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Relationship between Network Structure and Network Utilization

By Kardi Teknomo, PhD.

< Previous | Index | Next >

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 matrixA, path matrixP, external matrixE
  • The network utilization is represented by generalized origin-destination matrixD, flow matrixF, alternative route matrixT and substitute route flow matrixTc and desire lines or indirect flow matrixL.
  • Adjacency matrix is a subset of path matrix and therefore adjacency matrix is always less than or equal to path matrixorigin destination matrix.
  • Therefore, we can get the difference between adjacency matrix and path matrix, to what I called as External Matrixorigin destination 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 matrixorigin destination matrix
  • Desire line in transportation network can be drawn based on indirect flow matrixorigin destination 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 matricesorigin destination matrix.
  • When there is alternative route flow, we can find the relationship between network structure and network utilization as simple asorigin destination matrix.
  • Alternative route flow matrix origin destination matrixcounts 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.
  • origin destination matrix

    origin destination matrix

    origin destination matrix

    origin destination matrix

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These tutorial is copyrighted.

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/

 

 
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