page_title: Traffic flow
section_title: Variable speed limit assignment
hierarchical_section_title: Traffic flow / Variable speed limit assignment
caption_attribution_description: English: Case 2 Flow-Density Diagram for VSL (qU&gt;qA)
context_page_description: In mathematics and transportation engineering, traffic flow is the study of interactions between travellers and infrastructure, with the aim of understanding and developing an optimal transport network with efficient movement of traffic and minimal traffic congestion problems.
context_section_description: This is an upcoming approach of eliminating shockwave and increasing safety for the vehicles. The concept is based on the fact that the risk of accident on a roadway increases with speed differential between the upstream and downstream vehicles. The two types of crash risk which can be reduced from VSL implementation are the rear-end crash and the lane-change crash. Variable speed limits seek to homogenize speed, leading to a more constant flow. Different approaches have been implemented by researchers to build a suitable VSL algorithm.
  Variable speed limits are usually enacted when sensors along the roadway detect that congestion or weather events have exceeded thresholds. The roadway speed limit will then be reduced in 5-mph increments through the use of signs above the roadway (Dynamic Message Signs) controlled by the Department of Transportation. The goal of this process is the both increase safety through accident reduction and to avoid or postpone the onset of congestion on the roadway. The ideal resulting traffic flow is slower overall, but less stop-and-go, resulting in fewer instances of rear-end and lane-change crashes. The use of VSL’s also regularly employs shoulder-lanes permitted for transportation only under congested states which this process aims to combat. The need for a variable speed limit is shown by Flow-Density diagram to the right.
  In this figure ("Flow-Speed Diagram for a Typical Roadway"), the point of the curve represents optimal traffic movement in both flow and speed. However, beyond this point the speed of travel quickly reaches a threshold and starts to decline rapidly. In order to reduce the potential risk of this rapid rate of speed decline, variable speed limits reduce the speed at a more gradual rate (5-mph increments), allowing drivers to have more time to prepare and acclimate to the slowdown due to congestion/weather. The development of a uniform travel speed reduces the probability of erratic driver behavior and therefore crashes.
  Through historical data obtained at VSL sites, it has been determined that implementation of this practice reduces accident numbers by 20-30%.
  In addition to safety and efficiency concerns, VSL’s can also garner environmental benefits such as decreased emissions, noise, and fuel consumption. This is due to the fact that vehicles are more fuel-efficient when at a constant rate of travel, rather than in a state of constant acceleration and deacceleration like that usually found in congested conditions.
  Key Background Theory
  Fundamental relationships between volume (q), speed (u), and density (k) of traffic flow can explain the effectiveness of the VSL. The relationship between these variables is covered in the “Traffic stream properties” section of this page, but as an important takeaway for the purpose of VSL explanation, q=u*k. The Newell’s Simplified traffic flow theory is also utilized for this model to show the relationship displayed in the flow-density plot titled "Ideal Flow-Density Diagram".
  The figure "Ideal Flow-Density Diagram" shows there is a peak density that a roadway can sustain at an uncongested state, but if this density is surpassed then the roadway will fall into a congested traffic state. This density is known as the critical density, or KC. Shockwave theory is used in the VSL model to describe the effect of flow slow-down due to congestion. Shockwaves occur at the boundary between two different traffic flows, and their speeds can be shown as a ratio of a difference of density to the difference of volumes at the two traffic states.
  A VSL often creates a void in the time-space diagram in the space between a vehicle’s trajectory at normal speed and a vehicle at the reduced speed within the VSL’s effective boundary. Below, the two forms of a variable speed limit are shown.
  Initial Flow (“qA”) > Congested Upstream Flow (“qU”) (Case 1)
  When the initial roadway flow is greater than congested upstream flow, a shockwave is formed through the implementation of the VSL. The time-space diagram and flow-density fundamental diagram (simplified to a t
caption: Case 2 Flow-Density Diagram for VSL (qU>qA)
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