3.1 Traffic Volume, Speed, and Planning Studies

3.1 Traffic Volume, Speed, and Planning Studies

Traffic Volume Metrics and Calculations

Traffic volume is the number of vehicles passing a given point on a roadway during a specified time interval. In traffic engineering, volumes are normalized over different time frames to assist in planning, design, and operations.

Average Daily Traffic (ADT) and Annual Average Daily Traffic (AADT)

• Average Daily Traffic (ADT): The average number of vehicles passing a point during a period of time greater than one day and less than one year (typically 2 to 7 days). It is calculated as: $ADT = \frac{\text{Total Volume during Period}}{\text{Number of Days in Period}}$
• Annual Average Daily Traffic (AADT): The average number of vehicles passing a point daily over a full year (365 days). It is computed as: $AADT = \frac{\text{Total Volume in one Year}}{365}$

Because count programs cannot run continuously at all locations, short-term coverage counts (e.g., 48 hours) are adjusted to estimate AADT using monthly ($MF$), seasonal ($SF$), and daily ($DF$) adjustment factors derived from nearby Permanent Traffic Recorders (PTRs): $AADT = \text{ADT} \times MF \times DF$

Design Hourly Volume (DHV) and Directional Design Hourly Volume (DDHV)

Designing a highway for the absolute peak hourly volume is economically infeasible, while designing for the average volume results in congestion for half the year. Engineers balance this using the Design Hourly Volume (DHV), typically defined as the 30th highest hourly volume of the year ($30DHV$). $DHV = AADT \times K$ where $K$ (the proportion of daily traffic occurring during the design hour) typically ranges from:

• $0.08$ to $0.12$ for urban arterials
• $0.12$ to $0.18$ for rural highways

For multi-lane facilities, flow is directional. The Directional Design Hourly Volume (DDHV) represents the peak-direction volume during the design hour: $DDHV = AADT \times K \times D$ where $D$ is the directional distribution factor, expressing the proportion of traffic traveling in the peak direction (typically $0.50$ to $0.80$).

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Speed Studies: Statistical Definitions and Metrics

Speed is a key parameter in determining level of service, safety, and operational efficiency. Traffic speed studies utilize several key statistical metrics.

Time Mean Speed ($u_t$) vs. Space Mean Speed ($u_s$)

Traffic speed measurements differ based on whether they are taken at a single point over time or across a space segment:

1. Time Mean Speed ($u_t$): The arithmetic mean of the spot speeds of all vehicles passing a point during a specified time interval: $u_t = \frac{1}{n} \sum_{i=1}^{n} u_i$
2. Space Mean Speed ($u_s$): The harmonic mean of the speeds of all vehicles occupying a given section of road over a specified time interval. It represents the ratio of travel distance ($L$) to average travel time ($t_i$): $u_s = \frac{n}{\sum_{i=1}^{n} \frac{1}{u_i}} = \frac{n \cdot L}{\sum_{i=1}^{n} t_i}$

Space mean speed is always less than or equal to time mean speed ($u_s \le u_t$). The difference decreases as the variance in vehicle speeds ($\sigma_s^2$) approaches zero: $u_t = u_s + \frac{\sigma_s^2}{u_s}$ In capacity analysis and traffic flow theory ($q = k \cdot u$), the space mean speed $u_s$ must be used, as time mean speed will overestimate density.

Percentile Speeds

In spot speed studies, individual speeds are plotted as a cumulative frequency distribution:

• 85th Percentile Speed: The speed at or below which 85% of vehicles travel. It is the primary engineering standard used to set regulatory speed limits.
• 15th Percentile Speed: The speed at or below which 15% of vehicles travel. Often used to determine minimum speed limits or identify slow-moving hazards.
• 50th Percentile Speed (Median): The speed representing the middle of the distribution.

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Travel Time and Delay Studies: Moving Observer Method

The Moving Observer Method (or moving vehicle technique) is a field study method to determine average volume, density, and travel time along a segment using a single test vehicle. The test vehicle makes multiple runs in both directions (with and against the flow of interest).

Let the direction of interest be the westbound direction. The test vehicle makes runs going westbound (with the traffic, subscript $w$) and eastbound (against the traffic, subscript $a$). The following values are recorded:

• $t_w, t_a$: Travel times of the test vehicle with and against the stream, respectively.
• $x$: Number of vehicles met by the test vehicle when traveling against the stream (eastbound).
• $o$: Number of vehicles that overtake the test vehicle when traveling with the stream (westbound).
• $p$: Number of vehicles that the test vehicle overtakes when traveling with the stream (westbound).
• $y$: Net overtakes, where $y = o - p$.

The hourly flow rate ($q$) in the direction of interest (westbound) is calculated as: $q = \frac{x + y}{t_w + t_a}$ The average travel time ($\bar{t}$) of the traffic stream in the direction of interest is: $\bar{t} = t_w - \frac{y}{q}$ Once flow ($q$) and average travel time ($\bar{t}$) are known, the density ($k$) of the segment is found using the fundamental relationship: $k = \frac{q}{u_s} = \frac{q \cdot \bar{t}}{L}$

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Trip Generation and Modal Split

Transportation planning utilizes a macro-level approach to predict travel behavior.

Trip Generation

Trip generation models estimate the number of trip productions ($P$) and attractions ($A$) for each Traffic Analysis Zone (TAZ). It uses linear regression or cross-classification: $T = a + b \cdot X$ where $T$ is the number of trips, $X$ is an independent variable (e.g., household size, employment count), and $a, b$ are calibration coefficients.

Modal Split (Mode Choice)

Modal split models predict the proportion of travelers choosing a specific mode (e.g., auto, transit, walking). The multinomial logit model is the industry standard: $P(i) = \frac{e^{U_i}}{\sum_{j=1}^{m} e^{U_j}}$ where $P(i)$ is the probability of choosing mode $i$, and $U_i$ is the utility function of mode $i$ (commonly a function of travel time, cost, and comfort parameters): $U_i = a_i - \beta_1 (\text{Time}_i) - \beta_2 (\text{Cost}_i)$