What is Traffic Capacity?
Traffic capacity is the ability of a roadway to accommodate traffic volume — specifically, the maximum number of vehicles that can pass a given point on a lane or road during one hour under defined conditions. It depends on geometrical design features (lane width, gradient, curve radius), environmental conditions, and traffic mix.
Traffic capacity is a qualitative measure of maximum possible flow, while traffic volume is the quantitative actual rate of flow. Both have the same units (vehicles/hour/lane) but represent different things.
Three Types of Traffic Capacity
1. Basic Capacity
The maximum number of passenger cars that can pass a given point per lane per hour under the most nearly ideal roadway and traffic conditions. This is a theoretical maximum — conditions are rarely truly ideal. Two roads with the same physical features will always have the same basic capacity. Formula from space headway: C = 1000V/S
2. Possible Capacity
Maximum vehicles per lane per hour under prevailing (actual) roadway and traffic conditions. Generally much lower than basic capacity. It ranges from zero (complete gridlock) to basic capacity (ideal conditions). Formula from time headway: C = 3600/H_t
3. Practical Capacity (Design Capacity)
Maximum vehicles per lane per hour without causing unreasonable delay, hazard, or restriction of driver freedom to manoeuvre. This is the capacity actually used for design. Formula: C = 1000V/(L + SSD)
Greenshield’s Linear Model
Greenshield proposed the simplest model of traffic flow by assuming a linear relationship between speed and density:
V_s = V_f[1 − K/K_j]
Where V_f = free flow speed (speed at zero density), K_j = jam density (density at zero speed — vehicles standstill).
Volume-Density Relationship
Traffic volume q = K × V_s → substituting the linear model:
q = V_f[K − K²/K_j] → This is a parabola in K
Maximum Volume Condition
Differentiating q with respect to K and setting dq/dK = 0: K = K_j/2
q_max = V_f × K_j / 4
Maximum traffic volume occurs at density = half of jam density and at speed = half of free flow speed.
Key Traffic Flow Relationships
| Relationship | Formula | Notes |
|---|---|---|
| Volume-Density-Speed | q = KV (fundamental) | q in veh/hr, K in veh/km, V in km/hr |
| Maximum volume | q_max = V_f × K_j / 4 | Occurs at K = K_j/2, V_s = V_f/2 |
| Density per lane | K = 1/avg. space headway | K = vehicles per km of lane |
| Volume from headway | q = 1/avg. time headway | q in vehicles/hour |
| Min. space headway | S = 0.2V + L | V in km/h, L = vehicle length |
Level of Service (LOS)
| LOS | Description | Avg. Speed (% of free flow) |
|---|---|---|
| A | Free flow — complete freedom of speed | ~90% |
| B | Stable flow — reasonable freedom | ~70% |
| C | Stable, but interactions with others start affecting speed | ~50% |
| D | Approaching unstable — limit of stable flow | ~40% |
| E | Operating at/near capacity — reduced, uniform speeds | ~33% |
| F | Forced/breakdown flow — stop-and-go | 25–33% |
Poisson’s Distribution for Random Headways
In reality, time headway is not constant but follows a random distribution. The probability of n vehicles arriving in time t follows Poisson’s distribution:
P(n) = (λt)ⁿ × e^(−λt) / n!
Where λ = average vehicle flow in vehicles/second and t = duration of time interval.