 4 + 5)’’ and ‘‘the cumulative flow of each individual lane’’ yields values of0.6258, 0.9026, 0.4637, 0.1510, and 0.1657 for lanes-1, 2, 3, 4, and 5, respectively, thus revealing that the inner lanes havegreater influence on the entire system than the outer lanes. The low capacity drop and correlation coefficient of the outerlanes implies the presence of different traffic features in the inner lanes that can be characterized by diverse factors such

(a) Study area (b) Congested areaSpeed (km/hr)

Freq

uenc

y0

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6000

8000

Speed (km/hr)

Freq

uenc

y

0 20 40 60 80 100 120 0 20 40 60 80 100 120

050

0015

000

2500

035

000

Fig. 4. Speed distribution of individual vehicles from US 101 (lane-1–2, 07:50–08:00).


as multiple trucks, outgoing vehicles right after incoming lane-changes, and ‘‘slugs’’ (slow vehicles). This is supported by VDSand NGSIM data. Between 07:50 and 08:00, 0–1 trucks were observed in lanes 1 and 2, while trucks accounted for 10 out of406 vehicles (2.46%), 17 out of 393 vehicles (4.33%), and 13 out of 328 vehicles (3.96%) in lanes 3, 4, and 5, respectively.Higher truck ratios in the outer lanes can be one reason for the low capacity drop in these lanes because the behavioral fea-tures of trucks (such as lower acceleration capability and larger safety gaps than passenger vehicles) can lead to lower capac-ity. As for VDS speeds in the outer lanes at Station 717,488, we observed, on average, higher free-flow speeds in lanes 1 and 2(109–112 km/h for lanes 1 and 2) and relatively lower free-flow speeds (89.3–94.3 km/h in lanes 3–5) in the outer lanes dur-ing the 10-min period. Due to the heterogeneous features between the inner and the outer lanes, all lanes (lanes-1–5) arecovered in Section 3 in examining the impact of incoming lane changes on traffic flow; however, we concentrated on lanes1 and 2 in Sections 4 when covering the discharge rate analysis.

3. Impact of incoming lane change on traffic flow

A number of researchers have developed car-following models for microscopic simulations (Gipps, 1981; Kesting andTreiber, 2008). Theorists have developed driver’s behavior theory with regard to lane changes and argued for its negativeimpact on traffic, noting provocations for traffic oscillation (PT2: Daganzo et al., 1999; Mauch and Cassidy, 2002; Ahn andCassidy, 2007; Yeo and Skabardonis, 2009b; Jin, 2010; Duret et al., 2011; Zheng et al., 2011b) and the capacity drop phe-nomenon (PT3: Daganzo, 2002; Cassidy and Rudjanakanoknad, 2005; Chung et al., 2007; Laval and Daganzo, 2006; Lavalet al., 2005; Leclercq et al., 2011, 2014). And, lane changing models describing the impact of lane changes on traffic floware thoroughly reviewed by Zheng (2014). Zheng highlighted that the microscopic factors should be empirically validatedfor the advanced applicability. Because of this, a micro-approach to studying lane-changing behavior is important and isrequired to verify (i) the actual inserting gap of lane changers and (ii) the temporal impact of lane change on traffic flowand its follower for diverse situations. By introducing the measurement time T as 3, 6, and 9 s (T: the time after an incominglane change), we can estimate the gap (time and space headway) of lane changer and its follower. We investigate the innerbound lane changing cases (e.g., lane-2–1) during the 10 min across all lanes. Note that the estimation is limited to the 79lane changing cases and we exclude the rest cases due to the successive lane changing vehicles, the trucks’ lane change, andthe limited observation time (which provides trajectory less than the measurement time).

3.1. Inserting behavior of lane changer and its impact on traffic flow

For lane-changer’s inserting behavior, there are several explanations from previous studies. It was reported that vehiclesinvolved in lane change allow short gap during some period (PT4: Smith, 1985; Hidas, 2005; Laval and Leclercq, 2008). Andrecent studies explain the impact of lane changing on traffic streams with the effect of bounded acceleration (PT5: Laval andDaganzo, 2006; Laval, 2007; Leclercq et al., 2011, 2014). The observations quantitatively verifies the previous theories (PT),and remarks on the observations (R) are as follows:

R3.1: To verify this actual behavior, we first observe the headway of the lane changers. The estimation shows the adaptivebehavior of the lane changer temporarily accepting smaller gaps for practical strategy to change lanes, yielding a smallheadway of the incoming lane changer as 0.846–1.009 s on average according to T (Fig. 5). At 9 s after lane changing,the time gap between the lane changer and its leader vehicle is still short compared with the normal case.

