Study guide
14.3 Volume Count Methodologies & Expansion Factoring (ADT, AADT, PHF)
Professional Traffic Operations Engineer PTOE
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1 Introduction & PTOE Exam Overview
1.1 The PTOE Credential: Certification Overview & Industry Value 1.2 Core Industry Reference Standards in Traffic Operations 1.3 Study Guide Architecture, Blueprint Alignment & Exam-Day Strategy
2 Domain 1: Traffic Flow Theory & Fundamental Concepts
2.1 Macroscopic Traffic Stream Models & Fundamental Diagram (q = k × u) 2.2 Microscopic Traffic Characteristics & Car-Following Models 2.3 Hydrodynamic Shockwave Analysis & Traffic Queuing Models
3 Domain 1: Highway & Interrupted Flow Capacity Analysis (HCM)
3.1 Basic Freeway Segments & Multilane Highways (HCM 7th Edition) 3.2 Freeway Weaving, Merging, and Diverging Segments 3.3 Signalized Intersection Capacity & Delay Modeling (HCM)
4 Domain 1: Managed Lanes, Transit Priority, TSMO & Travel Demand Management
4.1 Unsignalized Intersections (TWSC, AWSC) & Modern Roundabouts Capacity 4.2 Managed Lanes, HOV/HOT Operations, & Ramp Metering 4.3 Transit Priority & Multimodal Signal Operations (TSP) 4.4 Transportation Systems Management and Operations (TSMO) & Regional ITS 4.5 Travel Demand Management (TDM) & Trip Reduction Strategies
5 Domain 2: Geometric Design Controls, Criteria, & Sight Distance
5.1 Functional Classification, Design Controls, & Context-Sensitive Design 5.2 Sight Distance Principles: Stopping, Decision, & Passing (AASHTO) 5.3 Horizontal Alignment, Curve Radius, & Superelevation Design
6 Domain 2: Roadway Cross-Sections & Access Management
6.1 Vertical Alignment: Tangent Grades, Crest & Sag Vertical Curves 6.2 Roadway Cross-Section Elements & AASHTO Clear Zone Concepts 6.3 Access Management Principles & Driveway Spacing Criteria
7 Domain 2: Intersection & Interchange Geometric Design
7.1 Intersection Channelization, Turn Lane Design, & Storage Length 7.2 Interchange Configurations & Operational Comparisons (Diamond, Cloverleaf, SPUI) 7.3 Diverging Diamond Interchanges (DDI / DCMI) Operational Principles 7.4 Modern Roundabout Geometric Design Elements & Fastest Paths 7.5 Multimodal Geometric Design: Pedestrian Facilities, Bikeways, & ADA
8 Domain 3: Traffic Safety Concepts, Human Factors, & Safe System
8.1 The Safe System Approach & Vision Zero Principles 8.2 Human Factors, Driver Expectancy, & Perception-Reaction Time (PRT) 8.3 Crash Collision Typologies & Statistical Rate Formulations (MEV, MVMT)
9 Domain 3: Highway Safety Manual (HSM) Predictive Methods & EB
9.1 Highway Safety Manual (HSM) Predictive Methodology & Part C Models 9.2 Safety Performance Functions (SPFs) & Crash Modification Factors (CMFs) 9.3 Empirical Bayes (EB) Method & Regression-to-the-Mean (RTM) Correction 9.4 Economic Appraisal of Safety Projects (Benefit-Cost Analysis, NPV)
10 Domain 3: Safety Countermeasures & Road Safety Audits (RSA)
10.1 Roadway Departure Countermeasures (Rumble Strips, Safety Edge, Barriers) 10.2 Intersection Safety Countermeasures (Sight Triangles, Left-Turn Calming, Roundabouts) 10.3 Vulnerable Road User (VRU) Safety Countermeasures (PHB/HAWK, RRFB, Curb Extensions) 10.4 Road Safety Audits (RSAs) & Systemic Safety Analysis
11 Domain 4: Traffic Signal Warrants & Isolated Timing (MUTCD/ITE)
11.1 MUTCD Traffic Signal Warrants (Warrants 1 through 9) 11.2 Signal Phasing Principles & NEMA Dual-Ring Operations 11.3 Clearance Intervals (ITE Kinematic Equations) & Pedestrian Timing Parameters
12 Domain 4: Signal Coordination, Networks, & ATSPMs
