Road Vehicle Performance

Road Vehicle Performance
Chapter 2 Principles of Highway Engineering and Traffic Analysis – 3rd Edition Fred Mannering, Walter Kilareski, Scott Washburn

Purpose of Lecture Chapter 2 involves understanding the forces that act on a vehicle Straight-line performance is reviewed Important concepts include: Understanding three sources of vehicle resistance Practical stopping distance

Road Vehicle Performance
Two functions Insight into highway design and traffic operations To be able to accommodate a large variety of vehicle types on the roads The basis to understanding vehicle designs and their impact on performance

Roadway Design Roadway design is governed by two main factors:
Vehicle capabilities acceleration/deceleration braking cornering (chap. 3) Human capabilities (late chap. 2, chap. 3) perception/reaction times eyesight (peripheral range, height above roadway)

Roadway Design & Vehicle Performance
Performance of road vehicles forms the basis for roadway design guidelines such as: length of acceleration / deceleration lanes maximum grades stopping-sight distances passing-sight distances setting speed limits timing of signalized intersections

Tractive Effort and Resistance
Two primary opposing forces Tractive effort is the force available at the road surface to do work Expressed in pounds or Newtons Resistance is the force impeding vehicle motion, 3 major sources Aerodynamic resistance Rolling resistance (originates from the roadway surface/tire interface) Grade or gravitational resistance

Ff + Fr = ma + Ra + Rrlf + Rrlr + Rg
F = ma + Ra + Rrl + Rg

Vehicle Motion For simplification, when summing forces along the longitudinal axis, traffic effort and rolling resistance at the front and rear tires is combined, giving: Where F is the available tractive force ma is the mass times acceleration Ra is the aerodynamic resistance Rrl is the rolling resistance Rg is the grade resistance

Aerodynamic Resistance
Aerodynamic resistance can impact vehicle performance, especially at high speeds Turbulent flow of air around vehicle body (85% of total resistance) Friction of the air passing over the body of the vehicle (12% of total resistance) Air flowing through the vehicle components (3% of total resistance)

Equations 2.3 and 2.4 can be used to determine aerodynamic resistance and the force required to overcome it based on factors such as drag coefficient of particular vehicle types; air density; frontal area of vehicle; vehicle speed relative to prevailing wind speed

* V is speed of vehicle relative to prevailing wind speed (we will assume wind speed of zero for purposes of this class)

Air density is a function of both elevation and temperature (see text Table 2.1).  altitude,  density  temperature,  density Drag coefficient is a term that implicitly accounts for all three of the aerodynamic resistance sources previously discussed Drag coefficient is measured from empirical data, either from wind tunnel experiments or actual field tests in which a vehicle is allowed to decelerate from a known speed with other sources of resistance (rolling and grade) taken into account

Overcoming Aerodynamic Resistance

As seen in equation 2.3, Ra is proportional to V 2. Thus, this resistance will increase rapidly with increasing speed. We can develop an expression for determining the power needed to overcome aerodynamic resistance

Rolling Resistance Refers to the resistance generated from a vehicle’s internal mechanical friction, and pneumatic tires and their interaction with the roadway surface. Primary source (about 90%) of this resistance is the deformation of the tire as it passes over the roadway surface. Tire penetration/roadway surface compression (about 4%) Tire slippage and air circulation around tire & wheel (about 6%)

Rolling Resistance Due to wide range of factors that affect rolling resistance, a simplifying approximation is used. Studies have shown that rolling resistance can be approximated as the product of a friction term (coefficient of rolling resistance) and the weight of the vehicle acting normal to the roadway surface.

Rolling Resistance Rolling resistance is the product of a friction term (coefficient of rolling resistance) and the weight of the vehicle acting normal to the roadway surface Coefficient of rolling resistance on paved surfaces is given as:

Rolling Resistance Thus, rolling resistance is approximated by:
However, since grades are often small, the equation is further simplified by assuming cos g = 1 (giving a slightly more conservative estimate), yielding: (Eq. 2.6)

Rolling Resistance & Horsepower
Horsepower to overcome rolling resistance, multiply eq 2.6 by speed

Example Problem A 2500 lb car is driven at sea level (ρ= slugs/ft3) on level paved surface. The car has drag coefficient CD=0.38 and 20ft2 frontal area. At max speed 50hp is expended to overcome rolling and aerodynamic resistance. What is the car’s max speed?

Example Problem continued

Grade Resistance Gravitational force parallel to the roadway acting on the vehicle Grades are generally given in percentages meaning that a 5% grade results in a 5 ft vertical rise over a 100 ft horizontal run

Grade Resistance   (Eq. 2.9)

Example #2.2 A 2,000 lb car has CD = 0.40, Af=20ft2 and available tractive effort of 255 lb. If the car is traveling at an elevation of 5000ft (ρ= slugs/ft3) on a paved surface at a speed of 70mph, what is the maximum grade this car could ascend and still maintain 70mph speed?

Example 2.2 Continued Need to understand the forces acting on the vehicle:

Principles of Braking For highway design and traffic analysis braking characteristics are most important aspect of vehicle performance Braking behavior influences geometric design, signal timing, sign placement, accident avoidance systems, roadway surface design

Sections 2.91-2.94 Review on your own
These sections deal more with how auto designers might approach braking principles or accident reconstruction if many variables are know (such as road adhesion, braking efficiency, air density, etc.) As highway designers, we have to generalize many of these factors in order to accommodate a variety of driver skills, vehicle types, pavement conditions and weather conditions

Practical Stopping Distance
Assuming constant deceleration V2=final vehicle speed in ft/s V1=initial vehicle speed in ft/s a =acceleration (negative for deceleration or stopping distance problems in ft/s2 d=deceleration distance (practical stopping distance) in ft Equations 2.45 and 2.46 are used when assuming deceleration (negative acceleration) and if the vehicle comes to a complete stop

Further Assumptions AASHTO recommends a deceleration rate of 11.2 ft/s2 Studies have shown that most drivers brake at rates greater than this Also that drivers can maintain control even on wet pavement at this rate

Accounting for Grade Equation 2.47 incorporates the effects of grade on braking distances g=gravitational constant, 32.2 ft/s2 G=roadway grade (+ for uphill; - for downhill) in percent/100

Accounting for Reaction Time
Up to this point only considering the distance traveled or required to stop a vehicle from the point of brake application Need to also account for the time passage when a driver is perceiving and reacting to the need to stop This distance is referred to as perception/reaction time

Perception/Reaction Time
V1 = initial vehicle speed in ft/s tr=time required to perceive and react to the need to stop in seconds dr=distance traveled during perception/reaction time, ft AASHTO recommends 2.5 seconds for tr; most drivers have reaction times of seconds

Total Required Braking Distance
Combination of braking distance and the distance traveled during perception/reaction time

Example – Practical Stopping Distance
Two drivers with reaction times of 2.5 sec. One is traveling at 55mph, the other at 70mph. How much distance will each of the drivers travel while perceiving/reacting to the need to stop? What is the total stopping distance for each? Assume a grade of %.