0

1

2

3

Tim

e he

adw

ay (s

ec)

3s 6s 9sMeasurement Time

Fig. 5. Headway of incoming lane changer.

3sMeasurement Time

6s 9s

2000

4000

3000

Flow

(veh

/hr)

qLC

qnormal

qLC

qnormal

qLC

qnormal

Fig. 6. Flow of normal and incoming lane-changing traffic.

Table 1Significant difference between normal and incoming lane-changing traffic.

p-value Student’s t test H0 : lqNormal¼ lqLC

Wilcoxon’s rank-sum test H0 : Q2qNormal¼ Q2qLC

T = 3 s 0.0033 0.0074T = 6 s 0.0197 0.0629T = 9 s 0.1093 0.2839

Note that l indicates the sample mean and Q2 indicates the sample median.


R3.2: We then show different statistical features to compare normal traffic (qNormal) and incoming lane-changing traffic(qLC). The flow of normal traffic is defined as the reciprocal of the average headway of four headways from a platoon:

qNormal ¼ 1= 14

P4i¼1hNi. Similarly, the flow of incoming lane-changing traffic is defined as qLC ¼ 1= 1

4 fðP4

i¼2hNiÞ þ hLCg, wherehLC is the headway between a lane changer and its leader vehicle. Throughout the estimation, the traffic including incom-ing lane changers was observed to have a higher rate on average than normal traffic, as shown in the distribution in Fig. 6.To determine the statistical gap between the distribution of normal and incoming lane-changing groups, we conductedboth parametric and nonparametric hypothesis tests (two-sided) for each case (Table 1). The two groups of normal andlane-changing traffic are different at a 90% confidence level, excluding the 9 s case. These statistical results support theargument that the incoming lane-changing events can temporarily increase flow (in the case of 3 and 6 s).R3.3: We also can quantify the temporal impact of incoming lane changes by estimating the flow change. The flow change(%) indicates how much the flow increases due to incoming lane changing and is calculated as follows: {(qLC � qNormal)/qNormal}. On the whole the flow increases (7.78–12.11%). The decrease in flow increase from the 3 s case (12.11%) to


the 9 s case (7.78%) indirectly alludes to the short-term relaxation process from a practical inserting behavior pattern to anormal behavior pattern after a lane change.

3.2. Impact of incoming lane change on lane changer and its follower according to leader’s traffic state

From Section 3.1, we observe the flow increase by the practical behavior of incoming lane changer. To improve our under-standing in detail, it is required to investigate the impact of lane changing event on the lane changer and follower’s behavior.Recently, Zheng et al. (2013) revealed the significant effect of lane change on the immediate follower that changes driver’sbehavioral characteristics, and commented the possible applicability of regressive effect on explaining capacity drop.Moreover, in addition to PT3, researchers emphasized the need of further investigation on the effect of lane change on capac-ity drop (PT6: Zheng et al., 2013; Jin, 2013; Chen et al., 2014). This section indirectly quantifies the impact of lane change onrelevant vehicles (lane changer and its follower), and compares the impact of lane change according to the traffic state inlane changing situation.

To estimate the impact of lane changing event in various situations, we classify the traffic state (that lane changer andfollower would encounter) with the leader’s behavior (Leader in constant, deceleration, and acceleration state) postulatedas follows:

– Leader in constant state

Dsleader 6 1ðmÞ and � 5ðm=sÞ 6 Dv leader 6 þ5ðm=sÞ

– Leader in deceleration state
Dsleader > 1ðmÞ and Dv leader < �5ðm=sÞ
– Leader in acceleration state
Dsleader > 1ðmÞ and Dv leader > þ5ðm=sÞ
where Dsleader and Dv leader indicates leader’s spacing and speed difference during the T (9 s) respectively.For the 79 lane-changing cases, we compare each category that satisfies the above conditions. For example, we regard the

lane changing situation as constant if the leader vehicle keeps (i) constant spacing which yields less than 1 m of Dsleader (90thpercentile of the Dsleader distribution) and (ii) constant speed which yields less than �5m=s of Dv leader . Fig. 7 depicts the dis-tribution of spacing of lane changer and its follower according to the leader’s state, and Table 2 lists the average spacing andspeed for each category. For the initial spacing, we can notice the smallest inserting gap of lane changer in constant state(17.32 m) compared with other state (20.2–22.5 m) in spite of same initial speed (50–51.1 m/s) across the categories. Themain observations according to the traffic state are as follows:

R3.4: In the constant state, the lane changer increases his spacing to 20.6 m, and it gives us the spacing expansion rate(SER ¼ ðs9s � sinitialÞ=T) as 0.365 m/s. The follower yields 0.435 m/s of SER in the constant state. Larger SER of followerimplies the greater impact of lane change compared with the impact of lane change on lane changer as pointed out inZheng et al. (2013). Speed of lane changer shows relative constant speed, however, the follower decreases his speed(47.6–43 m/s) even though the constant traffic environment. This verifies that the lane change act as a stimulation thatdisturbs the follower’s movement.

However, from other traffic situations, we can observe different car-following behavior meaning the deceleration andacceleration states influence the impact of lane changes on traffic streams:

R3.5: The deceleration state attenuates the effect of lane changes, while the acceleration state increases the impact. Thefollower increases his gap after lane changing event from both states, however, the amount of spacing expansion isgreater in acceleration (22.3–30.3 m) than deceleration state (23.8–25.7 m). Compared with the follower’s SER in con-stant state (0.435 m/s), the deceleration state yields smaller SER (0.217 m/s) while the acceleration state yields largerSER (0.886 m/s). According to the nonparametric statistical test (Wilcoxon’s rank-sum test), the medians of SER indeceleration and acceleration are significantly different at the 95% of confidence level (p-value = 0.0174) (R3.5r). Andinterestingly, lane changer adheres his short spacing for the deceleration state, while the follower slightly increaseshis spacing (R3.5s). The largest SER (0.446 and 0.886 m/s for lane changer and follower) in the acceleration state(R3.5t) indicates the amount of behavioral change is amplified in accordance with the asymmetric behavioral modelin PT1 and can also be ascribed to the limitations in the acceleration capability in PT5.

3.3. Discussion on the impact of lane changes on normal traffic and discharge rate

As mentioned in PT6, lane change has been pointed out as an inducement factor on discharge rate reduction. Jin (2010)developed lane-changing model incorporating a lane-changing intensity variable, describing the impact of lane-changing ondense traffic such that the formation of traffic oscillations, and theoretically explained the reason of capacity drop by linking

(b) Leader in deceleration state

(c) Leader in acceleration state

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(a) Leader in constant state

Fig. 7. Box plot for spacing of lane changer and its follower.

Table 2Average spacing (s) and speed (v) of lane changer and its follower according to the leader’s state.

Average spacing,speed, and SER

Leader in constant state Leader in deceleration state Leader in acceleration state

Lane changer Follower Lane changer Follower Lane changer Follower

s (m) v (m/s) s (m) v (m/s) s (m) v (m/s) s (m) v (m/s) s (m) v (m/s) s (m) v (m/s)

Initial(T = 0) 17.32 50.0 26.0 47.6 20.2 51.0 23.8 46.5 22.5 51.1 22.3 47.2T = 3 s 18.48 49.4 27.9 47.1 20.7 47.4 27.2 46.9 24.1 52.9 27.9 48.3T = 6 s 18.58 47.5 30.7 45.7 20.1 43.1 27.7 43.8 24.9 55.6 26.3 51.2T = 9 s 20.6 50.0 29.9 43.0 18.88 41.0 25.7 40.2 26.6 59.2 30.3 54.4SER 0.365 (m/s) 0.435 (m/s) �0.1432 (m/s) 0.217 (m/s) 0.446 (m/s) 0.886 (m/s)# Samples

for each T7 21 51


with the lane-changing intensity and the critical density. And, Jin (2013) highlighted the need of extensive study on theimpact of lane-changing on discharge rate reduction. The observations adduce evidences in support of the previous explana-tions previous theories. It is observed that lane changers generally cut in with a short gap (R3.1). This estimation shows theadaptive behavior of the lane changer allowing small gaps for practical strategy. This behavior is aimed at catching up tospeed or maintaining the safety gap with the leader vehicle. Accordingly, this event temporarily increases the flow (R3.2),but the lane changer’s return to normal behavior implies a short headway that is later relaxed (R3.3 showing relaxation


