### Bottleneck (traffic)

A **traffic bottleneck** is a localized disruption of vehicular traffic on a street, road, or highway. As opposed to a traffic jam, a bottleneck is a result of a specific physical condition, often the design of the road, badly timed traffic lights, or sharp curves. They can also be caused by temporary situations, such as vehicular accidents.

## Contents

## Causes

Traffic bottlenecks are caused by a wide variety of things:

- Construction zones where one or more existing lanes become unavailable (as depicted in the diagram on the right)
- Accident sites that temporarily close lanes
- Narrowing a low-capacity highway road
- Terrain (e.g., uphill sections, very sharp curves)
- Poorly timed traffic lights
- Slow vehicles that disrupt upstream traffic flow upstream (also known as a "moving bottleneck")
- Rubbernecking

Rubbernecking is an example of how bottlenecks can be induced by psychological factors; for example, vehicles safely pulled to the shoulder by a police car often result in passing drivers to slow down to "get a better look" at the situation.

## Graphical and theoretical representation

Traffic flow theory can be used to model and represent bottlenecks.

### Stationary bottleneck

Consider a stretch of highway with two lanes in one direction. Suppose that the fundamental diagram is modeled as shown here. The highway has a peak capacity of Q vehicles per hour, corresponding to a density of *k _{c}* vehicles per mile. The highway normally becomes jammed at

*k*vehicles per mile.

_{j}Before capacity is reached, traffic may flow at *A* vehicles per hour, or a higher *B* vehicles per hour. In either case, the speed of vehicles is *v _{f}* (or "free flow"), because the roadway is under capacity.

Now, suppose that at a certain location *x _{0}*, the highway narrows to one lane. The maximum capacity is now limited to

*D*’, or half of

*Q*, since only one lane of the two is available. State

*D*shares the same flowrate as state

*D'*, but its vehicular density is higher.

Using a time-space diagram, we may model the bottleneck event. Suppose that at time *t _{0}*, traffic begins to flow at rate

*B*and speed

*v*. After time

_{f}*t*, vehicles arrive at the lighter flowrate

_{1}*A*.

Before the first vehicles reach location *x _{0}*, the traffic flow is unimpeded. However, downstream of

*x*, the roadway narrows, reducing the capacity by half—and to below that of state

_{0}*B*. Due to this, vehicles will begin queuing upstream of

*x*. This is represented by high-density state

_{0}*D*. The vehicle speed in this state is the slower

*v*, as taken from the fundamental diagram. Downstream of the bottleneck, vehicles transition to state

_{d}*D'*, where they again travel at free-flow speed

*v*.

_{f}Once vehicles arrive at rate *A* starting at time *t _{1}*, the queue will begin to clear and eventually dissipate. State

*A*has a flowrate below the one-lane capacity of states

*D*and

*D'*.

On the time-space diagram, a sample vehicle trajectory is represented with a dotted arrow line. The diagram can readily represent vehicular delay and queue length. It's a simple matter of taking horizontal and vertical measurements within the region of state *D*.

### Moving bottleneck

For this example, consider three lanes of traffic in one direction. Assume that a truck starts traveling at speed *v*, more slowly than at the free-flow speed *v _{f}*. As shown on the fundamental diagram below, speed

*q*represents the reduced capacity (two-thirds of

_{u}*Q*, i.e., 2 out of 3 lanes available) around the truck.

State *A* represents normal approaching traffic flow, again at speed *v _{f}*. State

*U*, with flowrate

*q*, corresponds to the queuing upstream of the truck. On the fundamental diagram, vehicle speed

_{u}*v*is slower than speed

_{u}*v*. But once drivers have navigated around the truck, they can again speed up and transition to downstream state

_{f}*D*. While this state travels at free flow, the vehicle density is less because fewer vehicles get around the bottleneck.

Suppose that, at time *t*, the truck slows from the free-flow rate to *v*. A queue builds behind the truck, represented by state *U*. Within the region of state *U*, vehicles more slowly, as indicated by the sample trajectory. Because state *U* limits to a smaller flow than state *A*, the queue will back up behind the truck and eventually crowd out the entire highway (slope *s* is negative). If state *U* had the higher flow, there would still be a growing queue. However, it would not back up because the slope *s* would be positive.^{[1]}

## See also

- Three-phase traffic theory
- Traffic congestion: Reconstruction with Kerner’s three-phase theory
- Kerner’s breakdown minimization principle