ACULTY OF NGINEERING AND TECHNOLOGY
PHILADELPHIA UNIVERSITYFACULTY OF ENGINEERINGDEPARTMENTOFANDTECHNOLOGYCIVIL ENGINEERING.Transportation and Traffic EngineeringFundamental parameters of traffic flow2nd semester 2018/2019Eng. Amany Assouli
OVERVIEW22/14/2019The traffic stream itself is having some parameterson which the characteristics can be predicted. The traffic stream includes a combination of driverand vehicle behavior. The driver or human behavior being non-uniform,traffic stream is also non-uniform in nature. They will vary both by location and timecorresponding to the changes in the humanbehavior. The traffic engineer, for the purpose of planning anddesign, assumes that these changes are within certainranges which can be predicted.
2/14/2019TRAFFIC STREAM PARAMETERS:Macroscopic parameters:- Speed u (mile per hour, mph; km/hr) .- Flow q (vehicle per hour, v/h) .- Density k (vehicle per mile, v/m; v/km) Microscopicparameters:- Time Headway h (sec/ veh) .- Spacing (Space headway) s (km/veh) , (ft/ veh)3
SPEEDdu twhere,u :is the speed of the vehicled: is distance traveled in m in time t seconds.42/14/2019Speed (u) is the distance traveled by a vehicle duringa unit of time.It can be expressed in miles per hour (mi/h),kilometers per hour (km/h), or feet per second (ft/sec).Mathematically speed or velocity is given as:
TIME-SPACE DIAGRAMtime-space diagram is a graph that describesthe relationship between the location of vehiclesin a traffic stream and the time as the vehiclesprogress along the highway.2/14/2019 The5
SPEED2/14/2019Time mean speed: point measure of speed. Space mean speed: measure relating to length ofroadway. Running Speed: the total time during which vehicleis in motion while traveling a roadway segment(Stopping time is excluded). Operating speed: maximum safe speed a vehicle canbe driven without exceeding design speed. Posted speed speed limit . Average travel time: total time to traverse aroadway. 85th percentile speed: speed at which 85 % ofvehicles are traveling at or below.6
TIME MEAN SPEED2/14/2019 Timemean speed (spot speed) : is thearithmetic mean of the speeds of vehiclespassing a point on a highway during aninterval of time.(using radar or very shortsection)Where:ut: Time mean speed.ui: Spot speed of the vehicle (i).n: Number of spot speeds.7
SPACE MEAN SPEED is2/14/2019the harmonic mean of the speeds of vehiclespassing a point on a highway during an interval oftime. It is obtained by dividing the total distancetraveled by two or more vehicles on a section ofhighway by the total time required by thesevehicles to travel that distance. This is the speed that is involved in flow The time mean speed is equaldensity relationships.or higher than the space meanspeed.8
EXAMPLE 12/14/2019Assume a road section of 88 feet long . Fourcars are timed through the section. Theirtimes were: 1 , 1 , 2 , and 1.5 sec.What is the Time mean speed (TMS) ?What is the space mean speed (SMS )?9
SOLUTION 12/14/2019TMS:(88/1) (88/1) (88/2) (88/1.5) or individualspeeds of 60 mph, 60 mph, 30 mph, and 45mphTMS (60 60 30 40)/4 47.5 mphSMS:add up the travel times and divide by thenumber of vehicles. Then divide the length ofthe section by average timeSMS (4*88) / (1 1 2 1.5) 43.63 mphNote: SMS is always less than or equal to TMS10
TRAVEL TIME AND SPACE MEAN SPEED/EXAMPLE 2Find the average Travel Time and SpaceMean Speed?.2/14/2019Four cars traveling a section road of 300 m.The travel times for the road section areshown in the following table:11
TRAVEL TIME AND SPACE MEAN SPEED2/14/2019Solution 2:Average travel time ( 35 25 30 27)/4 29.25 sec.The average space mean speed 300 / 29.25 10.25 m/sec 36.9 km/hr.12
FLOW (Q)or volume, which is defined as the numberof vehicles (n) that pass a point on a highway or agiven lane or direction of a highway during aspecific time interval (T) . Units2/14/2019 Flowtypically (vehicles/hour)n: number of vehicles passing a point in the roadway inT sec.q: the equivalent hourly flow.13