Example - Continued

PART II VERTICAL CURVES & HORIZONTAL SIGHT DISTANCE
CHAPTER 3 PART II VERTICAL CURVES & HORIZONTAL SIGHT DISTANCE 36

Vertical Alignment Specifies the elevation of points along a roadway
Provides a transition between two grades Sag curves and crest curves Equal-tangent curves - half the curve length positioned before the PVI; half after 37

Notation Curve point naming is similar to horizontal curves, with addition of V for vertical PVC: Point of Vertical Curvature PVI: Point of Vertical Intersection (of initial and final tangents) PVT: Point of Vertical Tangency Curve positioning and length usually referenced in stations Stations represent 1000 m or 100 ft e.g., ft  (i.e., 12 stations & 58.5 ft)

Notation G1 is initial roadway grade
Also referred to as initial tangent grade G2 is final roadway (tangent) grade A is the absolute value of the difference in grades (generally expressed in percent) A = |G2 – G1| L is the length of the vertical curve measured in a horizontal plane (not along curve center line, like horizontal curves)

Fundamentals Parabolic curves are generally used for design
Parabolic function  y = ax 2 + bx + c y = roadway elevation x = distance from PVC c = elevation of PVC Also usually design for equal-length tangents i.e., half of curve length is before PVI and half after

First Derivative First derivative gives slope
At PVC, x = 0, so , by definition G1 is initial slope (in ft/ft or m/m) as previously defined

Second Derivative Second derivative gives rate of change of slope
However, the average rate of change of slope, by observation, can also be written as Giving,

Offsets Offsets are vertical distances from initial tangent to the curve 44

Offset Formulas For an equal tangent parabola,
Y = offset (in m or ft) at any distance, x, from the PVC A and L are as previously defined It follows from the figure that,

“K” Values The rate of change of grade at successive points on the curve is a constant amount for equal increments of horizontal distance, and Equals the algebraic difference between intersecting tangent grades divided by the length of curve, or A/L in percent per ft (m) The reciprocal L/A is the horizontal distance required to effect a 1% change in gradient and is, therefore, a measure of curvature The quantity L/A is termed ‘K’

“K” Values The K-value can be used directly to compute the high/low points for crest/sag vertical curves (provided the high/low point is not at a curve end) by, xhl = K  |G1| Where x = distance from the PVC to the high/low point Additionally, K-values have important applications in the design of vertical curves, which we will see shortly

Vertical Curves Controlling factor: sight distance
Stopping sight distance should be provided as a minimum Rate of change of grade should be kept within tolerable limits Drainage of sag curves is important consideration, grades not less than 0.5% needed for drainage to outer edge of roadway 48

Vertical Alignment Relationships
49

Example Problem: Vertical Curve
A vertical curve crosses a 4’ diameter pipe at right angles. Pipe at sta with centerline elevation of ’. PVI at sta elevation ’. Equal tangent curve, 600’ long with initial and final grades of +1.2% and -1.08%. Using offsets determine the depth below the surface of the curve the top of the pipe and determine the station of the highest point of the curve. 50

Solution

Solution Continued

Stopping Sight Distance & Crest Curves
Two different factors are important for crest curves The driver’s eye height in vehicle, H1 Height of a roadway obstruction object, H2

SSD & Curve Design It is necessary, when designing vertical curves, to provide adequate stopping-sight distance (SSD) Because curve construction is expensive, we want to minimize curve length, subject to adequate SSD

SSD and Curve Design SSD formulation was given in Chapter 2, i.e., ds = d + dr (Eq. 2.50) It is repeated in Chapter 3 as Eq. 3.12 Table 3.1 gives SSD values in 5mph increments based on this equation and a=11.2ft/s2 and tr = 2.5s

Minimum Curve Length By using the properties of a parabola for an equal tangent curve, it can be shown that the minimum length of curve, Lm, for a required SSD is

Minimum Curve Length For the sight distance required to provide adequate SSD, current AASHTO design standards use the following specifications: H1 (driver’s eye height) = 3.5 ft (1080 mm) H2 (object height) = 2.0 ft (600 mm)

Minimum Curve Length Substituting these values into previous two equations yields: Since using these equations can be cumbersome, tables have been developed, utilizing K=L/A (discussed earlier)

Example 3.5 A highway is being designed to AASHTO guidelines with a 70-mph design speed and, at one section, an equal tangent vertical curve must be designed to connect grades of +1.0% and –2.0%. Determine the minimum length of vertical curve necessary to meet SSD requirements.

3.5 Solution

K-values for adequate SSD
Design Controls for Crest Vertical Curves Based on SSD

Example 3.6 Solve Example Problem 5 using the K-values in Table 3.2.

Sag Vertical Curves Four criteria for establishing length of sag curves Headlight sight distance Passenger comfort Drainage control General appearance 63

Headlight Sight Distance
At night, the portion of highway that is visible to the driver is dependent on the position of the headlights and the direction of the light beam Headlights are assumed to be 2 ft (600 mm) and 1-degree upward divergence of the light beam from the longitudinal axis of the vehicle Equations 3-19 through 3-23 describe the required sight distance for sag curves 64

Sag Vertical Curve Length
The most controlling factor is headlight sight distance If for economic reasons such lengths cannot be provided, fixed source lighting should be provided to assist the driver. 65

Min Sag Curve Length Like crest curves, we need expressions for determining the minimum length of crest curve required for adequate SSD

Minimum Curve Length For the sight distance required to provide adequate SSD, current AASHTO design standards use the following specifications: H (headlight height) = 2.0 ft (600 mm)  (headlight angle) = 1°

Minimum Sag Curve Length
Substituting the recommended values for beta and H gives: If not sure which equation to use, assume SSD < L first (for either sag or crest curves)

K Values for Adequate SSD
Design Controls for Sag Vertical Curves Based on SSD Table 3.3

Passing Sight Distance & Crest Vertical Curve Design
Only a factor for vertical curves A consideration for two-lane highways Sag curves have unobstructed sight distance Assume driver eye height and height of object on roadway surface both 3.5’ 71

Stopping Sight Distance & Horizontal Curve Design
Adequate sight distance must be provided in the design of horizontal curves Cost of right of way or the cost of moving earthen materials often restrict design options When such obstructions exist, stopping sight distance is checked and measured along the horizontal curve from the center of the traveled lane 72

