3.2 Traffic Forecasts and Monitoring

3.2 Traffic Forecasts and Monitoring

Long-Term Traffic Growth Forecasting

Estimating future traffic volumes is essential for highway capacity planning, geometric design, and economic feasibility studies. Growth models extrapolate historical traffic volumes to a future target year (typically a 20-year design horizon).

Arithmetic Growth Model

Arithmetic growth assumes a constant increase in the absolute number of vehicles each year. This model is typical for mature, built-out areas where land development has stabilized: $V_n = V_0 (1 + n \cdot r)$ where:

• $V_n$: Predicted volume in year $n$.
• $V_0$: Baseline volume in year 0.
• $n$: Number of forecasting years.
• $r$: Annual arithmetic growth rate (decimal).

Geometric (Exponential) Growth Model

Geometric growth assumes traffic increases at a rate proportional to its current volume, representing compound growth. This is appropriate for rapidly developing suburban areas or newly opened corridors: $V_n = V_0 (1 + r)^n$ where $r$ is the annual geometric growth rate.

---

The Four-Step Travel Demand Model

For regional planning, traffic engineers use the traditional Four-Step Travel Demand Model to forecast traffic volumes based on land use and socio-economic forecasts.

1. Trip Generation

This step determines the total number of trips produced by ($P_i$) and attracted to ($A_j$) each Traffic Analysis Zone (TAZ). Data inputs include population, number of households, income levels, and employment density. Linear regression is commonly applied: $P_i = f(\text{Households}, \text{Income})$ $A_j = f(\text{Employment}, \text{Commercial floor space})$

2. Trip Distribution

This step links the trip origins (productions) with destinations (attractions) to create an Origin-Destination (O-D) matrix. The Gravity Model is the primary method used, drawing an analogy to Newton's law of gravity: $T_{ij} = P_i \frac{A_j \cdot F_{ij} \cdot K_{ij}}{\sum_{k} A_k \cdot F_{ik} \cdot K_{ik}}$ where:

• $T_{ij}$: Number of trips from zone $i$ to zone $j$.
• $P_i$: Trip productions in zone $i$.
• $A_j$: Trip attractions in zone $j$.
• $F_{ij}$: Friction factor, representing spatial separation (usually $F_{ij} = t_{ij}^{-b}$ where $t_{ij}$ is travel time and $b$ is a calibration parameter).
• $K_{ij}$: Socio-economic adjustment factor.

3. Mode Choice (Modal Split)

This step determines the travel mode (e.g., drive-alone, shared-ride, transit, non-motorized) chosen by travelers. Logit models compute probabilities based on mode utilities. A utility function $U_m$ is defined for each mode: $U_m = a_m - b \cdot (\text{Travel Time}) - c \cdot (\text{Travel Cost})$ The probability $P(m)$ of choosing mode $m$ is: $P(m) = \frac{e^{U_m}}{\sum e^{U_k}}$

4. Traffic Assignment (Route Choice)

This final step assigns the O-D trip matrix to specific routes on the transportation network. Link travel times are adjusted as volumes increase to simulate congestion.

• User Equilibrium (UE - Wardrop's First Principle): Traffic distributes such that travel times on all used routes between an origin and destination are equal and less than or equal to the travel time on any unused route. Under UE, no individual driver can unilaterally reduce their travel time by changing routes.
• System Optimum (SO - Wardrop's Second Principle): Traffic distributes to minimize the total travel time of all vehicles in the network. This represents a cooperative state and is rarely achieved naturally.

To model the relationship between traffic volume and travel time delay, the Bureau of Public Roads (BPR) link congestion function is used: $t_a = t_0 \left[ 1 + \alpha \left( \frac{V}{C} \right)^\beta \right]$ where:

• $t_a$: Link travel time under volume $V$.
• $t_0$: Free-flow travel time.
• $V$: Traffic volume on the link.
• $C$: Link capacity.
• $\alpha, \beta$: Calibration parameters (standard default values: $\alpha = 0.15$, $\beta = 4.0$).

---

Traffic Monitoring Methods and Data Collection

Traffic monitoring provides the baseline data needed for design and planning. Continuous data collection establishes seasonal trends, while short-term counts extend spatial coverage.

Equipment and Sensors

• Intrusive Sensors (In-Roadway):
  • Inductive Loops: Wire loops cut into the pavement. They detect change in inductance caused by a passing metal vehicle. Used for count, occupancy, and speed (when configured in dual-loop speed traps).
  • Pneumatic Road Tubes: Flexible tubes placed across lanes. They register air pressure pulses as vehicle axles cross them. Ideal for short-term coverage counts (48-hour).
• Non-Intrusive Sensors (Out-of-Roadway):
  • Radar/Microwave: Measures vehicle presence and speed via Doppler shift. Does not require pavement cuts.
  • Video Image Processing (VIP): Computer vision systems that analyze video feeds to count, classify, and track vehicles.
  • Probe Data (GPS/Bluetooth/Wi-Fi): Tracks MAC addresses or GPS location pings to measure segment travel times and O-D distributions.

Vehicle Miles of Travel (VMT)

A key metric for traffic monitoring, environmental planning, and highway funding is Vehicle Miles of Travel (VMT). For a specific roadway segment, it is calculated as: $VMT = ADT \times L$ where $L$ is the length of the segment in miles. VMT can be aggregated across a network or region to assess total travel demand.