[PPT] - Queuing under perimeter control: analysis and control strategy PowerPoint Presentation

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Queuing under perimeter control: analysis and control strategy

Mehdi Keyvan-Ekbatani, Rodrigo C. Carlson, Victor L. Knoop Serge P. Hoogendoorn and Markos Papageorgiou 10 de novembro de 2016

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SLIDE 2

Perimeter control

What is it?

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SLIDE 3

Perimeter control

What is it?

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Perimeter control

What is new? What has changed?

?

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NFD-based Perimeter Control

A new opportunity

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Perimeter Control

What is wrong with that?

?

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Feedback NFD-based Perimeter Control

Feedback regulator

qg(k) = qg(k − 1) − KP [TTS(k) − TTS(k − 1)] + KI

ˆ

TTS − TTS(k)

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Feedback NFD-based Perimeter Control

Flow distribution

qg

q1 q2 q3 q4q5 q6

n

i=1 qi = qg

qmin,i ≤ qi ≤ qmax,i

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SLIDE 9

Queue management

The queue model

Ni(k + 1) = Ni(k) + T[di(k) − qi(k)]

r

Ni(k + 1) = Ai(k) − Bi(k)qi(k) with Ai(k) = Ni(k) + Tdi(k) and Bi(k) = T

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SLIDE 10

Queue management

Queue balancing

min

n

i=1
Ai(k) − Bi(k)qi(k)

Nmax,i

2

s.t.:

n

i=1

qi = qg qmin,i ≤ qi ≤ qmax,i

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SLIDE 11

Simulation results

City center of Chania, Greece

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SLIDE 12

Simulation results

Protected network and gated links

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≈ 80 junctions — 27 with traffic lights and 165 links.

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SLIDE 13

Simulation results

Scenarios

NPC - no-perimeter-control Fixed-time traffic control PC - perimeter control without queue balancing Feedback perimeter traffic flow control with the flow distribution based on links’ saturation flows PCQ - perimeter control with queue balancing Feedback perimeter traffic flow control with the flow distribution from the solution of the relative queue balancing problem

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SLIDE 14

Simulation results

Simulation and control setup

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ˆ TTS = 600 veh·h/h, KP = 20 h−1 and KI = 5 h−1, T = 90 s

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SLIDE 15

Simulation results

Network performance Delay (s/km) Scenario PCQ PC NPC 100 200 300 400 500 600

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Simulation results

Analysis of the NFDs

TTD (veh·km/h) TTS (veh·h/h) 250 500 750 1000 1250 1500 1750 2000 1000 2000 3000 4000 5000 6000

NPC

TTD (veh·km/h) TTS (veh·h/h) 250 500 750 1000 1250 1500 1750 2000 1000 2000 3000 4000 5000 6000

PC

TTD (veh·km/h) TTS (veh·h/h) 250 500 750 1000 1250 1500 1750 2000 1000 2000 3000 4000 5000 6000

PCQ

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Simulation results

Analysis of relative queues

8 7 6 5 4 3 2 1 Relative queue: N/Nmax Time (h) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

NPC

8 7 6 5 4 3 2 1 Relative queue: N/Nmax Time (h) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

PC

8 7 6 5 4 3 2 1 Relative queue: N/Nmax Time (h) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

PCQ

◮ PC does not necessarily lead to larger queues than in the NPC case ◮ Throughput is higher with PC!

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Simulation results

Analysis of relative queues (PCQ)

Actual Ordered Flow (veh/h) Gated link number 1 2 3 4 5 6 7 8 200 400 600 800 1000 1200 1400 1600

All links

Actual Ordered Flow (veh/h) Time (h) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 200 400 600 800 1000 1200

Gated link 3

Actual Ordered Flow (veh/h) Time (h) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 400 800 1200 1600 2000 2400 2800

Gated link 7

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Simulation results

Analysis of delays 8 7 6 5 4 3 2 1 Delay (s/km) Time (h) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 200 400 600 800 1000 1200

PCQ

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Final remarks

◮ Higher throughput with PC and PCQ: smaller queues than with NPC

◮ Less interference at upstream junctions

◮ Unbalanced queues caused by localized congestion

◮ Avoid localized congestion within the PN by the use of traffic control ◮ PCQ + adaptive traffic control!

◮ Unbalanced delays (fairness)

◮ Delay balancing 20 / 22

SLIDE 21

Acknowledgement

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SLIDE 22

THANK YOU!

rodrigo.carlson@ufsc.br

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