2.1 Uninterrupted Flow Capacity and Level of Service (LOS)

Introduction to Uninterrupted Flow

In transportation engineering, highway facilities are categorized based on the presence of external factors that interrupt traffic. Uninterrupted flow facilities have no fixed control elements, such as traffic signals, stop signs, or toll plazas, that force traffic to stop. On these facilities, traffic flow is governed by the physical characteristics of the roadway, traffic volume, and the interactions among vehicles in the traffic stream. Typical examples include basic freeway segments, multilane highways (especially rural segments with low access-point densities), and two-lane highways.

Conversely, interrupted flow facilities feature external controls that periodically halt traffic or significantly restrict the flow. This section focuses on the capacity and operational analysis of uninterrupted facilities using the guidelines set forth in the Highway Capacity Manual (HCM) and tested in the NCEES PE Civil Transportation exam.

The Fundamental Traffic Flow Relationship

Traffic flow analysis is built upon the fundamental relationship between three key parameters: flow rate (q), space mean speed (u), and density (k). This relationship is expressed as:

q = u × k

Where:

• Flow Rate (q): The rate at which vehicles pass a point on a highway, typically expressed in vehicles per hour (veh/h) or passenger cars per hour per lane (pc/h/ln).

• Space Mean Speed (u): The average speed of vehicles over a given length of road, computed as the harmonic mean of the speeds of individual vehicles. It is different from Time Mean Speed (u_t), which is the simple arithmetic mean of speeds measured at a single point over time. Space mean speed is always less than or equal to time mean speed because it averages speeds over space rather than time. The formula for space mean speed is:

  u_s = n / Σ(1 / u_i)

  Where n is the number of speed measurements and u_i is the speed of vehicle i.

• Density (k): The concentration of vehicles over a given length of roadway, expressed in vehicles per mile (veh/mi) or passenger cars per mile per lane (pc/mi/ln).

The Fundamental Diagram of Traffic Flow

The relationship between these variables is visualized using three curves, collectively known as the Fundamental Diagram of Traffic Flow:

1. Speed-Density (u vs. k): As density increases, speed decreases. In Greenshields' classic linear model, this is represented as:

   u = u_f × (1 − k / k_j)

   Where u_f is the free-flow speed (speed at zero density) and k_j is the jam density (density when traffic stops completely).

2. Flow-Density (q vs. k): This relationship is parabolic. At zero density, flow is zero. As density increases, flow increases up to a maximum value, known as the capacity (q_max), which occurs at the critical density (k_c = k_j / 2). Beyond this point, further increases in density lead to congestion and a decrease in flow, eventually reaching zero at jam density (k_j).

3. Speed-Flow (u vs. q): This curve is backwards-bending. The upper portion represents stable, uncongested flow (high speed, low density). The lower portion represents unstable, congested flow (low speed, high density). The peak of the curve represents capacity.

Basic Freeway Segments Analysis

A basic freeway segment is a portion of a freeway that is outside the influence of ramp merges, diverges, and weaving areas. The HCM methodology evaluates these segments by calculating their Level of Service (LOS) using traffic density as the primary service measure.

Step-by-Step Methodology

1. Calculate the Adjusted Demand Flow Rate (v_p)

Raw traffic volumes must be adjusted to represent equivalent passenger-car flow rates under peak 15-minute conditions. The equation is:

v_p = V / (PHF × N × f_HV × f_p)

Where:

• V = Hourly traffic volume (veh/h).

• PHF = Peak Hour Factor, which measures the uniformity of flow within the peak hour. It is calculated as PHF = V / (4 × V_15), where V_15 is the maximum 15-minute volume.

• N = Number of travel lanes in one direction.

• f_HV = Heavy-vehicle adjustment factor, which accounts for the space occupied by trucks and recreational vehicles (RVs) and their lower performance capabilities. It is calculated as:

  f_HV = 1 / [1 + P_T × (E_T − 1) + P_R × (E_R − 1)]

  Where P_T and P_R are the proportions of trucks/buses and RVs in the traffic stream, respectively. E_T and E_R are the passenger-car equivalents. Under HCM guidelines, typical terrain-based equivalents are:

  • Level Terrain: E_T = 1.5, E_R = 1.2
  • Rolling Terrain: E_T = 2.5, E_R = 2.0

• f_p = Driver population factor. It is typically 1.00 for familiar commuter traffic, but ranges between 0.85 and 1.00 for recreational or unfamiliar driver populations.

2. Estimate the Free-Flow Speed (FFS)

Free-flow speed is the average speed of passenger cars under low volume conditions. On freeways, it is calculated by adjusting the Base Free-Flow Speed (BFFS) for physical characteristics:

FFS = BFFS − f_LW − f_TLC − f_N − f_ID

Where:

• BFFS = Base Free-Flow Speed (normally 70 or 75 mph).
• f_LW = Adjustment for lane width. The base lane width is 12 ft. Narrower lanes restrict flow, reducing FFS:
  • 11-ft lanes: f_LW = 1.9 mph
  • 10-ft lanes: f_LW = 6.6 mph
• f_TLC = Adjustment for right-side lateral clearance. The base right shoulder clearance is >= 6 ft. Reductions apply for narrower clearances and depend on the number of lanes per direction. For a 3-lane direction, a 4-ft clearance reduces FFS by 0.8 mph, while a 2-ft clearance reduces it by 2.4 mph.
• f_N = Adjustment for the number of lanes. Base is >= 5 lanes per direction. Reductions are:
  • 4 lanes: f_N = 1.5 mph
  • 3 lanes: f_N = 3.0 mph
  • 2 lanes: f_N = 4.5 mph
• f_ID = Adjustment for interchange density. Base is <= 0.5 interchanges per mile. FFS is reduced as the density increases (e.g., a reduction of 2.5 mph per unit increase above 0.5 interchanges/mi).

3. Estimate Space Mean Speed (S)

Once FFS and v_p are determined, the space mean speed is calculated. Under HCM speed-flow relationships, speed is constant at FFS up to a specific flow breakpoint. Beyond the breakpoint, speed decreases until it reaches capacity. For example, for a freeway with FFS of 75 mph, the breakpoint is 1,000 pc/h/ln, and speed decreases to 53 mph at capacity (2,400 pc/h/ln). For FFS of 65 mph, the breakpoint is 1,400 pc/h/ln.

4. Calculate Density (D) and Determine Level of Service (LOS)

Traffic density (D) represents the service measure. It is computed as:

D = v_p / S

Where D is in passenger cars per mile per lane (pc/mi/ln). LOS is determined using the density thresholds shown in the table below:

Multilane Highways

Multilane highways differ from freeways because they lack full access control, may feature at-grade intersections, and can have different median types. Free-flow speed is adjusted as:

FFS = BFFS − f_LW − f_TLC − f_M − f_A

Where f_M is the median adjustment (undivided is 1.6 mph, divided is 0.0 mph, TWLTL is 0.0 mph) and f_A is the access point density adjustment (reductions of 2.5 mph apply for every 10 access points per mile).