12.1 Actuated Signal Controller Parameters (Passage Time, Gap Reduction, Max Recall) 12.2 Traffic Signal Coordination: Bandwidth, Offsets, & Progression Models 12.3 Traffic Responsive & Adaptive Traffic Signal Control Systems (ASCS) 12.4 Automated Traffic Signal Performance Measures (ATSPMs) & High-Resolution Data
13 Domain 4: Signing, Markings, Work Zones, Grade Crossings & School Zones (MUTCD)
13.1 MUTCD Regulatory, Warning, & Guide Signs Principles and Placement 13.2 Sign Retroreflectivity Standards & Nighttime Visual Maintenance 13.3 Longitudinal Pavement Markings, Delineators, & Object Markers 13.4 Temporary Traffic Control (TTC) & Work Zone Safety (MUTCD Part 6) 13.5 Highway-Rail Grade Crossings: Warning Devices, Preemption & Storage 13.6 School Zone Traffic Control & Student Walk Route Planning
14 Domain 5: Traffic Studies & Applied Statistical Methods
14.1 Applied Statistical Distributions & Sample Size Determination 14.2 Spot Speed Studies, 85th Percentile Speed, & 10-mph Pace 14.3 Volume Count Methodologies & Expansion Factoring (ADT, AADT, PHF)
15 Domain 5: Traffic Impact Studies & Trip Generation (ITE)
15.1 Travel Time, Delay, & Intersection Queue Studies 15.2 Parking Supply, Duration, & Turnover Analysis 15.3 Traffic Impact Study (TIS) Scoping, Horizon Years, & Mitigation 15.4 ITE Trip Generation Handbook: Average Rates vs. Regression Equations
16 Domain 6: Environmental, Institutional, Ethics & Equity Issues
16.1 Vehicle Emissions, Air Quality Conformity, & Decarbonization 16.2 Traffic Noise Modeling (TNM) & Noise Abatement Criteria (NAC) 16.3 Long-Range Transportation Planning & the NEPA Environmental Review 16.4 Professional Engineering Ethics, Tort Liability, & Risk Management 16.5 Transportation Equity, Access & Multimodal Community Considerations
14.3 Volume Count Methodologies & Expansion Factoring (ADT, AADT, PHF)
Key Takeaways Explain This Topic AI
Average Daily Traffic (ADT) represents the average 24-hour volume over a sampling period of less than a full year, whereas Annual Average Daily Traffic (AADT) is the total annual volume divided by 365 days.
Short-duration (24-to-48 hour) counts are expanded to estimate AADT using monthly (M_i), daily of week (D_i), and axle (A_i) adjustment factors: AADT = Vol_24hr * M_i * D_i * A_i.
The K-factor (K = DHV / AADT) represents the proportion of daily traffic occurring during the design peak hour, typically ranging from 0.08 to 0.12 (8-12%) for urban corridors and 0.12 to 0.18 (12-18%) for rural roadways.
The Directional Distribution factor (D) defines the proportion of peak-hour traffic in the dominant flow direction, yielding Directional Design Hour Volume: DDHV = AADT * K * D.
The Peak Hour Factor (PHF = V / [4 * V_15max]) relates the hourly volume to the peak 15-minute flow rate (v = V / PHF), quantifying flow peakedness and capacity constraints during the peak hour.
Last updated: August 2026
14.3 Volume Count Methodologies & Expansion Factoring (ADT, AADT, PHF)
PTOE Exam Focus: Traffic volume studies and expansion factoring are among the most heavily tested quantitative topics in Domain 5. Candidates must master the calculation of AADT from short-term sample counts using monthly ( M i M_i M i ), daily ( D i D_i D i ), and axle ( A i A_i A i ) adjustment factors, compute Design Hour Volume (DHV) and Directional Design Hour Volume (DDHV) using K K K and D D D factors, and compute the Peak Hour Factor ( PHF = V 4 ⋅ V 15 , max \text{PHF} = \frac{V}{4 \cdot V_{15,\max}} PHF = 4 ⋅ V 15 , m a x V ) to convert hourly volumes into peak 15-minute flow rates for HCM capacity analysis.
