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A queue is a group of people or vehicles waiting for their turn for something—whether to be served by a cashier when queuing up in line at a retail store or to pass through an intersection. A queue can either be formal and organized, as with the first-come, first served line to purchase a bus ticket, or informal and disorganized or self-organizing, as with the jumble of people rushing to board an arriving bus. Queuing is the handling and organizing of the waiting elements of a queue. A police officer or other official directing traffic with a hand-held stop sign at the site of utility work or an accident is queueing traffic directly, for instance.

Queuing theory is the mathematical study of queues and the construction of mathematical models and simulations in order to investigate the effects of different actions, choices, or traffic events or features on queue lengths and wait times. Queuing theory, which originated in telecommunications, has applications in numerous areas (it is used in the design of hospitals and hospital procedure, for instance), and is especially important in traffic engineering.

Shockwaves

Shockwaves are propagating waves caused by an abrupt change to the medium through which they pass (in mechanics, a “shock” is a transient excitation caused by a sudden acceleration), and resulting in a rapid rise of density to the flow of that medium. The properties and behavior of shockwaves can be examined and discussed independently of the environment in which they occur—that is, behaviorally, the shockwaves in the air caused by a detonation and the shockwaves in traffic caused by a traffic jam share important characteristics with each other.

In traffic, shockwaves are a result of queuing in congested conditions, and are propagating waves that move through traffic, noticeable in transition changes experienced sequentially by drivers as they are suddenly able to accelerate again after an idle period, or must slow down or stop again after a period of normal speed. While posing an inconvenience to drivers and resulting in inefficient fuel use and greater wear and tear, shockwaves more importantly pose a safety concern because of the increased opportunities for rear-end accidents.

From the right perspective—usually outside the car, unless traffic is going up or down a slope—shockwaves are visible as a cascade of brake lights. The transition change is caused not simply by the affected car passing into a part of the roadway where the capacity has changed. Rather, the lead car in the queue passes through an area where capacity has changed—perhaps because of a lane being shut down for an accident or because of an intersection or traffic signal—and in stopping or slowing because of that change, causes following traffic to stop or slow.

Traffic backed up by an accident in New Britain, Connecticut, in September 2007. Rubbernecking at the scene of accidents or other road incidents can exacerbate shockwaves in traffic and can cause accidents. One study found rubbernecking to be the cause of 16 percent of distraction-related accidents in the era before smartphones and texting became a serious problem as well.

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