Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center for Future Urban Transport

References 1.Daganzo, C.F. (1996) “The nature of freeway gridlock and how to prevent it" in Transportation and Traffic Theory, Proc. 13th Int. Symp. Trans. Traffic Theory (J.B. Lesort, ed) pp , Pergamon Elsevier, Tarrytown, N.Y. 2.Daganzo, C.F. (2007) “Urban gridlock: macroscopic modeling and mitigation approaches” Transportation Research B 41, 49-62; “corrigendum” Transportation Research B 41, Daganzo, C.F. and Geroliminis, N. (2007) “How to predict the macroscopic fundamental diagram of urban traffic” Working paper, Volvo Center of Excellence on Future Urban Transport, Univ. of California, Berkeley, CA (submitted). 4.Geroliminis N., Daganzo C.F. (2007a) “Macroscopic modeling of traffic in cities” 86th Annual Meeting Transportation Research Board, Washington D.C. 5.Geroliminis, N. and Daganzo, C.F. (2007b) “Existence of urban-scale macroscopic fundamental diagrams: some experimental findings” Working paper, Volvo Center of Excellence on Future Urban Transport, Univ. of California, Berkeley, CA (submitted). 2

T x L Definitions Flow, q = VKT / TL (veh/hr) Density, k= VHT / TL (veh/km) Speed, v= VKT / VHT (km/hr) C-rate, f= Completions / TL (veh/km-hr) (Daganzo, 1996)

Link Laws k0k0 Optimum Density Density, kf max Max completion rate C-rate, f Flow, q q max, Capacity d, kms per completion (Daganzo, 2007) (q, k, v) related by FD q / f = d Optimal density (Capacity; Max C-rate)

Composition: J Identical Links LjLj L j = L d j = d k j, q j, v j, f j (Daganzo, 2007)

Network of identical links: Jensen’s inequality: q ≤ Q(k) If v i ~ constant: q~Q(k) f~Q(k) / d Density q ( k i, q i ) d f Flow C-rate (Daganzo, 2007) Conjectures Real Networks: An MFD exists Trip completions / Network flow ~ Constant

Outflow Vehicle Accumulation San Francisco Simulation: No Control (Geroliminis & Daganzo, 2007a)

Fixed sensors 500 ultrasonic detectors –Occupancy and Counts per 5min Mobile sensors 140 taxis with GPS –Time and position –Other relevant data (stops, hazard lights, blinkers etc) Geometric data Road maps (detector locations, link lengths, intersection control, etc.) (Dec data) 10 km 2 (Geroliminis & Daganzo, 2007b) Real World Experiment: Site Description

Real World Experiment: The Demand Occupancy by time-of-dayFlow by time-of-day (Geroliminis & Daganzo, 2007b)

Real World Experiment: The Detectors o i (%) q i (dimensionless)

Real World Experiment: The Detectors (Geroliminis & Daganzo, 2007b)

Real World Experiment: Taxis Conjecture: Passenger carrying taxis use the same parts of the network as cars (Geroliminis & Daganzo, 2007b) Then:

Filters to determine full vs. empty taxis A stop is a passenger move, if: hazard lights are ON or parking brake is used or left blinker is ON and taxi stops > 45 sec or speed 60sec A trip is valid if: trip duration > 5 min and length > 1.5 km and trip distance < 2 × “Euclidean distance” (Geroliminis & Daganzo, 2007b)

Illustration of Filter Results (Geroliminis & Daganzo, 2007b)

Illustration of Filter Results (Cont.) (Geroliminis & Daganzo, 2007b)

Real World Experiment: Taxis Conjecture: Passenger carrying taxis use the same parts of the network as cars (Geroliminis & Daganzo, 2007b) Then:

Real World Experiment: Results (Geroliminis & Daganzo, 2007b)

Aggregate Dynamics Given : inflow q in Output: e = G(n) e = G(n) q in n (Daganzo, 2007) n

Time Trips Ended No Control With Control Time Trips Ended Restrict vehicles from entering Finding: Effect of Control (Geroliminis & Daganzo, 2007a)

Ring Road Simulation: No Control (Daganzo, 1996)

Ring Road Simulation: Control (Daganzo, 1996)

Ongoing Work: San Francisco (Daganzo & Geroliminis, 2007)