1. Traffic Volume Counting Methodologies
Traffic volume data provides the fundamental demand input for highway capacity analysis, geometric sizing, pavement design, and signal warrant evaluation. Volume studies utilize three primary counting technologies: +-----------------------------------------------------------------------------------+
- | TRAFFIC VOLUME DATA COLLECTION TYPOLOGIES |
- | |
- | 1. Automated Traffic Recorders (ATRs): |
- | • Permanent continuous stations (inductive loops, piezos) operating 365 days. |
- | • Establish statewide seasonal, monthly, and day-of-week expansion factors. |
- | |
- | 2. Portable Automatic Counts (Mid-Block): |
- | • Pneumatic road tubes, radar side-fire sensors deployed for 24-48 hours. |
- | • Measure 24-hr daily volume, speed bins, and vehicle axle classification. |
- | |
- | 3. Manual / Video AI Turning Movement Counts (TMCs): |
- | • 2-hr to 4-hr intersection counts binned in 15-minute intervals. |
- | • Tallies passenger cars, heavy vehicles, buses, bicycles, and pedestrians. |
- +-----------------------------------------------------------------------------------+
- 2. Daily Volume Definitions: ADT vs. AADT
Traffic volume exhibits significant temporal variations by hour of the day, day of the week, and month of the year. Engineering standards define two distinct daily volume metrics:
1. Average Daily Traffic (ADT)
The total volume of traffic passing a point or segment over a specified observation period of greater than 1 day and less than 1 year (typically 24 to 72 hours 24\text{ to }72\text{ hours} 24 to 72 hours ), divided by the number of days in that period: ADT = Total Sample Volume Number of Sampling Days ( Q ) ( 1 < Q < 365 ) \text{ADT} = \frac{\text{Total Sample Volume}}{\text{Number of Sampling Days } (Q)} \quad (1 < Q < 365) ADT = Number of Sampling Days ( Q ) Total Sample Volume ( 1 < Q < 365 )
2. Annual Average Daily Traffic (AADT)
The total vehicular volume passing a point or roadway segment over an entire year (365 days), divided by 365: AADT = Total Annual Traffic Volume 365 \text{AADT} = \frac{\text{Total Annual Traffic Volume}}{365} AADT = 365 Total Annual Traffic Volume
Key Distinction: ADT is a localized sample measurement subject to seasonal and day-of-week bias, whereas AADT represents the unbiased annualized daily average used for state highway planning, HPMS reporting, crash rate calculations, and pavement structural design.
3. Expansion Factoring Methodology (Short-Term to AADT)
Because permanent ATR counters can only be maintained at a limited number of regional control stations, the vast majority of roadway counts are short-term counts ( 24 to 48 hours 24\text{ to }48\text{ hours} 24 to 48 hours ) collected via pneumatic road tubes on mid-week days (Tuesday, Wednesday, Thursday). These short counts are expanded to AADT using adjustment factors derived from nearby ATR stations on functionally similar highways. +------------------------+
- | Raw 24-hr Tube Count |
- | (Total Axle Strikes) |
- +-----------+------------+
- |
- v x Axle Correction Factor (A_i = 2 / Avg Axles)
- +-----------+------------+
- | Total Vehicles (24-hr) |
- +-----------+------------+
- |
- v x Daily Adjustment Factor (D_i = ADT_week / Vol_day)
- +-----------+------------+
- | Weekly Adjusted Volume |
- +-----------+------------+
- |
- v x Monthly Adjustment Factor (M_i = AADT / ADT_month)
- +-----------+------------+
- | Estimated AADT |
- +------------------------+
- 1. Monthly Expansion Factor ( M i M_i M i )
Adjusts for seasonal and monthly fluctuations: M i = AADT ADT month i M_i = \frac{\text{AADT}}{\text{ADT}_{\text{month } i}} M i = ADT month i AADT
In peak summer travel months (where ADT July > AADT \text{ADT}_{\text{July}} > \text{AADT} ADT July > AADT ), M July < 1.0 M_{\text{July}} < 1.0 M July < 1.0 .
In low winter travel months (where ADT Jan < AADT \text{ADT}_{\text{Jan}} < \text{AADT} ADT Jan < AADT ), M Jan > 1.0 M_{\text{Jan}} > 1.0 M Jan > 1.0 .