process (PT7: Laval and Leclercq, 2008; Zheng et al., 2013)). The large gap of following vehicles (R3.4 and R3.5) indirectlyimplies anticipation, deceleration, and overreaction to lane-changing disruptions that might lead to the generation of trafficwaves. Specifically, speed decrease and spacing extension of the immediate follower in constant state (R3.4) can furtherinfluence the following traffic, which might also give rise to localized traffic wave generation in PT2. Furthermore, the impactof lane change on relevant vehicles on diverse traffic situations (R3.5) verifies the explanation on the effect of deceleration/acceleration on driving style (PT1) and the effect of bounded acceleration (PT5). Thus, we infer that lane changes can increasethe probability of stop-and-go wave generation by disrupting traffic and that traffic waves influence overall traffic to move toan acceleration state after a deceleration state, resulting in a capacity loss described as a gap between the two curves on theasymmetric fundamental diagram.

4. Discharge rate analysis at downstream

4.1. Traffic passing stop-and-go wave on discharge rate

It is known that stop-and-go waves force drivers to lower their speed to sustain a safety gap with the lead vehicle (PT1). Inthe congested region of the NGSIM data, vehicle speeds fell from the congested speed (an average of 34.6 km/h) to a lowerspeed (even 0 km/h). Moreover, drivers show different acceleration and deceleration rates according to the severity of thewave, and this severity should be considered as a sub-factor influencing the discharge rate. Therefore, we speculate thatthe behavior downstream would vary according to each vehicle speed at the wave. The speed in the wave is segregated intotwo groups, with the 50th and 90th percentiles from the speed distribution at drop point (Fig. 8): one in a mild wave(19.24–38.23 km/h) and the other in a severe wave (0–19.24 km/h).

To address the speed drop points, we classify the traffic passing stop-and-go waves as three types: hW_type1, hW_type2, andhW_type3. Note that we measure the time headways of discharge flow by taking headway value of the vehicle at the certainlocation (the most downstream location: 640 m) in the study area according to the definitions in references (May, 1990;Daganzo, 2008). Based on the classification, we compare the lane-change related traffic and traffic passing stop-and-gowaves with the normal traffic case (hN) by estimating the headway from the study area during the 10-min observationperiod:

� hN: The time headway in a normal traffic case that is not influenced by (i) incoming and outgoing lane-changing events or(ii) traffic waves (r in Fig. 9).� hW_type1: The time headway of traffic passing a mild wave. The vehicle speed drops to 19.24–38.23 km/h in the wave (s in

Fig. 9).� hW_type2: The time headway of traffic passing a severe wave. The vehicle speed in the wave drops to 0–19.24 km/h (t in

Fig. 9).� hW_type3: The time headway of traffic passing two different waves (u in Fig. 9).

Descriptive statistics for the normal traffic and wave passing traffic are presented in Table 3 and illustrated in Fig. 10. Theobservations are as follows:

Freq

uenc

y

0 20 40 60 80 100

050

100

150

200

90th percentile: 38.23 km/hr50th percentile: 19.24 km/hr0th percentile: 0 km/hr

Speed (km/hr)

Fig. 8. Speed distribution at the drop point of individual vehicles from US 101 (07:50–08:00) – lanes 1–2.

t

x

Wave passing trafficLane-changing related traffic

Normal traffic

Mild wave:19.24~38.23(km/hr)

Severe wave:0~19.24(km/hr)

Mild wave:19.24~38.23(km/hr)

Severe wave:0~19.24(km/hr)

Studyarea

Fig. 9. Description of classification methodology of discharge flow.

Table 3Statistical properties of discharge flow: Normal traffic and wave passing traffic.

Headway types Normal traffic Wave passing traffic

r hNs hW_type1

t hW_type2u hW_type3

(a) lane-1Average h (s) 1.71 1.88 2.68 2.22Flow, q (veh/h) 2103 1911 1343 1620Max (sec) 4.40 3.60 6.00 3.20Min (s) 1 1.20 0.60 1.60Std (s) 0.71 0.59 1.02 0.55P

time headway (s) 73.60 81.00 319.00 40.0# Samples (veh) 43 43 119 18Time percentage (%) 13.71 15.08 59.4 7.45

(b) lane-2Average h (s) 1.54 2.10 2.56 –Flow, q (veh/h) 2333 1711 1408 –Max (s) 2.80 4.80 4.80 –Min (s) 0.80 0.60 0.80 –Std (s) 0.44 0.80 1.06 –P

time headway (s) 112.63 206.20 94.60 –# Samples (veh) 73 98 37 –Time percentage (%) 21.80 39.80 18.27 –