Sight Distance Relationships
74

Sight Distance Example
Horizontal curve with 2000’ radius; 12’lanes; 60mph design speed. Determine the distance that must be cleared from the inside edge of the inside lane to provide sufficient stopping sight distance. 75

Sight Distance Example Continued
*SSD is determined from Table 3.1 for 60mph design speed 76

Traffic Stream Parameters
Chapter 5 Traffic Stream Parameters 77

Traffic Streams Individual vehicles and drivers make up the traffic stream Local characteristics and driver behavior are major factors on its performance Drivers and vehicles are not uniform in their make up or behavior 78

Traffic Streams Uninterrupted – freeways, two-lane rural roads
Interrupted flow facilities – arterials, local roadways (have external devices that interrupted flow) 79

Interrupted Facilities
Vehicles flow in platoons A group of vehicles moving together with a significant gap between themselves and the next group of vehicles Signal timing plans try to take advantage of platoons for continuous flow Signals place less than 2 miles apart can be timed to allow for uninterrupted flow between signals 80

Traffic Stream Parameters
Macroscopic parameters – describe the traffic stream as a whole Traffic flow Speed Density Microscopic parameters - describe the behavior of the individual vehicle with respect to each other Spacing Headway 81

Macroscopic Parameters
Traffic flow – number of vehicles that pass a certain point during a specified time interval (vehicles/hour) Speed – rate of motion in distance/time (mph) Density – number of vehicles occupying a given length of highway or lane (vehicles per mile per lane, vpmpl) 82

Spacing and Time Headway
Spacing – the distance between successive vehicles in a traffic stream as they pass some common reference point on the vehicles Time headway – the time between successive vehicles in a traffic stream as they pass some common reference point on the vehicles 83

Traffic Flow and Time Headway
Traffic Flow given by: q= traffic flow in vehicles per unit time n= number of vehicles passing some designated roadway point during time t t= duration of time interval Flow measurements typically related to generalized period of time; Volume of traffic refers to vehicles per hour Time Headway given by: t= duration of time interval hi=time headway of the ith vehicle n= number of measured vehicle time headways at some designated roadway point 84

Time Headway and Traffic Flow
Time headway is defined as the time between the passage of successive vehicles (can be measured from front bumpers or rear bumpers) Substituting t into the flow equation gives: 85

Example Problem Given the following headways, determine the average headway and the flow: 4.74s, 3.33s, 4.74s, 8.97s, 11.63s, 3.83s, 14.40s 86

Speed and Travel Time Time mean speed – point measure of speed
Space mean speed – measure relating to length of roadway Average travel time – total time to traverse a highway Average running speed – total time during which vehicle is in motion while traversing a highway segment (no stop time included) 87

Speed and Travel Time Operating speed – maximum safe speed a vehicle can be driven without exceeding design speed 85th percentile speed – speed at which 85% of vehicles are traveling at or below 88

Time Mean Speed Arithmetic mean of vehicles speeds is given by:
ut=time-mean speed in unit distance per unit time ui=spot speed of the ith vehicle n=number of measured vehicle spot speeds 89

Space Mean Speed Time necessary for a vehicle to travel some known length of roadway us= space-mean speed in unit distance per unit time l=length of roadway used for travel time measurements of vehicles t(bar)= average vehicle travel time, defined as: ti= time necessary for vehicle i to travel a roadway section of length l 90

Traffic Density Measure using aerial photographs; think of it as the number of vehicles that occupy a length of roadway k=traffic density in vehicles per unit distance n=number of vehicles occupying some length of roadway at some specified time l=length of roadway si=spacing of the ith vehicle (the distance between vehicles i and i-1 measured from front bumper to front bumper 91

Spacing and Density Substituting the equation for roadway length into the density equation gives 92

Basic Traffic Stream Models
Example: average headway is 2.5 s/veh on single lane roadway; average vehicle spacing is 200’; determine average speed of traffic. 93

Speed-Density Model u=space mean speed in mi/hr
uf= free-flow speed in mi/hr k=density in veh/mi kj=jam density in veh/hr 94

Flow-Density Model 95

Speed-Flow Model 96

Example Problem Given an estimate of density of vpmpl at a speed of 60mph; determine the jam density and flow rate at 60mph. Assume car length is 15’ and at jam density spacing between vehicles is 15’. 97

Volume Planning (non-directional) volume measures
Average annual daily traffic (AADT) Average annual weekday traffic (AAWT) Average daily traffic (ADT), average 24 hour volume that can be measured by season, month, week, day, etc. 98

Volume Hourly volumes – used for design and operational analysis
Peak hour volume – single highest hourly volume Directional design hour volume – AADT x K x D = DDHV (K = proportion of daily traffic during peak hour, D = proportion of peak traffic traveling in peak direction) 99

Volume Peak hour factor – describes the relationship between hourly volume and maximum rate of flow within the hour PHF = hourly volume/maximum rate of flow OR PHF = V/(4 x V15) PHF range – 1.0 (each 15 minute period equal) to 0.25 (one 15 min period contains all traffic) 100

Peak Hour Factor Example
15 min period Vehicle Count Flow Rate (vph) 7:20AM 389 1556 7:35AM 495 1980 7:50AM 376 1504 8:05AM 363 1452 7:20-8:20AM 1623 101

Peak Hour Factor Example
Determine the Peak Hour Factor 102

Chapter 5 Models of Traffic Flow 103

Introduction Macroscopic relationships and analyses are very valuable, but A considerable amount of traffic analysis occurs at the microscopic level In particular, we often are interested in the elapsed time between the arrival of successive vehicles (i.e., time headway)

Introduction The simplest approach to modeling vehicle arrivals is to assume a uniform spacing This results in a deterministic, uniform arrival pattern—in other words, there is a constant time headway between all vehicles However, this assumption is usually unrealistic, as vehicle arrivals typically follow a random process Thus, a model that represents a random arrival process is usually needed

Introduction First, to clarify what is meant by ‘random’:
For a sequence of events to be considered truly random, two conditions must be met: Any point in time is as likely as any other for an event to occur (e.g., vehicle arrival) The occurrence of an event does not affect the probability of the occurrence of another event (e.g., the arrival of one vehicle at a point in time does not make the arrival of the next vehicle within a certain time period any more or less likely)

Introduction One such model that fits this description is the Poisson distribution The Poisson distribution: Is a discrete (as opposed to continuous) distribution Is commonly referred to as a ‘counting distribution’ Represents the count distribution of random events

Poisson Distribution P(n) = probability of having n vehicles arrive in time t λ = average vehicle arrival rate in vehicles per unit time t= duration of time interval over which vehicles are counted e= base of the natural logarithm 108

Example Application Given an average arrival rate of 360 veh/hr or 0.1 vehicles per second; with t=20 seconds; determine the probability that exactly 0, 1, 2, 3, and 4 vehicles will arrive. 109

Poisson Example Example:
Consider a 1-hour traffic volume of 120 vehicles, during which the analyst is interested in obtaining the distribution of 1-minute volume counts 110

Poisson Example What is the probability of more than 6 cars arriving (in 1-min interval)?

