page_title: Traffic flow
section_title: Moving bottleneck
hierarchical_section_title: Traffic flow / Traffic bottleneck / Moving bottleneck
caption_attribution_description: English: Tractor on the road. Picture taken at Cacouna, Québec, Canada, 12th of June 2005.
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: As explained above, moving bottlenecks are caused due to slow moving vehicles that cause disruption in traffic. Moving bottlenecks can be active or inactive bottlenecks. If the reduced capacity(qᵤ) caused due to a moving bottleneck is greater than the actual capacity(μ) downstream of the vehicle, then this bottleneck is said to be an active bottleneck. Figure 20 shows the case of a truck moving with velocity 'v' approaching a downstream location with capacity 'μ'. If the reduced capacity of the truck (qᵤ) is less than the downstream capacity, then the truck becomes an inactive bottleneck.
  Laval 2009, presents a framework for estimating analytical expressions for the capacity reductions caused by a subset of vehicles forced to slow down at horizontal/vertical curves on multilane freeway. In each of the lane the underperforming stream is described in terms of its desired speed distribution and is modeled as per Newell’s kinematic wave theory for moving bottlenecks. Lane changing in the presence of trucks can lead to a positive or negative impact on capacity. If the target lane is empty then the lane-changing increases capacity
  For this example, consider three lanes of traffic in one direction. Assume that a truck starts traveling at speed v, slower than the free flow speed vf. As shown on the fundamental diagram below, qᵤ represents the reduced capacity (2/3 of Q, or 2 of 3 lanes available) around the truck.
  State A represents normal approaching traffic flow, again at speed vf. State U, with flowrate qᵤ, corresponds to the queuing upstream of the truck. On the fundamental diagram, vehicle speed vᵤ is slower than vf. But once drivers have navigated around the truck, they can again speed up and transition to downstream state 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 free-flow to v. A queue builds behind the truck, represented by state U. Within the region of state U, vehicles drive slower 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.
caption: Figure 21. A slow tractor creates a moving bottleneck.
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