Capacity drop: A relation between the speed in congestion and the queue discharge rate

Delft University of Technology

Capacity drop: A relation between the speed in congestion and the queue discharge rate

Yuan, K; Knoop, VL; Hoogendoorn, SP Publication date

2015

Document Version Final published version Citation (APA)

Yuan, K., Knoop, VL., & Hoogendoorn, SP. (2015). Capacity drop: A relation between the speed in

congestion and the queue discharge rate. Poster session presented at Transportation Research Board 94th annual meeting, Washington, United States.

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Delft University of Technology

Transport & Planning

China Scholarship Council

中国国家留学基金管理委员会 中国国家留学基金管理委员会 中国国家留学基金管理委员会 中国国家留学基金管理委员会（（（（CSC）））） Kai Yuan Victor L. Knoop Serge P. Hoogendoorn

Capacity Drop: A Relation Between The Speed In

Congestion and The Queue Discharge Rate

Abstract

It has been empirically observed for years that the queue discharge rate is lower than the pre-queue capacity. This is called the capacity drop. The magnitude of capacity drop varies over a wide range depending on the local traffic conditions. However, up to now it is unknown what determines the capacity drop value. In fact, there is still no thorough empirical analysis revealing a reliable relation between the congestion level and the capacity drop. This paper tries to fill in the gap by revealing the relation between the vehicle speed in congestion and the queue discharge rate through empirical analysis. The queue discharge rate is shown to increase considerably with increasing speed in the congestion. This finding indicates a promising speed-control scheme for increasing queue discharge rates.

•

Lane-drop bottleneck

•

On-ramp bottleneck

• Two freeways (A4 & A12) in the Netherlands;

• Lane-drop & On-ramp bottlenecks

• 1 min aggregated loop data

• 6 days of observations (3 days for each site)

Project: there is plenty of room in the other lane

• Analyze a traffic scenario: a bottleneck gets active immediately after a stop-and-go wave passes

• Apply shock wave analysis to identify traffic situations

• Apply slanted cumulative counts to calculate queue discharge rates

• Speed in stop-and-go wave is the average of all the lowest speed in downstream locations when wave passes

• Speed in standing queue is the average of speed at location close to congestion front

• Analyses data in different weather and freeways to see whether it is necessary to do situation-specific validation

Shock Wave Analysis

Methodology

a) Fundamental diagram b) x—t plot

Freeway A4

Freeway A12

Study Sites

• Around 500m between every two detect locations

• At least 3.5km homogeneous freeway section in the downstream of the bottleneck

• Two sunny days and one rainy day (March 18, 2011) of observations on freeway A12

• Three sunny days of observations on Freeway A4

c) Fundamental diagram d) x—t plot

Flow increases Observation location Flow increases Observation location

Delft University of Technology

Transport & Planning

China Scholarship Council

中国国家留学基金管理委员会 中国国家留学基金管理委员会 中国国家留学基金管理委员会

中国国家留学基金管理委员会（（（（CSC））））

Conclusions

As the speed in congestion

decreases, the outflow decreases

substantially. In this study, the range of speed in congestion is broad

enough, from 6 km/h to 60 km/h.

The flow at three-lane section ranges from 5220 veh/h to 6840 veh/h. The quantitative relation requires

calibration because discharge rates are greatly influenced by local traffic situations, such as weather and

proposition of trucks. The finding can provide fundamental theory for

promising control strategies. Kai Yuan, Msc

TRAIL Research School Delft University of Technology

Transport & Planning k.yuan@tudelft.nl Transportation Research Board

94th Annual Meeting, January 11-15, 2015 Paper nr. 15-4064 0 20 40 60 80 4000 4500 5000 5500 6000 6500 7000 7500 Speed in congestion (km/h)

Queue discharge rate (veh/h)

relation

Empirical data in A4 Empirical data in A12

Rainy day (8.8mm, A12) Linear fitting discharge 29 congestion 5000 Q = ⋅ v + 16:00 17:00 18:00 34 36 38 40 42 44 46 0 20 40 60 80 100 120 12 km 10 km 8 km 6 km 4 km 2 km 0 km 16:00 17:00 18:00 19:00 120 100 80 60 40 20 0 Speed (km/h)

17:00

17:30

18:00

18:30

0 km

0.5 km

1 km

1.2 km

2 km

2.5 km

3 km

3.5 km

0

50

100

A4, May 28, 2009 A12, March 24, 2011

• The bottleneck got activated immediately after a stop-and-go wave passes by • The downstream traffic states of

congestion are free flow

A4, May 28, 2009 A12, March 24, 2011

• Observe the traffic flow at the location furthest downstream

• Traffic remains in free flow state after the

passing of a stop-and-go wave

• Flow increases if the outflow of the

stand-ing queue reaches the downstream point

• Shock wave theory predicts this

Data

Observations

Relation between speed in congestion and queue discharge rates

• A linear equation can fit the relation between the speed in congestion and the queue discharge rate very well

• When the speed in congestion is high enough, the observed queue discharge rates in this study can be much higher than three-lane pre-queue capacity (6300 veh/h) on freeways with a higher percentage of trucks (15%)