DENSITY2/14/2019Density (concentration) is defined as the numberof vehicles occupying a given length of highwayor lane and is generally expressed as vehiclesper km/mile. One can photograph a length ofroad (l), count the number of vehicles() inone lane of the road at that point of time andderive the density k as:nrk l14
TIME HEADWAY (HEADWAY)2/14/2019 Timeheadway (h): is the difference between thetime the front of a vehicle arrives at a point on thehighway and the time the front of the next vehiclearrives at that same point. Timeheadway is usually expressed in seconds Themicroscopic character related to volume isthe time headway or simply headway.15
If2/14/2019all headways h in time period, t , overwhich flow has been measured are addednthen,t hii 1But the flow is defined as the number of vehiclesn measured in time interval t, that is:q nn hi 11 hi3,600Flow rate veh / hr headway s / veh 16
(SPACING (SPACE HEADWAYSk nn si 12/14/2019Space headway (S) is the distance between the frontof a vehicle and the front of the following vehicleand is usually expressed in feet1 si17
EXAMPLE 3/HEADWAY AND FLOW2/14/2019The following headway values were measured:2, 3, 5, 6, 8, 1, 3, 5 sec.Compute average headway and flow ?.Solution 3:Number of headways 8 .Average ḧ (2 3 5 6 8 1 3 5)/8 4.125 sec.Flow 1/ḧ 1/ 4.125 0.242 v/sec 873 v/h.18
DETERMINING FLOW, DENSITY, TIME MEAN SPEED, ANDSPACE MEAN SPEED/ EXAMPLE 42/14/2019Figure shows Locations and speeds of 4 vehiclestravelling between section x & y on a 2 lane highwayat an instant of time by photography. An observerlocated at point X observes the four vehicles passingpoint X during a period of 15 sec. The velocities of thevehicles are measured as 45, 45, 40, and 30 mi/h,respectively. Calculate the flow, density, time meanspeed, and space mean speed.19
SOLUTION The flow is calculated by:2/14/2019q 4*3600 /15 960 (veh/h) With L equal to the distance between X and Y (ft), densityis: The time mean speed is found by20
The space mean speed is found by :note:1 mile 5280 ft1 mi/hr 1.47 ft/sec2/14/2019where ti : is the time it takes the ith vehicle to travel from X to Y at21speed ui, and L (ft): is the distance between X and Y.
TRAFFIC FLOW2/14/2019Uninterrupted flow:A vehicle traversing a section of lane or roadway is notrequired to stop by any cause external to the trafficstream (Ex: Freeways)Interrupted flow:A vehicle traversing a section of a lane or roadway isrequired to stop by a cause outside the traffic stream,such as signs or signals at intersections or junctions(Ex: Urban Arterials). Stoppage of vehicles by a cause internal to the trafficstream does not constitute interrupted flow22
RELATIONSHIPS AMONG MACROSCOPICTRAFFIC FLOW PARAMETERS2/14/2019The three basic macroscopic parameters of atraffic stream (flow, speed and density) arerelated to each other by the following equation: Flow density * space mean speed q k * us23
TRAFFIC FLOW PRINCIPLES MOREFLOW-DENSITY RELATIONSHIPS2/14/2019Flow (q) 1/ ave. headway (h) ave. Space Mean Speed (u) Flow (q) x ave. Spacing (s) Density (k) 1/ ave. Spacing (s) average space headway space mean speed * averagetime headway Density flow * ave. travel time for unit distance Average time headway ave. space headway* averagetravel time for unit distancespacingave.spaceSpeed 24headway
FUNDAMENTAL DIAGRAM2/14/201925
SPEED VS. DENSITYSpeedufFree Flow SpeedDensity26kjJam Density 2/14/2019 kus u f 1 kj
FUNDAMENTAL DIAGRAM2/14/2019 Speed-Density relationship―If density is 0 (No vehicle), Maximum speed isavailable―As density increases from 0, speed decreasesinitially―If density is maximum, speed is 027
FLOWVS.DENSITY2/14/2019Congested FlowFLow (veh/hr)Optimal flow,capacity, qmUncongested FlowkmOptimal densityDensity28kjJam Density
FUNDAMENTAL DIAGRAM2/14/2019 Flow-Density relationship―If density is 0, flow is 0 (No vehicle).―As density increases from 0, flow increasesinitially.―After the max flow point (qmax),flow decreases asdensity increases.―flow is 0 (Traffic Jam), Maximum jam density(kj).29
FLOW VS. SPEED2/14/2019ufFree Flow SpeedSpeedUncongested FlowumCongested FlowOptimal flow,Flow (veh/hr) capacity, qm30
