Stream Variables Volume (V), flow rate (q) and headway (h) Speed (u) Density (k), Concentration and Spacing (s)
Volume, flow rate and headway Volume - the total number of vehicles that pass over a given point and section of a lane or roadway during a given time interval Flow Rate - the equivalent hourly rate at which vehicles pass over a given point or section of a lane or roadway during a given interval of less than 1 hour, usually 15 minutes Headway - the time between successive vehicles as they pass a point on a lane or roadway, measured from the same point on each vehicle (e.g., front bumper, rear axle, tec.)
Volume, flow rate and headway Volume Daily volume – Planning purpose Hourly volume – design and operational analysis purpose Peak-hour volume - The single hour of the day that has the highest hourly volume. It is the traffic volume within this hour that is of greatest interest to traffic engineers in design or operational analysis.
Volume, flow rate and headway Estimated directional peak hour volume DDHV = AADT K D DDHV-Directional Design Hour Volume (vph) AADT - Average Annual Daily Traffic (vpd) K - The proportion of daily traffic occurring during the peak-hour. (decimal) D - The proportion of peak-hour traffic traveling in the peak direction (decimal)
Volume, flow rate and headway Subhourly Volumes and Rates of Flow A facility may have capacity adequate to serve the peak-our demand, but short-term peaks of flow within the peak hour may exceed capacity, thereby creating a breakdown.
Volume, flow rate and headway Peak Hour Factor (PHF) For analysis purposed, in Highway Capacity manual, 15 minute interview is used. HV – Hourly Volume V 15 – Maximum 15 minute volume within the hour
Volume, flow rate and headway Peak Hour Factor (PHF) Example: HV= 3000 vehicles V 15 = 1000 vehicles PHF = 3000/(4*1000) = 0.75 NOTE: - 0.25 PHF 1.00, normal between 0.70 and 0.98 - Lower PHF indicates a greater degree of variation in flow during the peak-hour.
Volume, flow rate and headway Relationship between headway (h) and flow (q):
Speed v - speed (mph or fps) d - distance traversed (mi or ft) t - time to traverse distance d (hr or sec)
Speed Time mean speed and space mean speed: Time Mean Speed (TMS) is defined as the average speed of all vehicles passing a point on a highway over some specified time period. Point A TMS = (alternative way)
Speed Time mean speed and space mean speed: Space Mean Speed (SMS) is defined as the average speed of all vehicles occupying a given section of a highway over some specified time period. D SMS = (alternative way)
Speed Relationship between TMS and SMS: Time Mean Speed (spot speed) is a point measure, while Space Mean Speed is a measure relating to a length of highway or lane. (Proved by Wardrop in 1952)
Average Travel Speed and Average Running Speed : Travel time (t t ) is defined as the total time to traverse a given highway segment. Running time (t r ) is defined as the total time during which the vehicle is in motion while traversing a given highway segment. Average Travel Speed = Average Running Speed = D B
Speed Operating Speed and Percentile Speed : Operating Speed is defined as the maximum safe speed at which a vehicle can be conducted in a given traffic stream, without exceeding the design speed of the highway segment. A Percentile Speed is a speed below which the stated percent of vehicles in the traffic stream travel. The 85 th percentile speed is often used as a measure of the maximum reasonable speed for the traffic stream. The 15 th percentile speed may be used as a measure of the minimum reasonable speed for the traffic stream.
Density, concentration & spacing Density or concentration (k) is defined as the number of vehicles occupying a given length of highway or lane (vpm) or (vpmpl). Spacing (s) is defined as the distance between successive vehicles in a traffic stream, measured from the same point on each vehicle (e.g., front bumper, rear axle, tec.) Spacing 1 mile *average spacing
Density, concentration & spacing u - space mean speed (mph) q - flow rate (vph)
Time Space t1t1 Spacing 1 t2t2 Spacing 2 Headway 1 Headway 2 x1x1 x2x2 Time-distance diagram of flow
Highways: Uninterrupted Flow Background Level of Service Freeway Base Conditions Freeway Capacity and Level of Service Freeway Congestions Quantification Capacity Restrictions
Background Only for “Basic freeway segment”: outside the area of influence of: Freeway weaving areas Freeway ramp junctions Level of service based on average passenger car speed vs flow rate curve (u-q) with thresholds defined by concentration (k) – range from LOS A (free flow) to LOS F (unstable flow)
Level of Service (LOS) A – free flow; 480 ft min spacing (k<11 pc/mi/ln) B – reasonably free flow; 290 ft min spacing (k<18 pc/mi/ln) C – nearly free flow speed; maneuvers limited; reduced comfort; 200 ft min spacing (k<26 pc/mi/ln) D – reduced speeds; limited freedom to maneuver; potential for queuing; 150 ft min spacing (k<35 pc/mi/ln) E – at capacity; unstable flow; 120 ft min spacing (k<45 pc/mi/ln) F – extensive queuing behind breakdown points
Freeway base conditions 12-ft minimum lane width 6-ft minimum right side lateral clearance between the edge of the travel lane and the nearest object that influences driving behavior 2-ft minimum lateral clearance from left-side median All passenger-car traffic composition Five or more lanes per direction (urban freeways only) Access spacing of 2 mi or greater Level terrain (grades no greater than 2%) Driver population consisting mostly of regular users of the facility (commuters)
Volume and flow rate Volume - the total number of vehicles that pass over a given point and section of a lane or roadway during a given time interval Flow Rate - the equivalent hourly rate at which vehicles pass over a given point or section of a lane or roadway during a given interval of less than 1 hour, usually 15 minutes
Peak Hour Factor Criterion for LOS based on equivalent hourly flow rate for peak 15 minute period Convert full hour demand volume by using peak hour factor (PHF): v = V/PHF v is equivalent hourly flow rate for peak 15 minutes V = full-hour volume (vph) Peak Hour Factor (PHF): PHF = V (4 * peak 15 minute volume)
Example of a PHF question PeriodVolume (vph) 7:00 - 7:15100 7:15 - 7:30120 7:30 - 7:45130 7:45 - 8:00125 8:00 - 8:15135 8:15 - 8:30140 8:30 - 8: 45125 8:45 - 9:00115 When is the peak hour? What is the peak hour volume? What is the PHF?
Solution of the PHF question Period Volume (vph) Accumulated Volume (vph) 7:00 - 7:15100 7:15 - 7:30120 7:30 - 7:45130 7:45 - 8:00125475 8:00 - 8:15140515 8:15 - 8:30135530Largest 8:30 - 8: 45125525 8:45 - 9:00115515 The peak hour is from 7:30 AM to 8:30 AM The peak hour volume is 530 vph The PHF = 530 / (4*140) = 0.946
Example 4.5: LOS Estimation An extended urban freeway segment with largely level terrain has three 11 ft wide lanes per direction, a 3-ft lateral clearance, and about one interchange per mile. It has an observed volume of 3080 veh/h with corresponding PHF=0.88 and 154 trucks and buses, and no recreational vehicles. An all-commuter motorist composition may be assumed. Estimate the LOS for this set of conditions.