Poisson Example What is the probability of between 1 and 3 cars arriving (in 1-min interval)?

Poisson distribution The assumption of Poisson distributed vehicle arrivals also implies a distribution of the time intervals between the arrivals of successive vehicles (i.e., time headway)

Negative Exponential Substituting into Poisson equation yields
To demonstrate this, let the average arrival rate, , be in units of vehicles per second, so that Substituting into Poisson equation yields (Eq. 5.25)

Negative Exponential Note that the probability of having no vehicles arrive in a time interval of length t [i.e., P (0)] is equivalent to the probability of a vehicle headway, h, being greater than or equal to the time interval t.

Negative Exponential So from Eq. 5.25, (Eq. 5.26) Note:
This distribution of vehicle headways is known as the negative exponential distribution.

Negative Exponential Example
Assume vehicle arrivals are Poisson distributed with an hourly traffic flow of 360 veh/h. Determine the probability that the headway between successive vehicles will be less than 8 seconds. Determine the probability that the headway between successive vehicles will be between 8 and 11 seconds.

By definition,

Negative Exponential For q = 360 veh/hr

Negative Exponential

Queuing Systems Queue – waiting line
Queuing models – mathematical descriptions of queuing systems Examples – airplanes awaiting clearance for takeoff or landing, computer print jobs, patients scheduled for hospital’s operating rooms 122

Characteristics of Queuing Systems
Arrival patterns – the way in which items or customers arrive to be served in a system (following a Poisson Distribution, Uniform Distribution, etc.) Service facility – single or multi-server Service pattern – the rate at which customers are serviced Queuing discipline – FIFO, LIFO 123

D/D/1 Queuing Models Deterministic arrivals Deterministic departures
1 service location (departure channel) Best examples maybe factory assembly lines 124

Example Vehicles arrive at a park which has one entry points (and all vehicles must stop). Park opens at 8am; vehicles arrive at a rate of 480 veh/hr. After 20 min the flow rate decreases to 120 veh/hr and continues at that rate for the remainder of the day. It takes 15 seconds to distribute the brochure. Describe the queuing model. 125

M/D/1 Queuing Model M stands for exponentially distributed times between arrivals of successive vehicles (Poisson arrivals) Traffic intensity term is used to define the ratio of average arrival to departure rates: 126

M/D/1 Equations When traffic intensity term < 1 and constant steady state average arrival and departure rates: 127

M/M/1 Queuing Models Exponentially distributed arrival and departure times and one departure channel When traffic intensity term < 1 128

M/M/N Queuing Models Exponentially distributed arrival and departure times and multiple departure channels (toll plazas for example) In this case, the restriction to apply these equations is that the utilization factor must be less than 1. 129

M/M/N Models 130

Basic Freeway Sections
NHI Course No Highway Capacity and Quality of Flow Basic Freeway Sections

What Is a Freeway? Divided highway Full control of access
NHI Course No Highway Capacity and Quality of Flow What Is a Freeway? Divided highway Full control of access Two or more lanes in each direction Uninterrupted flow No signals No stop-controlled at-grade intersections

Freeway System Components
NHI Course No Highway Capacity and Quality of Flow Freeway System Components CH 3: Basic Freeway Sections CH 6: Freeway Systems CH 5: Ramps and Ramp Junctions CH 4: Weaving Areas

Basic Freeway Section Influence Area
NHI Course No Highway Capacity and Quality of Flow Basic Freeway Section Influence Area Sections of the freeway that are not affected by the merging or diverging movements at nearby ramps or by weaving movements. Basic Freeway Segment 500’ 2500’

Freeway Capacity & Free-flow speed
NHI Course No Highway Capacity and Quality of Flow Freeway Capacity & Free-flow speed Freeway capacity: Definition: the maximum sustained 15-min rate of flow in pcphpl that can be accommodated by a uniform freeway segment under prevailing traffic and roadway conditions in a specified direction. Free-flow speed. Mean passenger car speed under low to moderate flow rates (under 1000 veh/hr/ln) and under prevailing roadway and traffic conditions

NHI Course No Highway Capacity and Quality of Flow Base Conditions Conditions under which the full capacity of a basic freeway section is achieved are: Good weather Good visibility No incidents Reduction in one of these conditions will mean the speed, LOS, capacity of the freeway section tend to be reduced

Ideal Freeway Conditions
NHI Course No Highway Capacity and Quality of Flow Ideal Freeway Conditions 12-ft minimum lane widths 6-ft minimum right-shoulder lateral clearance and 2-ft median clearance All passenger cars Most drivers familiar with the facility Ten or more total lanes (in urban areas only) Interchange spacing  2 miles Level terrain (grades  2%)

Freeway Capacity Ideal Capacity:
NHI Course No Highway Capacity and Quality of Flow Freeway Capacity Ideal Capacity: 2,400 pcphpl for freeways with free-flow speeds > 70 mph 2,250 pcphpl for freeways with free-flow speeds of 50 mph Note: capacity varies by free-flow speeds and not by number of lanes.

Speed-flow Relationship
NHI Course No Highway Capacity and Quality of Flow Speed-flow Relationship

Service Measure for Freeways
NHI Course No Highway Capacity and Quality of Flow Service Measure for Freeways q= flow in veh/hr u=speed in mi/hr, and k=density in veh/mi

Free Flow Speed Influenced By:
NHI Course No Highway Capacity and Quality of Flow Free Flow Speed Influenced By: Number and width of lanes Lateral clearance Interchange density Other factors: Horizontal and vertical alignment speed limit Level of Enforcement Lighting conditions Weather

NHI Course No Highway Capacity and Quality of Flow Basic Relationships Determination of Level of Service for a basic freeway section generally involves three components: Flow rate Free-flow speed Level of Service

NHI Course No Highway Capacity and Quality of Flow Free-Flow Speed Free-flow speed is the mean speed of passenger cars measured under low to moderate flows ( < 1300 pc/hr/ln) Two methods to establish FFS: Field measurement Estimation procedure