FUNDAMENTAL DIAGRAM2/14/2019Flow-Speed relationship―If flow is 0 (No vehicle), Maximum speedis available.―As flow increases from 0, speed decreases initially( Uncongested flow ).―After the max flow point (qmax),speed decreasesas flow decreases(Congested flow ).31
2/14/2019This equation states that the flow or traffic volumeis equal to the product of speed and density. So if a 1-mile of a roadway contains 20 vehicles, and themean speed of the 20 vehicles is 40 mile/h. After 1 hour, 800 vehicles (40 x 20) would have passed. The value of the flow (q) or traffic volume in this casewould be equal to 800 v/hr. 32
EXAMPLE 5:2/14/2019Data obtained from aerial photography showed8 vehicles on a 250-m-long section of highway.Traffic data collected at the same time indicatedan average time headway of 3 sec. Determine : the density on the highway. the flow on the highway. the mean speed.33
SOLUTION 5:2/14/2019 The density could be calculated as follows:Density (k) 8/0,250 32 v/km. Flow (q) 1/average time headway (1/3 ) x 3600 1200 v/hr.Finally we have:q u*k then u q / k. Speed (u) 1200/32 37.5 km / h.34
MATHEMATICAL RELATIONSHIPS DESCRIBINGTRAFFIC FLOW2/14/2019Macroscopic ApproachGreenshields Model:He hypothesized that a linear relationship existed betweenspeed and density which he expressed asCorresponding relationships for flow and density and forflow and speed can be developed. Since , substituting for kin previous Eq. gives:Also substituting q/k for in Eq. gives:The maximum flow for the Greenshields relationship :35
FUNDAMENTAL DIAGRAM k us u f 1 kj 2 usq k j us uf 2/14/20192 kq uf k kj 36
CALIBRATION OF MACROSCOPICTRAFFIC FLOW MODELS2/14/2019-The traffic models discussed thus far can be used to determinespecific characteristics, such as the speed and density at whichmaximum flow occurs, and the jam density of a facility.-This usually involves collecting appropriate data on theparticular facility of interest and fitting the data pointsobtained to a suitable model. The most common method ofapproach is regression analysis.-This is done by minimizing the squares of the differencesbetween the observed and expected values of a dependentvariable.When the dependent variable is linearly related to theindependent variable, the process is known as linearregression analysis.37
CALIBRATION OF MACROSCOPICTRAFFIC FLOW MODELS2/14/2019If a dependent variable y and an independentvariable x are related by an estimated regressionfunction, then38
CALIBRATION OF MACROSCOPICTRAFFIC FLOW MODELSwheren :number of sets of observationsxi : ith observation for xyi: ith observation for y2/14/2019The constants a and b could be determined fromEqs. :39
COEFFICIENT OFDETERMINATION R22/14/2019A measure commonly used to determine the suitability of anestimated regression function is the coefficient ofdetermination (or square of the estimated correlationcoefficient) R2, which is given by:where Yi is the value of the dependent variable ascomputed from the regression equations.- The closer R2 is to 1, the better the regression fits404023/7/2015
2/14/2019414123/7/2015
2/14/2019424223/7/2015
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VARIATION OF TRAFFIC VOLUME2/14/2019Several types of measurements of volume arecommonly adopted which will be used inmany design purposes:1- Average Annual Daily Traffic (AADT):The average 24-hour traffic volume at a givenlocation over a full 365-day year, i.e. the totalnumber of vehicles passing the site in a yeardivided by 365.44
2/14/20192- Average Annual Weekday Traffic(AAWT):The average 24-hour traffic volume occurring OnWeek days over a full year. It is computed bydividing the total weekday traffic volume for theyear by 260.3- Average Daily Traffic (ADT):An average 24-hour traffic volume at a givenlocation for some period of time less than a Year.It may be measured for six months, a season, amonth, a week, or as little as two days.4- Average Weekday Traffic (AWT):An average 24-hour traffic volume occurring onweekdays for some period of time less than oneyear, such as for a month or a season.45