2. Daily Expansion Factor ( D i D_i D i )
Adjusts for day-of-the-week fluctuations: D i = Average Weekday Daily Traffic (AWDT) Volume on Specific Day i D_i = \frac{\text{Average Weekday Daily Traffic (AWDT)}}{\text{Volume on Specific Day } i} D i = Volume on Specific Day i Average Weekday Daily Traffic (AWDT)
3. Axle Correction Factor ( A i A_i A i )
Pneumatic road tubes record one count for every two axle strikes (1 pulse = 2 axles). Because multi-axle commercial trucks (3-axle, 4-axle, 5-axle semi-trailers) register multiple pulses for a single vehicle, raw tube counts overestimate vehicle volumes. The axle correction factor compensates for this stream composition: A i = Actual Vehicles Recorded Pulses = 2 n ˉ axles A_i = \frac{\text{Actual Vehicles}}{\text{Recorded Pulses}} = \frac{2}{\bar{n}_{\text{axles}}} A i = Recorded Pulses Actual Vehicles = n ˉ axles 2
Where n ˉ axles \bar{n}_{\text{axles}} n ˉ axles is the weighted average number of axles per vehicle in the traffic stream.
Master AADT Expansion Equation: AADT = Vol raw 24hr × A i × D i × M i \text{AADT} = \text{Vol}_{\text{raw 24hr}} \times A_i \times D_i \times M_i AADT = Vol raw 24hr × A i × D i × M i
4. Design Hour Volume (DHV) & The K K K -Factor
Designing a highway to accommodate the single highest hourly volume of the year is economically wasteful, as that capacity would sit idle for 8 , 759 hours 8,759\text{ hours} 8 , 759 hours . Conversely, designing for the average hourly volume would result in severe oversaturation and gridlock during daily commute hours.
The 30th Highest Hourly Volume ( 30 HV 30\text{HV} 30 HV )
Standard engineering practice establishes the Design Hour Volume (DHV) as the 30th highest hourly volume of the year ( 30 HV 30\text{HV} 30 HV ). On a curve of hourly volumes ranked from highest to lowest (1 to 8760), the slope transitions from very steep to relatively flat near the 30th hour, providing the optimal economic balance between construction capital and operational congestion.
The K K K -Factor Formulation
The K K K -factor is the ratio of the Design Hour Volume to the Annual Average Daily Traffic: K = DHV AADT = 30 HV AADT ⟹ DHV = AADT × K K = \frac{\text{DHV}}{\text{AADT}} = \frac{30\text{HV}}{\text{AADT}} \implies \text{DHV} = \text{AADT} \times K K = AADT DHV = AADT 30 HV ⟹ DHV = AADT × K
Typical K K K -Factor Ranges:
Urban Arterials / Freeways: K = 0.08 to 0.12 K = 0.08\text{ to }0.12 K = 0.08 to 0.12 ( 8 % to 12 % 8\%\text{ to }12\% 8% to 12% ). Urban corridors experience peak spreading and constrained capacity, leading to lower K K K -values.
Rural / Recreational Highways: K = 0.12 to 0.18 + K = 0.12\text{ to }0.18+ K = 0.12 to 0.18 + ( 12 % to 18 % 12\%\text{ to }18\% 12% to 18% ). Rural and tourist routes experience sharp, highly concentrated weekend and seasonal peaks.
5. Directional Distribution ( D D D -Factor) & DDHV
Traffic during peak hours is rarely distributed equally between travel directions. The Directional Distribution Factor ( D D D ) represents the proportion of total peak hour bidirectional traffic traveling in the dominant (peak) direction: D = V peak-direction DHV D = \frac{V_{\text{peak-direction}}}{\text{DHV}} D = DHV V peak-direction
Directional Design Hour Volume (DDHV)
To determine the required number of travel lanes for a specific approach or direction, highway capacity analyses use the Directional Design Hour Volume (DDHV) : DDHV = AADT × K × D \text{DDHV} = \text{AADT} \times K \times D DDHV = AADT × K × D
Typical D D D -Factor Ranges:
Radial Suburban Commuter Corridors: D = 0.60 to 0.70 D = 0.60\text{ to }0.70 D = 0.60 to 0.70 ( 60 % to 70 % 60\%\text{ to }70\% 60% to 70% inbound AM / outbound PM).
