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 1 / 22
Perimeter control What is it? 2 / 22
Perimeter control What is it? 3 / 22
Perimeter control What is new? What has changed? ? 4 / 22
NFD-based Perimeter Control A new opportunity 5 / 22
Perimeter Control What is wrong with that? ? 6 / 22
Feedback NFD-based Perimeter Control Feedback regulator � ˆ � q g ( k ) = q g ( k − 1) − K P [ TTS ( k ) − TTS ( k − 1)] + K I TTS − TTS ( k ) 7 / 22
Feedback NFD-based Perimeter Control Flow distribution q 1 q 2 q g q 6 q 3 q 4 q 5 � n i =1 q i = q g q min , i ≤ q i ≤ q max , i 8 / 22
Queue management The queue model N i ( k + 1) = N i ( k ) + T [ d i ( k ) − q i ( k )] or N i ( k + 1) = A i ( k ) − B i ( k ) q i ( k ) with A i ( k ) = N i ( k ) + Td i ( k ) and B i ( k ) = T 9 / 22
Queue management Queue balancing � 2 n � A i ( k ) − B i ( k ) q i ( k ) � min N max , i i =1 s.t.: n � q i = q g i =1 q min , i ≤ q i ≤ q max , i 10 / 22
Simulation results City center of Chania, Greece 11 / 22
Simulation results Protected network and gated links 2 3 4 1 5 8 7 6 ≈ 80 junctions — 27 with traffic lights and 165 links. 12 / 22
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 13 / 22
Simulation results Simulation and control setup 2 3 4 1 5 8 7 6 TTS = 600 veh · h/h, K P = 20 h − 1 and K I = 5 h − 1 , T = 90 s ˆ 14 / 22
Simulation results Network performance 600 500 Delay (s/km) 400 300 200 100 NPC PC PCQ Scenario 15 / 22
Simulation results Analysis of the NFDs 6000 6000 6000 5000 5000 5000 TTD (veh · km / h) TTD (veh · km / h) TTD (veh · km / h) 4000 4000 4000 3000 3000 3000 2000 2000 2000 1000 1000 1000 0 0 0 0 250 500 750 1000 1250 1500 1750 2000 0 250 500 750 1000 1250 1500 1750 2000 0 250 500 750 1000 1250 1500 1750 2000 TTS (veh · h / h) TTS (veh · h / h) TTS (veh · h / h) NPC PC PCQ 16 / 22
Simulation results Analysis of relative queues 1 . 4 1 . 4 1 . 4 1 1 1 Relative queue: N / N max Relative queue: N / N max Relative queue: N / N max 1 . 2 1 . 2 1 . 2 2 2 2 1 . 0 1 . 0 1 . 0 3 3 3 4 4 4 0 . 8 0 . 8 0 . 8 5 5 5 0 . 6 0 . 6 0 . 6 6 6 6 7 7 7 0 . 4 0 . 4 0 . 4 8 8 8 0 . 2 0 . 2 0 . 2 0 0 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 0 Time (h) Time (h) Time (h) PCQ NPC PC ◮ PC does not necessarily lead to larger queues than in the NPC case ◮ Throughput is higher with PC! 17 / 22
Simulation results Analysis of relative queues (PCQ) 1600 1200 2800 Ordered Ordered Ordered 1400 2400 1000 Actual Actual Actual 1200 2000 Flow (veh/h) 800 Flow (veh/h) Flow (veh/h) 1000 1600 600 800 1200 600 400 800 400 200 400 200 0 0 0 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 1 2 3 4 5 6 7 8 Time (h) Time (h) Gated link number All links Gated link 3 Gated link 7 18 / 22
Simulation results Analysis of delays 1200 1 1000 2 3 Delay (s/km) 800 4 5 600 6 400 7 8 200 0 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 Time (h) PCQ 19 / 22
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
Acknowledgement 21 / 22
THANK YOU! rodrigo.carlson@ufsc.br 22 / 22
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