R4.1: The wave passing traffic (hW_type1, hW_type2, hW_type3) shows a larger headway than normal traffic, which explains theflow reduction at downstream. The headway of wave passing traffic is 110–157% and 137–166% that of normal traffic inlanes 1 and 2, respectively. Results of nonparametric statistical hypothesis tests (Wilcoxon’s rank-sum test) are presentedin Table 4 to show how the groups are different. It is apparent that the headway groups were significantly different withnormal traffic, at a 95% confidence level, excluding the case of traffic passing a mild wave in Test 1 for lane-1 (p-value was0.0551).R4.2: As the severity of the traffic wave increased, it became increasingly difficult to return to normal behavior from anacceleration state. Moreover, traffic passing a severe wave (hW_type2) showed greater headway than traffic passing a mildwave (hW_type1), implying a negative relationship between the severity of the traffic wave and the discharge rate. In addi-tion, these two groups showed significantly different behavior (Test 4 in Table 4).R4.3: The average headway of vehicles passing a mild wave after a severe wave (hW_type3) in Table 3 fall between that of avehicle passing a mild wave (hW_type1) and one passing a severe wave (hW_type2); the difference is confirmed in thosegroups through Tests 5 and 6 in Table 4. Interestingly, drivers exhibit different behavior in the same conditions of meetinga mild wave (hW_type1 and hW_type3). We conjecture that consecutive traffic waves afford an educative experience to drivers,allowing them to prepare for the next potential deceleration wave by maintaining a greater spacing.

(a) lane-1 (b) lane-2

02

46

8

Tim

e he

adw

ay (s

ec)

02

46

8

Tim

e he

adw

ay (s

ec)

Fig. 10. Boxplot of headway for each type in discharge rate: Normal traffic and wave passing traffic.

Table 4Significant difference between normal and wave passing traffic.

p-value H0 : Q2hN¼Q2hW type 1 H0 : Q2hN

¼Q2hW type 2 H0 : Q2hN¼Q2hW type 3 H0 : Q2hW type1

¼Q2hW type 2 H0 : Q2hW type1¼Q2hW type 3 H0 : Q2hW type2

¼Q2hW type 3

Test 1 Test 2 Test 3 Test 4 Test 5 Test 6

lane-1 0.0551 4.427e�09 (<0.0001) 0.0004 2.011e 06 (<0.0001) 0.0279 0.0488lane-2 1.817e�07 (<0.0001) 4.92e�08 (<0.0001) – 0.0185 – –

Note that Q2 indicates the sample median.


4.2. Lane change related traffic on discharge rate

In the study area (downstream of the bottleneck), the recovery flow is directly influenced by the lane-change relatedevents (e.g., incoming/outgoing lane changers and following vehicles) and the traffic passing stop-and-go waves. As observedin Section 3, the discharge rate is expected to be momentarily increased by the incoming lane changes; however, the follow-ing traffic will contribute to a reduction in the discharge rate because of the onset of disturbance effects by the incoming lanechanges (see also Zheng et al. (2013) for the detail mechanism). To examine this explanation from study area, we estimatedthe time headway of lane-change related traffic (hinLCer, hnext to inLCer, houtLCer).

� hinLCer: The time headway between an incoming lane changer and its leader (v in Fig. 9).� hnext to inLCer: The time headway between an incoming lane changer and its follower (w in Fig. 9).� houtLCer: The time headway between leader of outgoing lane changer and its follower (x in Fig. 9).

In addition to the description of wave passing traffic, statistics for the lane-change related vehicles are provided in Table 5and Fig. 11 which indicate the following remarks:

R4.4: Analogous with the R3.1, the average headway of incoming lane changers (hinLCer) is shorter than that of normal traf-fic (hN). For both lanes 1 and 2, the average gap between the two groups is 49.1% and 64.8%, respectively, and this lanechanging behavior can be ascribed to risk-taking adaptive behavior for practical strategy (R4.4r). However, the traffic ofthe following vehicles (hnext to inLCer) shows a large headway that falls to low flow as R3.4 and R3.5. (R4.4s).R4.5: In the case of the outgoing lane change (houtLCer), a natural flow reduction is observed because the outgoing lanechangers create a void in the lane. Based on the existence of high and low flows in lane-change related traffic, we cansee that the overall effect of incoming and outgoing lane changes can cancel out each other (this is particularly relevantin lane-1, which has a similar sample size in hinLCer, hnext to inLCer, and houtLCer). Due to the numerous outgoing vehicles inlane-2, however, the traffic of followers and outgoing lane changers contributes to a reduction in the discharge rate.