Urban Downtown Grid / Circumferential Belts: D = 0.50 to 0.55 D = 0.50\text{ to }0.55 D = 0.50 to 0.55 (balanced two-way demand).
6. Peak Hour Factor (PHF) & Sub-Hourly Flow Rates
Within the peak hour, vehicle arrivals are not uniformly distributed. Flow surges occurring within localized 15 -minute 15\text{-minute} 15 -minute intervals can cause temporary breakdown even if the total hourly volume is within nominal capacity.
Mathematical Formulation
The Peak Hour Factor (PHF) quantifies the relationship between total hourly volume and the maximum flow rate within that hour: PHF = V 4 × V 15 , max \text{PHF} = \frac{V}{4 \times V_{15,\max}} PHF = 4 × V 15 , m a x V
Where:
V V V = Total hourly volume (vehicles per hour, veh/h)
V 15 , max V_{15,\max} V 15 , m a x = Maximum volume recorded during any single 15 -minute 15\text{-minute} 15 -minute interval within the peak hour
- 4 4 4 = Number of 15 -minute 15\text{-minute} 15 -minute periods in one hour
- Peak 15-Minute Equivalent Flow Rate ( v v v )
In Highway Capacity Manual (HCM) analyses, all demand volumes are converted to equivalent peak 15 -minute 15\text{-minute} 15 -minute hourly flow rates ( v v v ): v = V PHF = 4 × V 15 , max v = \frac{V}{\text{PHF}} = 4 \times V_{15,\max} v = PHF V = 4 × V 15 , m a x
Key PHF Properties:
Range: 0.25 ≤ PHF ≤ 1.00 0.25 \le \text{PHF} \le 1.00 0.25 ≤ PHF ≤ 1.00
PHF = 1.00 \text{PHF} = 1.00 PHF = 1.00 : Perfectly uniform flow ( V 15 V_{15} V 15 is identical in all four quarters).
PHF = 0.25 \text{PHF} = 0.25 PHF = 0.25 : Extreme peaking (all hourly volume arrives in a single 15-minute window).
Typical Field Values:
Dense urban networks / congested freeways: PHF = 0.92 to 0.98 \text{PHF} = 0.92\text{ to }0.98 PHF = 0.92 to 0.98
- Suburban arterials: PHF = 0.85 to 0.92 \text{PHF} = 0.85\text{ to }0.92 PHF = 0.85 to 0.92
- Rural or low-volume roads: PHF = 0.70 to 0.85 \text{PHF} = 0.70\text{ to }0.85 PHF = 0.70 to 0.85
Traffic Volume Factoring Parameters & Typical Design Ranges
Parameter / Factor Mathematical Definition Typical Range (Urban) Typical Range (Rural) Primary Engineering Purpose
Monthly Factor (M_i) M_i = AADT / ADT_month 0.90 - 1.10 0.75 - 1.35 Removes seasonal bias from short-duration sample counts
Daily Factor (D_i) D_i = AWDT / Vol_day 0.95 - 1.05 0.85 - 1.20 Adjusts for day-of-week variation (Tuesday vs Friday)
Axle Factor (A_i) A_i = 2 / Avg Axles per Veh 0.92 - 0.98 0.85 - 0.94 Converts pneumatic tube axle strikes into actual vehicle counts
K-Factor K = DHV / AADT (30HV) 0.08 - 0.12 (8 - 12%) 0.12 - 0.18 (12 - 18%) Determines Design Hour Volume from annualized daily traffic
D-Factor D = V_peak-dir / DHV 0.50 - 0.65 0.55 - 0.75 Allocates peak hour traffic to the critical direction of travel
Peak Hour Factor (PHF) PHF = V / (4 * V_15max) 0.90 - 0.98 0.70 - 0.85 Expands hourly volume to peak 15-minute flow rate for HCM capacity
Loading diagram... Hierarchical Traffic Volume Factoring & Design Volume Calculation Flow
Peak Hour Volume Fluctuation Across 15-Minute Bins (V = 1,420 veh/hr, V_15max = 420 veh, PHF = 0.845)
- 7. Worked Calculation Examples
- Example 1: Full AADT Expansion from 24-Hour Tube Counts
Problem: A 24-hour pneumatic tube count conducted on a Wednesday in April records 22 , 400 total axle pulses 22,400\text{ total axle pulses} 22 , 400 total axle pulses (where 1 pulse = 2 axles). Classification data indicates the average number of axles per vehicle on this corridor is n ˉ axles = 2.15 \bar{n}_{\text{axles}} = 2.15 n ˉ axles = 2.15 . The state DOT ATR group factors for this highway classification are:
- Monthly Factor ( M April M_{\text{April}} M April ): 1.08 1.08 1.08
- Day-of-Week Factor ( D Wednesday D_{\text{Wednesday}} D Wednesday ): 0.96 0.96 0.96
Calculate the estimated Annual Average Daily Traffic (AADT).
