Relationship between Network Structure and Network Utilization

By Kardi Teknomo, PhD.

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Several interesting concepts we presented in our paper are as follow:

• Generalized Origin-Destination (OD) matrix is the superset of traditional Origin-Destination matrix in which every node in the network is considered as either source or sink. Generalized OD can be obtained and updated from tracking devices installed in probe vehicles such as public utilities vehicles, taxis and commercial vehicles as well as private cars.
• Given trajectories on the physical network from any tracking devices such as GPS, mobile phone, RFID, blue tooth, video camera and soon, it is possible to obtain the flow matrix and generalized origin destination matrix directly from these trajectories. We presented two algorithms to obtain the flow matrix and generalized origin destination matrix from trajectories.
• Transportation network can be categorized into two parts: the network structure (such as physical road network or pedestrian network) and the network utilization (how the network is utilized by agents such as cars or pedestrians).
• The network structure is represented by adjacency matrix, path matrix, external matrix
• The network utilization is represented by generalized origin-destination matrix, flow matrix, alternative route matrix and substitute route flow matrix and desire lines or indirect flow matrix.
• Adjacency matrix is a subset of path matrix and therefore adjacency matrix is always less than or equal to path matrix.
• Therefore, we can get the difference between adjacency matrix and path matrix, to what I called as External Matrix.
• Flow-set matrix is a subset of the corresponding Generalized Origin-Destination-set matrix and therefore Flow matrix is less than or equal to generalized origin destination matrix
• Desire line in transportation network can be drawn based on indirect flow matrix.
• When there is no alternative route flow, we can find the relationship between network structure and network utilization as simple as element wise product of the matrices.
• When there is alternative route flow, we can find the relationship between network structure and network utilization as simple as.
• Alternative route flow matrix counts the number of agents that pass through other routes other than the corresponding direct link.
• More comprehensive relationship between network structure and network utilization are given by the following formulas which proofs can be found in the paper.

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Preferable reference for this tutorial is

Teknomo, Kardi. (2013) Relationship between Generalized Origin Destination and Flow Matrix – A Tutorial
http://people.revoledu.com/kardi/research/trajectory/od/