Estimation of FFS FFS = BFFSi - fLW - fLC - fN - fID Where:
NHI Course No Highway Capacity and Quality of Flow Estimation of FFS FFS = BFFSi - fLW - fLC - fN - fID Where: FFS = estimated free-flow speed (mph) BFFSi = estimated free-flow speed for base conditions, 70 mph (urban areas) or 75 mph (rural areas) fLW = lane width adjustment factor (Table 6.3) fLC = Lateral clearance adjustment factor (Table 6.4) fN = Number of lanes adjustment factor (Table 6.5) fID = Interchange density adjustment factor (Table 6.6)

Determination of Flow Rate
NHI Course No Highway Capacity and Quality of Flow Determination of Flow Rate Peak flow rate (pcph) vp = V PHF x N x fHV x fP vp = 15-min passenger-car equivalent flow rate (pcphpl) V = hourly volume (vph) PHF = Peak Hour Factor N = Number of lanes fHV = Heavy-vehicle adjustment factor (eq. 6.5) fp = Driver population factor

NHI Course No Highway Capacity and Quality of Flow Peak Hour Factor (PHF) Represents the temporal variations in traffic flow during an hour Flow rates found in the peak 15-min period within an hour are normally sustained during the entire hour On freeways, typical PHF values range from 0.85 to 0.95 Lower PHF values are characteristic of rural freeways or off-peak conditions

Heavy Vehicle Equivalents
NHI Course No Highway Capacity and Quality of Flow Heavy Vehicle Equivalents Concept is based on observations of freeway conditions in which the presence of heavy vehicles, including trucks, buses and RV's creates less-than-ideal conditions. These conditions: create gaps (in front and behind) reduce speeds require more physical space (2 to 3 times a car length) To deal with this, HCM converts each heavy vehicle into the equivalent number of passenger cars

Heavy Vehicles Adjustment Factors
NHI Course No Highway Capacity and Quality of Flow Heavy Vehicles Adjustment Factors Heavy Vehicle Factor (fHV) Tables 6.7 to 6.10 fHV = __________ 1___________ 1 + PT (ET - 1) + PR(ER - 1) ET = Passenger Car Equivalent Factor for Trucks/Buses PT= Percentage of Trucks/Buses PR= Percentage of RV’s ER= Passenger Car Equivalent Factor for RV’s

Terrain Categories Level (Table 6.7) Rolling (Table 6.7)
NHI Course No Highway Capacity and Quality of Flow Terrain Categories Level (Table 6.7) HV maintain same speed as autos Generally less than 2% grade Rolling (Table 6.7) HV reduce speed below auto Doesn't require HV to operate at crawl speeds Mountainous (Table 6.7) HV operate at crawl speeds Specific Grades (Table )

NHI Course No Highway Capacity and Quality of Flow Level of Service (LOS) Density is the parameter used to define levels of service for basic freeway sections.

LOS Criteria NHI Course No. 13305 Highway Capacity and Quality of Flow

Examples NHI Course No. 13305 Highway Capacity and Quality of Flow

NHI Course No Highway Capacity and Quality of Flow Example #1 Six-lane freeway, rolling terrain, 11’ lanes, obstructions 2’ from right edge of traveled pavement, 1.5 interchanges per mile. Commuter traffic, directional weekday peak-hour volume 2200 vehicles, with 700 vehicles during the 15-min peak period. 15% large trucks/buses; no RVs, determine LOS.

Multi-lane Highways - Divided
NHI Course No Highway Capacity and Quality of Flow Multi-lane Highways - Divided

Multi-lane Highways - Undivided
NHI Course No Highway Capacity and Quality of Flow Multi-lane Highways - Undivided

Multi-Lane Highways Similar analysis to freeways
NHI Course No Highway Capacity and Quality of Flow Multi-Lane Highways Similar analysis to freeways Multi-lane highways include at-grade intersections, driveways (they do not have full access control) May be divided or undivided Traffic signals may be present Design standards are typically lower than freeways Typically 4-6 total lanes; posted speeds between mph

Analyzing Multi-Lane Highways
NHI Course No Highway Capacity and Quality of Flow Analyzing Multi-Lane Highways Similar to freeways except inclusion of a few different adjustment factors to determine FFS Base conditions for multi-lane highways: 12’ lanes 12’ min total lateral clearance from roadside objects in travel direction Only passenger cars No direct access along roadway Divided highway Level terrain Commuter population Free-flow speed of 60mph or more LOS thresholds different than freeways

Service Measure for Multi-lane Highways
NHI Course No Highway Capacity and Quality of Flow Service Measure for Multi-lane Highways Density as with freeways Multi-lane highways are typically analyzed for areas in which greater than 2 miles separate traffic signals

FFS for Multi-Lane Highways
NHI Course No Highway Capacity and Quality of Flow FFS for Multi-Lane Highways FFS = estimated free-flow speed in mph BFFS = estimated free-flow speed for base conditions, mph fLW = adjustment for lane width in mph fLC = adjustment for lateral clearance in mph fM = adjustment for median type in mph fA = adjustment for number of access points along the roadway in mph

Lateral Clearance Adjustment
NHI Course No Highway Capacity and Quality of Flow Lateral Clearance Adjustment 1st determine the total lateral clearance TLC = total lateral clearance in ft LC R = lateral clearance on the right side of the Travel lanes to the obstruction LC L = lateral clearance on the left side of the travel Lanes to obstructions For undivided highways there is no adjustment for left-side Lateral clearance because this is already taken into account By the median type adjustment factor. If an individual lateral clearance exceeds 6 feet, use 6 feet In the above equation. TWLTLs are considered to have LC left equal to 6 feet

Lateral Clearance Adjustment Factor
NHI Course No Highway Capacity and Quality of Flow Lateral Clearance Adjustment Factor Once total lateral clearance is calculated, then table 6.13 can be used to determine the lateral clearance adjustment factor, fLC

NHI Course No Highway Capacity and Quality of Flow Multi-Lane Example 6-lane divided highway; rolling terrain with 2 access pts/mile. 10’lanes, 5’ shoulder on right, 3’ shoulder on left. PHF =0.80; directional peak hour volume is 3000 vph. 6% trucks; 2% buses; 2% RVs; unfamiliar road-users; posted speed =55mph. Determine LOS.