Step-by-Step Solution:
Axle Correction Factor ( A i A_i A i ): A i = 2 n ˉ axles = 2 2.15 = 0.9302 A_i = \frac{2}{\bar{n}_{\text{axles}}} = \frac{2}{2.15} = 0.9302 A i = n ˉ axles 2 = 2.15 2 = 0.9302
Actual 24-Hour Vehicle Count ( Vol 24 hr \text{Vol}_{24\text{hr}} Vol 24 hr ): Vol 24 hr = 22 , 400 × 0.9302 = 20 , 836.5 vehicles \text{Vol}_{24\text{hr}} = 22,400 \times 0.9302 = 20,836.5\text{ vehicles} Vol 24 hr = 22 , 400 × 0.9302 = 20 , 836.5 vehicles
Compute AADT using Master Expansion Formula: AADT = Vol 24 hr × D Wed × M April \text{AADT} = \text{Vol}_{24\text{hr}} \times D_{\text{Wed}} \times M_{\text{April}} AADT = Vol 24 hr × D Wed × M April AADT = 20 , 836.5 × 0.96 × 1.08 = 20 , 003.04 × 1.08 = 21 , 603.3 ≈ 21 , 603 veh/day \text{AADT} = 20,836.5 \times 0.96 \times 1.08 = 20,003.04 \times 1.08 = 21,603.3 \approx 21,603\text{ veh/day} AADT = 20 , 836.5 × 0.96 × 1.08 = 20 , 003.04 × 1.08 = 21 , 603.3 ≈ 21 , 603 veh/day
Example 2: DDHV and Peak 15-Minute Flow Rate Calculation
Problem: A planned 4-lane suburban divided highway has an estimated AADT of 32 , 000 veh/day 32,000\text{ veh/day} 32 , 000 veh/day . Traffic engineering studies establish the following design parameters:
- Design Hour Factor: K = 0.11 K = 0.11 K = 0.11
- Directional Split: D = 0.65 D = 0.65 D = 0.65
- Peak Hour Factor: PHF = 0.88 \text{PHF} = 0.88 PHF = 0.88
Compute the Directional Design Hour Volume (DDHV) and the peak 15 -minute 15\text{-minute} 15 -minute equivalent hourly flow rate ( v v v ).
Step-by-Step Solution:
Compute Directional Design Hour Volume (DDHV): DDHV = AADT × K × D \text{DDHV} = \text{AADT} \times K \times D DDHV = AADT × K × D DDHV = 32 , 000 × 0.11 × 0.65 = 3 , 520 × 0.65 = 2 , 288 veh/h \text{DDHV} = 32,000 \times 0.11 \times 0.65 = 3,520 \times 0.65 = 2,288\text{ veh/h} DDHV = 32 , 000 × 0.11 × 0.65 = 3 , 520 × 0.65 = 2 , 288 veh/h
Compute Peak 15-Minute Equivalent Flow Rate ( v v v ): v = DDHV PHF = 2 , 288 veh/h 0.88 = 2 , 600 veh/h v = \frac{\text{DDHV}}{\text{PHF}} = \frac{2,288\text{ veh/h}}{0.88} = 2,600\text{ veh/h} v = PHF DDHV = 0.88 2 , 288 veh/h = 2 , 600 veh/h
Capacity Implication: If lane capacity is 1 , 900 veh/h/ln 1,900\text{ veh/h/ln} 1 , 900 veh/h/ln , two directional lanes provide 3 , 800 veh/h 3,800\text{ veh/h} 3 , 800 veh/h capacity, comfortably accommodating the 2 , 600 veh/h 2,600\text{ veh/h} 2 , 600 veh/h peak flow rate ( v / c = 0.68 v/c = 0.68 v / c = 0.68 , Level of Service C).