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Traffic Flow Characteristics. Recap . Spacing. Recap . Clearance. Recap . # vehicles/Distance. Density. Recap…. Speed ( v or u ) – ft/sec or mph Flow ( q ) – veh/sec or vph Density ( k ) – veh/ft or vpm Spacing ( s ) – ft/veh Headway ( h ) – sec/veh Clearance ( c ) – ft/veh
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Recap... # vehicles/Distance Density
Recap… • Speed (v or u) – ft/sec or mph • Flow (q) – veh/sec or vph • Density (k) – veh/ft or vpm • Spacing (s) – ft/veh • Headway (h) – sec/veh • Clearance (c) – ft/veh • Gap (g) – sec/veh
Fundamental Relationships • q = k v (veh/hr) = (veh/mi) (mi/hr) • h = 1 /q (sec/veh) = 1 / (veh/hr) (3600) • s = 1 /k (ft/veh) = 1 / (veh/mi) (5280)
Two Categories of Traffic Flow (Models) 1) Uninterrupted flow • Vehicle drivers are interactive with other drivers only, without interference from other control devices (e.g. Traffic signals, crosswalk, pedestrians, etc. ) to affect the flow • freeways, multilane highways, 2 lane highways
Two Categories of Traffic Flow (Models) 2) Interrupted Flow • Vehicle drivers are subjected to many other control devices, such as traffic controls, stop signs, pedestrians, etc.signalized streets, unsignalized streets with stop signs, arterials, transits, pedestrian walkways, and bicycle paths
Characteristics of Uninterrupted Flow q= n/t=n/t*[(1/l)/(1/l)]= k*v q= flow in vehicles per unit time n= number of vehicles passing some designated roadway during time t t= duration of time interval l= length of roadway used for travel time measurement of vehicles v= space mean speed (mph) k= density (veh/mi)
General Speed-Density Relationship S V Free normal flow forced flow Traffic Jam Q Capacity K Density at Capacity Jam Density
General Speed-Density Relationship K V Traffic Jam Free forced flow normal flow Q Capacity K Density at Capacity Jam Density
General Speed-Density Relationship Q V Capacity Free Traffic Jam V K Density at Capacity Jam Density
Capacity • The maximum flow for the facility • When area under speed vs. density curve is at maximum • Reached when the product of increasing density (k) and decreasing speed (v) result in the maximum of vehicles passing a certain point.
Congested (unstable) Flow • High density-low speed • No available gaps for entering vehicles • Any vehicles that do enter create a disturbance not easily dissipated
Uncongested (stable) Flow • Low density-high speed - Plenty of gaps for merging traffic
Greenshield’s Model • Assume a linear relationship between v and k: vf Low Density = High Speed High Density = Low Speed kj
vf v0 Greenshield’s Model Q Max flow qmax K Kj K0
Greenshield’s Model V Vf 1/k0=s0 V0 Q Qmax Max flow
q, v, k – Greenshield’s Free flow (measured) v Jam Density (measured) k
q, v, k – Greenshield’s Free flow (measured) Max Flow v v Jam Density (measured) q k
q, v, k – Greenshield’s Max Flow q Density at Capacity k Free flow (measured) Max Flow v v Jam Density (measured) q k
Capacity Same flow! q, v, k – Greenshield’s • How do you asses quality of service? • What region possesses better quality of service?
Example I-5 over the ship canal bridge has 4 lanes in each direction. The northbound capacity is 8200 veh/hr/lane and the free-flow speed is 65 mph. What is the maximum flow rate, maximum density, jam density? If a one-hour vehicle count in the northbound direction for the outside lane gives 7034 vehicles in a non-congested condition, what is the estimated space mean speed of these 7034 vehicles?