Case10-Implementing the Garin-Lowry Model in a Hypothetical City

Chapter 10 System of Linear Equations and Application of Garin-Lowry Model in Simulating Urban Population and Employment Patterns

This chapter introduces the method for solving a system of linear equations (SLE) . The method is fundamental in numerical analysis (NA) and often used as a building block in other NA tasks such as solving a system of nonlinear equations and the eigenvalue problem. Here, the SLE is illustrated in the Garin-Lowry model, a model widely used by urban planners and geographers for analyzing urban land use structure. In short, given a basic employment pattern and a distance matrix, the Garin-Lowry model derives the population and service employment patterns.

Case Study 10 Implementing the Garin-Lowry Model in a Hypothetical City

The case study uses a hypothetical city to illustrate the Garin-Lowry model. Various scenarios are simulated to help us understand some empirical observations as reported in the literature. The case study is built upon the work reported in Wang (1998). The city is partitioned by a transportation network made of 10 circular rings and 15 radial roads. The CBD tract as a circle occupies a central location, and nine concentric rings expand to the edge with an equal width and intersect with 15 sectors to form a total of 1 + 9*15 = 136 tracts.

The data folder SimuCity contains:

1. a polygon feature tract.zip (136 tracts) and its centroids feature trtpt.zip ,

2. a feature dataset road.zip for the road network, and

3. Python files for matrix calculation include I-GTmatrix.py for I-GT, Matrixdot.py for matrix dot product, and SLE.py for solving systems of linear equations.

Computational Methods and GIS Applications in Social Science - KNIME Lab Manual
Lingbo Liu, Fahui Wang

External resources

• Github for Geospatial Analytics
• Github for Workbook Issue Report