Two Lane Rural Highways Ch 6
NHI Course No Highway Capacity and Quality of Flow Two Lane Rural Highways Ch 6 The majority of our Nation’s highways paved highways are considered rural (80%) Of these, 85% are two lane highways Thus the focus of many states is design and operational analysis of two lane highways Chapter 8: Two-Lane Highways

Primary Functions Mobility Access
NHI Course No Highway Capacity and Quality of Flow Primary Functions Mobility State and County primary highways, carry large numbers of users Access Low volume roadways, provide basic all-weather access to remote or sparsely-developed areas HCM has defined two classes of TLTW rural highways Class I (high speeds, intercity routes) Class II (scenic routes, recreational areas) Chapter 8: Two-Lane Highways

NHI Course No Highway Capacity and Quality of Flow Passing Maneuvers Passing is a unique characteristic of two lane rural highways Directional flow has a major effect on operational performance As traffic in one direction increases, the demand for passing also increases in that direction If traffic is significant in the opposing direction, platoons begin to form and drivers are no longer able to choose their own travel speed Chapter 8: Two-Lane Highways

NHI Course No Highway Capacity and Quality of Flow Passing Maneuvers Heavy vehicles also have a significant impact on operational performance of two lane highways Again, with the inability to pass slow moving vehicles, platoons can begin to form and operational performance deteriorate quickly Therefore, operational analysis is performed for the entire facility, not by direction of traffic flow Chapter 8: Two-Lane Highways

Two-lane Quality Definitions
NHI Course No Highway Capacity and Quality of Flow Two-lane Quality Definitions Average Travel Speed The segment length divided by the avg. travel time of ALL vehicles. % Time Spent Following The avg % of travel time that all vehicles are delayed due to inability to pass. This can be estimated by measuring the percentage of vehicles traveling at headways less than 5 seconds. **weakness of MOE** to date this factor has not been linked to the length of segment. Utilization of Capacity The ratio of the demand flow rate to the capacity of the facility. Chapter 8: Two-Lane Highways

NHI Course No Highway Capacity and Quality of Flow Level of Service Determined by Average Travel Speed and Percent Time Spent Following for Class I facilities Determined only by Percent Time Spent Following for Class II facilities Chapter 8: Two-Lane Highways

Ideal Conditions Rural two-lane highways
NHI Course No Highway Capacity and Quality of Flow Ideal Conditions Rural two-lane highways Ideal Conditions 12 ‘ Lane Widths 6’ Shoulders No “No Passing” Zones 50/50 Directional Split Passenger Cars Only 60 mph Design Speed Level Terrain Chapter 8: Two-Lane Highways

NHI Course No Highway Capacity and Quality of Flow Free-Flow Speed Expected operating conditions can be estimating by knowing the free-flow speed Recommended that it be measured in the field when possible Can be estimated by the following when total flow levels greater than 200 pc/hr Sm = mean speed of the measured sample, mph vf=observed flow rate for the period of speed Sample, veh/hr fhv=heavy vehicle adjustment factor Chapter 8: Two-Lane Highways

Free-Flow Speed May also be estimated using technique from HCM
NHI Course No Highway Capacity and Quality of Flow Free-Flow Speed May also be estimated using technique from HCM FFS = free-flow speed for the facility, mi/hr BFFS = base free-flow speed for the facility, mi/hr (typically use design speed or speed limit) fLS= adjustment for lane and shoulder width, mi/hr (Table 6.16) fA = adjustment for access point density, mi/hr (Table 6.15) Chapter 8: Two-Lane Highways

NHI Course No Highway Capacity and Quality of Flow Demand Flow Rate Need to adjust the hourly vehicle demand volume into demand flow rate (pc/hr) v=demand flow rate, pc/hr V = hourly demand volume under prevailing conditions, veh/hr PHF = peak hour factor fHV= adjustment for heavy vehicle presence (Table 6.18) fG = adjustment for grades (Table 6.17) Chapter 8: Two-Lane Highways

Demand Flow Rate Things to note:
NHI Course No Highway Capacity and Quality of Flow Demand Flow Rate Things to note: When estimating average travel speed (ATS) and Percent Time Spent Following (PTSF) need to determine two different sets of adjustment factors When performing two-directional analysis, total volume is used to determine v; when one-directional, two v’s must be determined Chapter 8: Two-Lane Highways

NHI Course No Highway Capacity and Quality of Flow Estimating ATS Once you have iteratively determined the demand flow rate (using your heavy vehicle and grade adjustment factors) next you can determine ATS and PTSF Again as before, you need to keep consistent with one-directional or two-directional analysis Chapter 8: Two-Lane Highways

NHI Course No Highway Capacity and Quality of Flow Example Class I 2-lane highway has rolling terrain and 500 v/hr with PHF % trucks, 2% buses, 6% RVs. Determine the Average Travel Speed (ATS) and the % Time Spent Following (PTSF). Chapter 8: Two-Lane Highways

NHI Course No Highway Capacity and Quality of Flow Example 6.7 Now that we know the flow rates that are to be used to determine the LOS based on ATS and PTSF, continue the example. Additional information: 11’lanes 2’shoulders 10 access points/mile 50% no-passing zones Base FFS=55mph 60/40 directional split Chapter 8: Two-Lane Highways

Chapter 7 Traffic Control and Analysis at Signalized Intersections
Principles of Highway Engineering and Traffic Analysis, 2005 Third Edition Fred Mannering, Walter Kilareski Scott Washburn 177

Basic Concepts 178

Signal Timing Terminology
Indication: illumination of signal lenses which informs the driver as to which movements are permitted or prohibited Cycle: one complete rotation through all of the indications provided Cycle length: time required to complete one rotation, given in seconds, C Yellow time: the change interval, warns drivers that the signal is changing from green to red Clearance interval: the all red indication Green time: the “go” indication for a particular movement or set of movements Red time: the “stop” indication for a particular movement or set of movements Phase: a green interval plus the change interval and clearance intervals that follow it (typically related to a particular movement or approach) 179

Modes of Operation Pretimed Operation: preset cycle lengths and intervals. 3-dial signal controllers allow for three different cycles throughout the day. Semi-Actuated: detectors at minor approaches. Green for major street unless vehicle detected on minor street Fully Actuated: every approach has detectors. Green time allocated based on vehicle detection. Each cycle different, limits placed on min/max green times and min gaps between vehicles to maintain green indication. Computer Controlled: System wide control. Optimal progression patterns determined for system wide operation. In order to optimize, however, cycle lengths must be the same or multiples of a base to achieve optima performance. 180

Inductive Loop 182

Machine-Vision Camera Detectors
183

Left Turn Timing Permitted Left Turns: drivers permitted to cross opposing traffic but must select their own gap (green ball on signal head) Protected Left Turns: left turns made without opposing through vehicular traffic (green arrow on signal head) Protected/Permitted or Permitted/Protected: left turns protected at the beginning of a phase, then permitted during through movement green time 184

Dual-Ring Configuration
Allows for maximum flexibility to control phase duration and sequencing of intervals Best hardware to have when implementing fully-actuated signals See Figure 7.3 Movements 1-4 can occur simultaneously with movements 5-8 (as long as the occur on the same side of the barrier) The dual ring ability allows for skipping of phases where there isn’t a need for them due to low flow Allows the unused green to be allocated to more congested phases 185