4.3. Discussion on the impact of wave passing traffic on discharge rate

The capacity drop phenomenon refers to a discharge rate reduction after an active bottleneck observable downstream ofthe bottleneck. The discharge rate is essentially a recovery flow from congested traffic where many stop-and-go waves aregenerated. Aforementioned, the behavioral transition of drivers from the congested region (D-state) to the recovery phase(A-state) results in a difference of the maximum Q.

Table 5Statistical property of discharge flow: Normal traffic and Lane-change related traffic.

Headway types (lane-1) Normal traffic Lane-change related traffic

r hNv hinLCer

w hnext to inLCerx houtLCer

(a) lane-1Average h (s) 1.71 0.84 1.92 3.20Flow, q (veh/h) 2103 4286 1875 1125Max (s) 4.40 1.000 2.40 3.40Min (s) 1 0.60 1.40 2.80Std (s) 0.71 0.17 0.46 0.35P


(b) lane-2Average h (s) 1.54 1.00 2.08 3.87Flow, q (veh/h) 2333 3600 1731 930Max (s) 2.80 1.40 2.60 7.00Min (s) 0.80 0.60 1.00 1.80Std (s) 0.44 0.28 0.64 1.27P


(a) lane-1 (b) lane-2

02

46

8

Tim

e he

adw

ay (s

ec)

02

46

8

Tim

e he

adw

ay (s

ec)

Fig. 11. Boxplot of headway for each type in discharge rate: Normal traffic and Lane-change related traffic.


The discharge rate analysis with headway groups supports this explanation, as traffic passing stop-and-go waves(hW_type1, hW_type2, hW_type3) is determined to be one of the contributing factors to flow reduction downstream (R4.1). Theimpact of stop-and-go waves would vary according to the number of lanes: as the number of lanes increases, the impactof stop-and-go waves on the discharge rate reduction decreases (due to the outer lanes’ properties in Section 2.2). This pointcan explain the negative relationship between the amount of capacity drop and the number of lanes in Oh and Yeo (2012).

As for the observations from the study area (Table 3 and 5), the contribution of each flow type to the discharge rate isdifferent for lane-1 and 2: more traffic is influenced by stop-and-go waves in lane-1 than in lane-2 (81.93%(=15.08 + 59.4 + 7.45) in lane-1 and 58.07% (=39.8 + 18.27) in lane-2 (Table 3)). Therefore, in lane-1, the formation of astop-and-go wave can be recognized as the possible factor explaining the discharge rate reduction. Meanwhile, more out-going vehicles are observed from lane-2 than lane-1 (1.79% in lane-1, 17.19% in lane-2 (Table 5)) lead us to the remark 4.6:

R4.6: There were a total of 236 vehicles in lane-1 and 241 vehicles in lane-2 over approximately 9 min (8.95 min for lane-1 and 8.63 min for lane-2). By then using the flow and time percent in Table 3 and 5, the expected discharge flow for eachlane (lane-1 (QD

1) and lane-2 (QD2)) may be calculated as:

Q 1D ¼ 236 ðveh=8:95 minÞ ¼

Xðq �%Þ ¼ 2103:26 � 0:1371þ 1911:12 � 0:1508þ 1342:94 � 0:594þ 1620 � 0:0745

þ 4285:71 � 0:00782þ 1875 � 0:01788þ 1125 � 0:01788 ¼ 1582 ðveh=hÞ


Q2D ¼ 241 ðveh=8:63 minÞ ¼

Xðq �%Þ ¼ 2333:33 � 0:218þ 1710:96 � 0:398þ 1408:03 � 0:1827þ 3600 � 0:00966

þ 1730:7 � 0:0201þ 930:23 � 0:1719 ¼ 1675:5 ðveh=hÞ

This is lower than the general discharge flow (QD1 and QD

2) of a 5-lane freeway of macroscopic data (Oh and Yeo, 2012),which gave values of 2230.71 veh/h for QD

1 and 2007.11 veh/h for QD2. Two possible reasons for the lower values of QD

1

and QD2 in this case are that (i) this area was a weaving section that contained an off-ramp downstream and (ii) the

9 min rate of this section was lower than the 5 min rate estimated in the macroscopic analysis.

