Location, Transport and Land-use : Modelling Spatial-Temporal Information

1. Location, Transport and Land-use: Modelling Spatial-Temporal Information Yupo Chan, PhD PE Professor & Founding Chair Department of Systems Engineering University of Arkansas at Little Rock

2. Underlying Principles for • Siting Facility location Competitive allocation of products & service • Product/service delivery Location-routing • Community development Land-use planning Spatial forecasting

3. When asked about the three most important factors for fast-food success, McDonald's founder : "Location, location, location.” E-Commerce: Location, price, service

4. Extremal Solution • Network facility-location models • Nodal-optimality property • Extremal conditions also exist in planar location models

5. Solutions to 3-city configuration

6. Cost Functions of Distance cij = dij

7. Image Processing Using p-medoid Method Original Picture (from GOES satellite IR2 channel)

8. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 *2 2 1 2 *1 2 2 1 2 1 1 1 0 0 0 1 1 0 1 1 1 4 *2 2 2 2 4 2 2 1 0 0 0 0 0 0 1 2 2 2 2 5 2 3 2 2 1 2 0 0 0 0 0 0 2 1 2 1 1 1 1 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 (a) Raw image (b) Spectral pattern- recognition (w=0) (c) Spectral and spatial pattern-recognition (0.5<w< 1.0) Legend * Representative pixel Contextual image-classification using p-medoid method

9. Result Classification using p-medoid (3 classes) W=0.5

10. 3-dimensional Space-filling Curve z j i i´ Y X Legend demands facility i, i´ j

11. 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 i Hospital XiLatitude YiLongitude Zi Patients  1 Charlotte 35.21 80.44 0 0.03125 2 Ft Gordon 33.37 81.97 39 0.8125 3 Ft Bragg 35.17 79.02 234 0.8594 4 Ft Jackson 33.94 81.12 44 0.9063 5 Charleston SC 32.90 80.04 29 0.9531 Medical-evacuation Problem

12. zij= lateral re-supply from node i to j

13. SOLUTIONS: A COMPARISON

14. Braess-paradox Game

15. Spatial Location & Allocation • Gaming • Generalized transportation model – Includes regional input-outputs • Equilibrium vs. Disequilibrium –Generalized multi-regional growth equilibria • Entropy –freq. with which an event occurs • Entropy maximization –to capture all possible patterns (information-minimization or spatial uncertainty principle)

16. Legend Wi Facility in zone i pi Price of goods and services at zone i ri Land rent in zone i A probable configuration of zonal activities

17. Facility stock at zone 1 W3(t) W2(t) W1(t) W4(t) Facility stock at zone 2 0.22– 0.2– 0.4– 0.17– 0.26– 0.3– 0.29 – 0.12 – 0.2 – Facility stock at zone 3 & 4 time t time t time t 0 0 0 | 2.5 | 2.5 | 2.5 | 5.0 | 5.0 | 5.0 | 7.5 | 7.5 | 7.5 < 14 = 70 = 70  = 0.35  = 14  = 70  = 14  = 0.35 Responses to a New Shopping Center in zone 2

18. Dallas 1 2 3 4 . . . STUDY AREA San Antonio Houston . . . 398 399 400 Pixel map of Texas Gulf Coast

19. Single Pixel NVI Forecast Series

20. Spatial-Temporal Canonical-Analysis

21. Random or Poisson Field • Backshift operator, lag operator, image-processing mask, & spatial location/allocation All based on a weight matrix • Homoscedasticity, stationarity, homogeneity If the correlation parameters are finite, the derived local averaging field become a continuous parameter Gaussian field. • Ergodicity and isotropy A useful property & through proper local-averaging, such properties can often be obtained

22. Emerging Techniquesfor • Emergency-response to natural and manmade hazards • Supply-chain management • Intelligent transportation systems • Real-estate development • Urban land-use plans • Satellite remote-sensing • Environmental planning • Infrastructure management