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**Capacity, Level of Service, Intersection Design (1)**

Lecture 8 (6/3/10)

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**Capacity, Level of Service, Intersection Design**

Vehicular Stream Models (Textbook 3.2) Stream Variables (Textbook 3.3) (1) Vehicular Stream Equations and Diagrams (Textbook 3.4) Highways: Uninterrupted Flow (Textbook 4.5) (2) Highways: Interrupted Flow (Textbook 4.6) (3) Capacity of Signalized Intersections (Textbook 4.7) (4)

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Traffic stream A given flow of traffic through streets, highways of defined characteristics will vary by both location, time, and vehicle mix.

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**Uninterrupted and interrupted Flows**

Uninterrupted Flow Freeways Multilane Highways Two-lane Highways Interrupted Flow Signalized Intersections Unsignalized Intersections Urban and Suburban Arterials Roundabouts

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**Vehicular Stream Models**

Vehicle Following

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**Vehicular Stream Models**

Notation:

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**Vehicular Stream Models**

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**Stream Variables Volume (V), flow rate (q) and headway (h) Speed (u)**

Density (k), Concentration and Spacing (s)

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**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.)

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**Volume, flow rate and headway**

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.

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**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)

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**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.

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**Volume, flow rate and headway**

Peak Hour Factor (PHF) For analysis purposed, in Highway Capacity manual, 15 minute interview is used. HV – Hourly Volume V15 – Maximum 15 minute volume within the hour

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**Volume, flow rate and headway**

Peak Hour Factor (PHF) Example: HV= 3000 vehicles V15 = 1000 vehicles PHF = 3000/(4*1000) = 0.75 NOTE: PHF 1.00, normal between 0.70 and 0.98 - Lower PHF indicates a greater degree of variation in flow during the peak-hour.

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**Volume, flow rate and headway**

Relationship between headway (h) and flow (q):

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**Speed v - speed (mph or fps) d - distance traversed (mi or ft)**

t - time to traverse distance d (hr or sec)

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**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. TMS = Point A (alternative way)

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**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)

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**Speed Relationship between TMS and SMS: (Proved by Wardrop in 1952)**

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)

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Speed

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**Speed Average Travel Speed and Average Running Speed :**

Travel time (tt) is defined as the total time to traverse a given highway segment. Running time (tr) is defined as the total time during which the vehicle is in motion while traversing a given highway segment. Average Travel Speed = D B Average Running Speed =

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**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 85th percentile speed is often used as a measure of the maximum reasonable speed for the traffic stream. The 15th percentile speed may be used as a measure of the minimum reasonable speed for the traffic stream.

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**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

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**Density, concentration & spacing**

u - space mean speed (mph) q - flow rate (vph)

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**Time-distance diagram of flow**

Space t1 Spacing1 t2 Spacing2 Headway1 Headway2 x1 x2

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**Time-distance diagram: uniform flow **

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**Vehicular Stream Equations and Diagrams**

Fundamental equation of a vehicular stream Case of uniform flow Note:

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**Vehicular Stream Equations and Diagrams (highway flow)**

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**Examples of realistic q-u-k relationship**

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**Vehicular Stream Equations and Diagrams (highway flow)**

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**Vehicular Stream Equations and Diagrams (highway flow)**

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**Capacity, Level of Service, Intersection Design (2)**

Lecture 9 (6/3/10)

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**Highways: Uninterrupted Flow**

Background Level of Service Freeway Base Conditions Freeway Capacity and Level of Service Freeway Congestions Quantification Capacity Restrictions

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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)

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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

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**Speed-Flow Curve and LOS**

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**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)

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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

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Peak Hour Factor

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Peak Hour Factor V = 250 veh/h

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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)

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**Example of a PHF question**

Period Volume (vph) 7:00 - 7:15 100 7:15 - 7:30 120 7:30 - 7:45 130 7:45 - 8:00 125 8:00 - 8:15 135 8:15 - 8:30 140 8:30 - 8: 45 8:45 - 9:00 115 When is the peak hour? What is the peak hour volume? What is the PHF?

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**Solution of the PHF question**

Period Volume (vph) Accumulated Volume 7:00 - 7:15 100 7:15 - 7:30 120 7:30 - 7:45 130 7:45 - 8:00 125 475 8:00 - 8:15 140 515 8:15 - 8:30 135 530 Largest 8:30 - 8: 45 525 8:45 - 9:00 115 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

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**Freeway capacity and level of service (LOS)**

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**Speed-Flow curve for basic freeway segment (HCM)**

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**Freeway capacity and level of service (LOS)**

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**Freeway capacity and level of service (LOS)**

Important Concept: Compute Vp and S in order to Compute D. Use “density thresholds” to determine LOS

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**Freeway capacity and level of service (LOS)**

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**Freeway capacity and level of service (LOS)**

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**Freeway capacity and level of service (LOS)**

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**Freeway capacity and level of service (LOS)**

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**Freeway capacity and level of service (LOS)**

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**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.

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Solution of Example 4.5

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**Freeway congestion quantification**

In addition to LOS, there are other measures: Travel rate Delay Relative delay Total delay Corridor mobility index Accessibility

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**Capacity restrictions**

Freeway capacity can be reduced due to: Accidents Spilled loads Disabled and slow-moving vehicles, and Other extraordinary events

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