page_title: Traffic flow
section_title: Solution for Newell-Daganzo Merge Model
hierarchical_section_title: Traffic flow / Newell-Daganzo Merge Models / Solution for Newell-Daganzo Merge Model
caption_attribution_description: English: graphical solution of newell model
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: The flows that pass through the merging process, q₁ and q₂, are determined by split priority or, merge ratio. The state of each branch of roadways is determined by graphically with the input of the demands for each branch of roadways, q₁ᴰ and q₂ᴰ. There are four possible states for the merge system, both inlets in free flow, one of the inlets in congestion, and both inlets in congestion.
  A common approach to calculate the merge ratio p is called "zipper rule" which p is calculated based on the number of lanes of the single roadway when both inlets are in congestion. If there are n lanes of the single roadway, then under the zipper rule, p=1/(2n-1). This merge ratio is also the ratio of minimum capacities of the inlets μ₁* and μ₂*. μ₁* + μ₂* = μ. As a result, q₁=(μ₁*/μ)*μ and q₂=(μ₂*/μ)*μ.
  The state of each branch of roadways is determined by the graphical solution which is shown in the right. The x-axis is the possible value of q₁ and the y-axis is the possible value of q₂.The feasible region of demands is the defined by the maximum possible values for q₁ᴰ and q₂ᴰ which are μ₁ and μ₂. The feasible region for q₁ and q₂ is defined as the intersection between the line of q₁ + q₂ = μ and the feasible region of demands. The merge ration, p, is plotted from the origin to the line of q₁ + q₂ = μ.
  The four possible states of the merge system are shown in the graph by the regions noted by A1, A2, A3, and A4. A specific states of a merge system is determined by the region where the input data fall into. The region A1 represents the state when both inlet 1 and inlet 2 are in free flow. The region A2 represents the state when inlet 1 is in free flow and inlet 2 is in congestion. The region A3 represents the state when inlet 1 is in congestion and inlet 2 is in free flow. The region A4 represents the state when both inlet 1 and inlet 2 are in congestion.
caption: Graphical solution of Newell–Daganzo merge model.
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