Discharge Headway Discharge headway: time passage between successive vehicles as they cross the curb line during a green phase. Measured at rear wheels of vehicles. First headway longer than others. Includes driver reaction time, and acceleration time. Second headway shorter, reaction and acceleration times overlap. Eventually headways level out, typically around 4-5 vehicle. Once this occurs, saturation headway can be measured. 187

Saturation Flow Rate Saturation headway: h=headway achieved by stable moving platoon of vehicles passing through a green indication Saturation Flow Rate: every vehicle assumed to occupy h seconds of green time, and if signal always green, then s vehicles/hour could enter intersection s = 3600/h If signal always green, could simply multiply by the number of lanes to estimate the capacity of the approach. *units of measure: vehicles per hour of green time per lane, (vphgpl) 188

Lost Time Time that is not effectively serving any movement or traffic
Total lost time includes start-up and clearance lost times Start-up lost time = signal indication turns from red to green and vehicles do not instantly move at the saturation flow rate Clearance lost time= later portion of the yellow phase + all red phase 189

Start-up Lost Time Need to account for the time lost when first few vehicles crossing intersection Start-up lost time (l): actual headway-saturation headway multiplied by number of vehicles (n) traveling at headways greater than saturation headway (h) Lost time also occurs when a movement is stopped (at the beginning of the clearance interval) 190

Total Lost Time 191

Effective Green Time Amount of time available to be used at a rate of one vehicle every h seconds gi=Gi + Yi +AR– tL gi=effective green time Gi=actual green time for movement i,sec Yi=sum of yellow plus all red time for movement i,sec tL=total lost time per phase, sec Total lost time includes start up time and clearance lost time (tL=tsl + tcl) 193

Green Ratio Ratio of effective green time to cycle length for a particular movement Simple capacity can be determined using: ci=si(gi/C) ci=capacity of lanes serving movement i, vph C=Signal cycle length, sec si=saturation flow rate for movement i, sec gi=effective green time for movement i,sec 194

Effective Red Time Effective red time is the time in which the intersection is not being utilized by traffic r= effective red time for a traffic movement in seconds R = displayed red time for a traffic movement in seconds tL= total lost time for the movement during a cycle in seconds 195

Simple Capacity Estimation
Approach or movement capacity can be estimated through a simple relationship c= capacity of a lane group or approach that are served by a particular “g” s = saturation flow rate in veh/hr g/C = ratio of the effective green time to the total cycle length 196

Using Simple Queuing Models to Estimate Signal Performance
Ex 7.1 in text Pretimed signal with sat flow rate of 2400 vph 24 sec of effective green time in 80 s cycle Flow at approach is 500 vph Estimate operational performance using D/D/1 queuing. 197

Example Continued Put arrival and departure rates in similar units 198

Example Continued A variety of measures can be determined using equations 199

Estimating Delay at Real-World Signals
The D/D/1 models are limited by their assumption of uniform arrivals For signals, non-uniform arrivals are much more likely than uniform arrivals To determine LOS, control delay is estimated for traffic signals and unsignalized intersections Control delay = deceleration time, queue move-up time, stop time, and acceleration time through the intersection 200

HCM Delay Model Total Average Individual Stopped Delay for Random Arrivals (sec/veh) 201

HCM Delay Model d=average signal delay per vehicle in sec
d1=avg delay per vehicle due to uniform arrivals in sec PF=progression adjustment factor d2=avg delay per vehicle due to random arrivals in sec d3=avg delay per vehicle due to initial queue at start of analysis period in sec 202

HCM Delay Model C=cycle length, sec
g=effective green time for lane group in sec X=v/c ratio for lane group T=duration of analysis period in hours k=delay adjustment factor that is dependent on signal controller mode I=upstream filtering adjustment factors c=lane group capacity in veh/hr 203

Example An approach to a pretimed signalized intersection has:
s= 2400 veh/hr 24 sec effective green C = 80 sec Given flow = 500 veh/hr; no initial queue and flow accounts for 15-min period, determine average approach delay per cycle. 204

Example Continued Calculate uniform delay first: 205

Example Continued Calculate Random Delay 206

Chapter 7 Part II Traffic Control and Analysis at Signalized Intersections
Principles of Highway Engineering and Traffic Analysis, 2005 Third Edition Fred Mannering, Walter Kilareski Scott Washburn 207

Development of Traffic Signal Phasing and Timing Plan
A cycle is made up of individual phases (where a phase include green, yellow and all red for a particular movement) The most basic operation is referred to as 2-phase When left-turn volumes cannot be serviced without long delays, then 3-phase designs are used 208

Figure 7.7 209

When to Use 3-Phase Operations
The Highway Capacity Manual recommends that when the product of the left-turning vehicles and the opposing traffic exceeds 50,000 during peak hour for one opposing lane, or 90,000 for two opposing lanes or 110,000 for three opposing lanes, then a protected left turn phase is required 210

Example 7.6 Refer to this example to see how to determine if a protected left turn phase is needed for a particular approach 212

Solution Do you need an exclusive left turn phase for WB traffic?

Lane Groups From HCM 2000: Movements made simultaneously from the same lane are treated as a lane group Exclusive turn lanes are normally treated as a separate lane group If an approach contains an exclusive turn lane, the remaining lanes are considered a single lane group If working with a multi-lane approach with more than one movement utilizing a lane, analyst must determine the primary use of the lane (de facto lanes) 216

Typical Lane Groupings
217

Lane Groups for Example 7.6
EB and WB left turn movements will each be a lane group (have separate/exclusive lane) EB and WB through/right will be processed as a lane group (lane “group” does not necessarily mean just one-lane processing a “group”) NB and SB lefts have an exclusive lane so each will be processed as a lane group (on each approach) NB and SB through/right will be processed as a lane group 218

Lane Groups for Analysis of Example 7.6 (Maple & Vine)
219

Critical Lane Concept Involves how or what time will be allocated
Critical lane: the lane that carries the most traffic during a signal phase One and only one critical lane in each signal phase Signal timing must be timed to accommodate this lane group 220

Ex 7.8 determining Flow Ratios
First determine the saturation flow rates for each lane group moving in each phase Phase 1 Phase 2 Phase 3 EB L: 1750veh/hr EB T/R:3400veh/hr SB L: 450veh/hr NB L: 475veh/h WB L:1750veh/hr WB T/R:3400veh/hr SB T/R:1800veh/hr NB T/R: 1800veh/hr 221

