Coordinated Perimeter Control for Multiregion Heterogeneous Networks Based on Optimized Transfer Flows

Algorithm 1

Two-layer partitioning algorithm of heterogeneous urban networks.

	Step 0: determination of the test road network.
	Step 1: the first-layer division of network.(i)Discovering initial congested communities is done according to definition of congestion seed intersection and an intersection with node strength greater than or equal to 3 is chosen as congestion seed intersection.(ii)Expanding these initial communities is made by adding edges with minimum recursive variance.(iii)Merging adjacent communities is based on spatial overlap and modularity model. The spatial overlap is the ratio of the number of overlapping links to the number of links after merging. And the calculation of modularity can refer to our recent research [18] for details.(iv)The congested regions i, j, h, and l are extracted.
	Step 2: the second-layer division of network.(i)Based on the extraction results in the previous step, calculate the relative distance between the boundary intersection and the centroid of each congested region. The relative distance can be calculated as  where and are the longitude and latitude coordinates of centroid of congested region i; and are the longitude and latitude coordinates of a boundary intersection int.(ii)Divide the intersections of the gray part in Figure 1(a). The specific basis of subdivision is that a boundary intersection belongs to the boundary region between two congested regions with the smallest sum of relative distances:  where is the set of adjacent congested regions of a boundary intersection int; i and j are the congested regions.(iii)The boundary regions , and are obtained. Note that the size of boundary region is measured by the number of streets across the boundaries of congested regions, usually up to 2 streets.
	Step 3: two-layer network partitioning is derived.