5. Conclusion

In this paper, we analyzed the capacity drop from a microscopic perspective. To verify the adverse impact of lane changeon traffic flow, we investigated the gap of lane changer and its follower for diverse traffic situations. Then, we found severalfactors influencing the discharge flow changes, based on an investigation of traffic flow involving diverse traffic situations.One of the influencing factors for discharge rate reduction was a driver’s tendency to take a large headway after passing stop-and-go waves. The stop-and-go wave might be caused in consequence of the traffic influenced by lane changes, and thisstatement can be inferred by the follower’s spacing expansion and speed decrease after lane changing event in diverse trafficsituations.

The main findings are as follows:

(a) Actual inserting behavior of lane changer

Headway estimation shows the adaptive incoming behavior of lane-changer temporarily allowing short gaps for the prac-tical strategy to change lane in dense traffic (R3.1), which supports PT4. Conversely, large headway of following vehicles wasobserved (R3.4).

(b) Quantification of the impact of lane change on traffic flow according to traffic state

We indirectly quantified the impact of lane change on relevant vehicles, and compared the impact depending on the traf-fic state in lane changing situation. This verifies the disturbance effect of lane change on the following traffic (R3.4).Moreover, it was shown that the deceleration and acceleration state influences the impact of lane changes on the relevantvehicles (R3.5). Followers show different SER according to traffic state, however, they clearly increase the gap regardless oftraffic state. On the other hand, lane changers adhere the short gap in constant and deceleration state except the accelerationstate. The measurement can be used to evaluate the previous theories including the regressive effect (Zheng et al., 2013),relaxation process (PT7) and asymmetric behaviors (PT1), and might further be used for prediction of the intensity of local-ized oscillations (PT2).

(c) One of the main causal factors for discharge rate reduction: Traffic passing stop-and-go waves

After passing the waves, the flow dropped, alluding to a discharge rate reduction of the active bottleneck (R4.1).Conversely, the practical inserting behavior pattern of lane changers caused a temporary increase in the discharge rate(R4.4r). Although we observed higher flow from incoming lane changers, the events ultimately caused adverse impacts traf-fic by generating traffic waves (R4.4s). Based on this observation, we regarded both lane changes and stop-and-go wavesupstream as the responsible factors for the capacity drop downstream of the active bottleneck. This empirical investigationsupports PT1; the wider headway after passing stop-and-go waves causing a flow reduction can be explained as a behavioralshift to an acceleration state that has a lower flow in asymmetric nature.

(d) Detrimental impact of severity of stop-and-go wave on the discharge rate

As the severity of wave increased, the amount of discharge rate reduction increased (R4.2). Severity of wave can increasethe amount of behavioral change, then this finding can support the theories and simulation results presented in PT1.Moreover, the consecutive wave can trigger a series of capacity drop on a macroscopic domain, as the first wave might causean anticipation to drivers to prepare subsequent disturbance (R4.3).

(e) Contribution of relevant causal factors on discharge rate reduction

The large portion of traffic influenced stop-and-go wave in discharge rate can explain discharge rate reduction. Thecontribution of traffic passing stop-and-go wave in discharge rate was estimated as 81.93% and 58.07% in lane-1 and 2respectively, outperforming the contribution of lane change related traffic on discharge rate (R4.5 and R4.6).

The results presented in this paper can contribute to the development of strategies for maintaining higher flows for free-way operations by providing the critical conditions for preventing a capacity drop. To extend the applicability of this study,


an advanced methodology (e.g., multivariate algorithm, time–frequency–transformation) for the identification of trafficwaves should be developed. Future work should also include the development of methodological models based on theempirical results (e.g., extending the asymmetric models on capacity drop). To provide statistical significance for preliminaryarguments (i.e., the relaxation process as a stimulus to traffic wave generation in Section 3, the negative relationshipbetween the severity of traffic waves and discharge flow and the impact of consecutive traffic waves on driving behaviorin Section 4) and discover other unrevealed features, a large-scale data analysis is required.

Acknowledgements

This research was supported by the MSIP (Ministry of Science, ICT and Future Planning), South Korea, under the ITRC(Information Technology Research Center) support program (NIPA-2014-H0301-14-1006) supervised by the NIPA(National IT Industry Promotion Agency).

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Impact of stop-and-go waves and lane changes on discharge rate in recovery flow

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