Determine Critical Lane Groups
Phase 1 Phase 2 Phase 3 EB L 300/1750= 0.171 EB T/R: 1100/3400=0.324 SB L: 70/450=0.156 NB L: 90/475= 0.189 WB L: 250/1750=0.143 WB T/R: 1150/3400 = 0.338 SB T/R: 370/1800=0.206 NB T/R: 390/1800= 0.217 222

Determine Sum of Flow Rates for Critical Lane Groups
Also, lost time for the cycle is equal to: 3 phases X 4 seconds/phase = 12 seconds 223

Steps to Signal Design Development of a phase plan and sequence
Determination of cycle length Allocating of effective green time or green splits Establishment of yellow and all red for each phase Checking pedestrian crossing requirements 224

Cycle Length Cmin = min cycle length to accommodate critical
lane groups, sec L = total lost time for cycle, sec Xc = critical v/c ratio for the intersection (established by Agency or analyst. When operating at capacity = 1.0) Can Also be solved for, see page 255) v/sci = flow ratio for critical lane group i n= number of critical lane groups 225

Webster’s Optimum Cycle Length
Seeks to minimize delay 226

Calculate the Min and Optimal Cycle Lengths for the Example
Most agencies will establish performance metrics which determine What they operate their signals for. For example: minimize overall Delay or optimize throughput of vehicles in the arterial system. This will determine which of the cycle lengths you would work with to develop Signal timing. 227

Allocation of Green Time
Many methods to allocate green time This method is simplest to allocate green time gi= effective green time for phase i (v/s)ci= flow ratio for critical lane group i C = cycle length in seconds Xi= v/c ratio for lane group i 228

Allocate Green Time Example
Using the outcome for the 3-phase operation using the Minimum cycle length: 229

Change Interval The change interval (yellow interval) tells drivers that the green has ended and the red interval is about to begin ITE recommends yellow interval equal to: Y = yellow time (rounded to the nearest 0.5 seconds tr= driver perception/reaction time, assumed to be 1.0 sec V = speed of approaching vehicle in ft/s a= deceleration rate for approaching vehicle, normally assumed to be 10ft/sec2 g= acceleration due to gravity G = percent grade/100 230

All-Red Interval AR = all-red time (usually rounded up to the nearest 0.5 sec) w= width of the cross street in ft l=length of the vehicle, usually assumed to be 20 ft V= speed of approaching traffic in ft/s 231

Avoid Creating Dilemma Zones
Dilemma Zones are created when signal timing is implemented that does not provide enough time for the driver to stop when the yellow indication begins or to clear the intersection before the red begins Make sure your yellow and all red time is equal to or greater than the sum of equations 7.23 and 7.24 See page 232

Pedestrian Crossing Time
Pedestrians cross when opposing traffic is stopped Gp= min pedestrian green time in sec 3.2 = pedestrian start-up time in sec L = crosswalk length in ft Sp= walking speed of peds, 4.0 ft/s Nped= number of peds crossing during interval WE= effective crosswalk width in ft 233

LOS for Signalized Intersections
Average delay for a movement, approach and for the entire intersection can be calculated Next the LOS for each can be determined using the HCM 2000 thresholds (nationally defined, can be redefined to better reflect local conditions) 234

LOS Criteria for Signalized Intersections
Control delay per vehicle A ≤ 10 seconds B >10-20 seconds C >20-35 seconds D >35-55 seconds E >55-80 seconds F >80 seconds 235

Approach Delay Approach delay represents an aggregate of lane group delay dA = average delay per vehicle on approach A, sec di= average delay per vehicle for lane group i (on approach A), sec vi= analysis flow rate for lane group i in veh/hr 236

Intersection Average Delay
By aggregating the approach delays an intersection average delay can be calculated dI = average delay per vehicle for the intersection, sec dA= average delay for approach A, sec vA= analysis flow rate for approach A, veh/hr 237

In-Class Example Traffic Volumes & Lanes

Phasing Other Information: Assume 4 s of lost time per phase
Assume critical lane v/c = Xc = 0.80 T = 0.25 (15 min) k = 0.5 (pretimed control) I = 1.0 (isolated mode)

Analysis Flow Rates and Adj. Sat. Flow Rates
Adjusted Analysis Flow Rates Use given volumes Adjusted Saturation Flow Rates Phase 1 (E/W prot. LT’s): 1800 veh/h Phase 2 (E/W Th/RT’s): 3450, 3500 veh/h Phase 3 (N/S perm. LT’s): 500, 350 veh/h (N/S Th/RT’s): 1800 veh/h

Determine the Following
Cmin Green times for each phase Delay for EB approach including d1, d2 for both the left turns and the through/right vehicles

Chapter 8 Part I Travel Demand and Traffic Forecasting
From: Principles of Highway Engineering and Traffic Analysis Third Edition Fred Mannering, Walter Kilareski and Scott Washburn 242

Travel Demand & Traffic Forecasting
Necessary understand the where to invest in new facilities and what type of facilities to invest Two interrelated elements need to be considered Overall regional traffic growth/decline Potential traffic diversions 243

Traveler Decisions Four key traveler decisions need to be studied and modeled: Temporal decisions – the decision to travel and when to travel Destination decisions – where to travel (shopping centers, medical centers, etc.) Modal decisions – how to travel (auto, transit, walking, biking, etc) Route decisions – which route to travel (I-66 or Rt 50?) 244

Trip Generation Objective of this step is to develop a model which can predict when a trip will be made Typical input information Aggregate decision making units – we study households not individual travelers typically Segment trips by type – three types 1) work trips 2) shopping trips and 3) social/recreational trips Aggregate temporal decisions – trips per hour or per day 247

Trip Generation Model Typically assume linear form
Typical variables which influence number of trips are Household income Household size Number of non-working household members Employment rates in the neighborhood Etc. 249

Typical Trip Generation Model
250

Trip Generation Model Example Problem
Number of peak hour vehicle-based shopping trips per household = (household size) (annual household income in $1,000s) – 0.15 (employment in the household’s neighborhood in 100s) A household with 6 members; annual income of $50k; current neighborhood has 450 retail employees; new neighborhood has 150 retail employees. 251

Trip Generation with Count Data Models
Linear regression models can produce fractions of trips which are not realistic Poisson regression can be used to estimate trip generation for a given trip type to address this problem 252

Poisson Regression Model
253

Estimating Poisson Parameter
254

Example 8.4 Given: BZi= -0.35 + 0.03 (household size) +
(0.004) annual household income in 1,000s – 0.10 (employment in household’s neighborhood in 100s) Household has 6 members; income of $50k; lives in neighborhood with 150 retail employment; what is expected no of peak hour shopping trips? What is prob household will not make peak hour shopping trip? 255

Road Vehicle Performance

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