Newell–Daganzo merge model

Overview

In traffic flow theory, the Newell-Daganzo merge model describes a simple procedure on how to determine the flows exiting two branch roadways and merging to flow through a single roadway. The model is simple in that it does not consider the actual merging process between vehicles as the two branch roadways come together. The only information required to calculate the flows leaving the two branch roadways are the capacities of the two branch roadways and the exiting capacity, the demands into the system, and a value describing how the two input flows interact. This latter input term is called the split priority, or merge ratio, and is defined to be the proportion of the two input flows when both are operating in congested conditions.

History from Daganzo and Newell. What papers discuss this is 1982 and 1994.

In a simplified model of the merging process, the available capacity exiting the system is defined to be μ, and the capacities of the input branches are μ₁ and μ₂. The demands entering the system are q₁^D and q₂^D, which is defined to be the demand for the merge passing through μ₁ and μ₂, and thus the maximum demand is the capacity of the inlet branches. The output of the model is the resulting flows that pass through the merge, q₁ and q₂. The assumption is made that the combined capacities of the two inlet branches are less than the capacity of the outlet branch, μ₁+ μ₂ ≤ μ.

Solution for Model

There are four possible states for the system to have based on the level of flow occurring in each inlet. Each inlet can be either in free flow or congestion, and thus the system can have both inlets in free flow, one or other in congestion, or both in congestion. The flow conditions of the inlets are the determining factors in the solution of the model.

The split priority, or merge ration