2/14/2019TRAFFIC FORECASTINGTraffic forecasting is the process of estimatingthe number of vehicles or people that will usea specific transportation facility in the future.Future AADT Current AADT x ((1 AAGR) n)Where n number of years.- AAGR is the Average Annual GrowthRate used to develop the future trafficforecast.464623/7/2015
TRAFFIC FORECASTING2/14/2019Example:If AADT for the year 2015 2500 veh/day.Find the AADT for the year 2035,if the AAGR 3%.Solution:2035 AADT 2015 AADT x ((1 AAGR) n). 2500 x ((1 0.03) 20 ). 2500 x 1.806 4515 veh/day.474723/7/2015
DESIGN HOURLY VOLUME2/14/2019 In design, peak-hour volumes are sometimesestimated from projections of the AADT (Bothdirections). Design hourly volume (DHV):- Traffic volume used for design calculations- Typically between 10th and 50th highest volumehour of the year.48
DESIGN HOURLY VOLUME2/14/2019Which hour?-Usually use 30 highest hourly volume of the year.Why 30 DHV?Compromise: too high is wastefultoo low poor operationDesign Hourly Volume (DHV):- Future hourly volume (both directions) used fordesign, typically 30 DHV in the design year49
2/14/201950
DESIGN HOURLY VOLUME2/14/2019DHV K * AADTK: is defined as the proportion of annual averagedaily traffic occurring in an hourDirectional Design Hourly Volume (DDHV):Directional distribution factor (D):- Factor reflecting the proportion of peak-hourtraffic traveling in the peak direction.- Often there is much more traffic in on directionthan the other.51
EXAMPLE2/14/2019Urban freeway, 2 lanes each direction.,Passenger car only facility, AADT 35000 v/day, D 65 %.Find the Directional Design HourlyVolume DDHV.Solution:K 0.12 (urban freeway ).Directional Design Hourly Volume (DDHV):DDHV AADT*K*D 3500 *0.12*0.65 2730 v/h.52
RATES OF FLOW2/14/2019Generally stated in units of "vehicles per hour," butrepresent flows that exist for periods of time lessthan one hour. A volume of 200 vehicles observed over a 15minute period may be expressed as a rate of 200* 4 800 v/h even though 800 vehicles would notbe observed if the full hour were counted.800 v/h becomes a rate of flow that exists a 15minute interval.53
VOLUME & FLOW RATE2/14/2019The distinction between volume and flowrateis important.Volume is the number of vehiclesobserved or predicted to pass a pointduring a time interval.Flow rate represents the number ofvehicles passing a point during a timeinterval less than1 h, but expressed as an equivalent hourly rate.For example, a volume of 100 vehiclesobserved in a 15-min period implies aflow rate of 100 v/0.25h or 400 v/h.54
EXAMPLE2/14/201955
EXAMPLESolution:The total volume for the hour is the sumof these counts, or 4,300 v/h.The flow rate, however, varies for each15-min period. During the I5-minperiod of maximum flow, the flow rateis 1,200 v/0.25h, or 4,800 v/h.2/14/2019Find the volume and the flow rate?56
PEAK-HOUR FACTOR2/14/2019Peak flow rates and hourly volumes produce the peak-hourfactor (PHF), the ratio of total hourly volume to the peakflow rate within the hour, computed by Equation:* If 15-min periods are used, the PHF may becomputed by EquationWhere:PHF peak- hour factorV hourly volume (v/h) andV15 volume during the peak 15 min of the peakhour(v/15 min).57
EXAMPLE/2/14/2019Then from the figure:Hourly volume 75 75 150 75 375 v/h.Peak flow rate 4*150 600 v/h.PHF 375 / 600 0.625.58
PASSENGER CAR UNIT2/14/2019Different types of vehicles in a traffic streamhave different characteristics like width, lengthand height and sometimes they produceinconvenience for other vehicles, so forexpressing highway capacity, a unit is usedcalled PASSENGER CAR UNIT.In this one car is considered as one unit.59
PASSENGER CAR UNIT TABLEEquivalent Factor1Bus2SUT2.5Trailer3.52/14/2019Vehicle TypePC60
NUMBER OF LANE2/14/201961
TIME HEADWAY (HEADWAY) Time headway (h): is the difference between the time the front of a vehicle arrives at a point on the highway and the time the front of the next vehicle arrives at that same point. Time headway is usually expressed in seconds The microscopic character related to volume is the time headway
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