Emmanouil Tranos

University of Bristol, Alan Turing Institute

e.tranos@bristol.ac.uk, @EmmanouilTranos, etranos.info

Empirical data

Data analytics

Applied science: improve the efficiency of movements / spatial constraints

Why in this unit?

Distance

Accessibility: the capacity of a location to be reached by, or to reach different locations

Spatial interaction: movement of people, freight or information between an origin and destination

Transportation and land use models

Source: Rodrigue (2020)

Source: Rodrigue (2020)

Abstraction

Represent the structure not the appearance

Terminal = node

Node (vertex)

Link (edge)

Sub-graph - Loop (buckle)

Planar graph

Non-planar graph

Cycle, circuit

Tree \((e = v-1)\)

Source: Rodrigue (2020)

\(\beta = e / v\), where \(e\) is the number of links & \(v\) the number of nodes

\(Gamma\) AKA network density (number of liks / maximum number of links)

planar: \(\gamma = \frac{e}{3(v-2)}\)

non-planar: \(\gamma = \frac{2e}{v(v-1)}\)

Degree centrality

Eccentricity: the distance from a given node to the farthest node from it in the network

Shimbel index, or nodal accessibility, or Fareness (see Lecture 3

\(c_đť‘–= \sum_j d_{ij}\)

This is a purely topological accessibility metric, remember this for later.

Which node has the shortest distance to other nodes

Instead of focusing on the number of links, the focus turns to the network distances

Different definitions:

Closeness, \(c_{i} = 1/\sum_{j} d_{ij}\)

Fareness, \(c_{i} = \sum_{j} d_{ij}\)

`igraph`

calculates closeness

Inequality measure

- 0: perfect equality
- 1 :perfect inequality

Ordered X and Y, cumulative percentage

Mostly used for income inequalities, but can be more widely used

\(Gini = A / (A + B)\)

Source: Rodrigue (2020)

Source: Rodrigue (2020)

Source: Rodrigue (2020)

Degree of concentration of a certain activities

Very common for regional analysis too

\(M_{ti}\) is the traffic of a merchandise \(t\) at a terminal \(i\)

\(Mi\) is the traffic of all merchandise at a terminal \(i\)

\(M_{t}\) is the total of all merchandises of type \(t\) for all terminals, and

\(M\) is the total of all types of merchandises for all terminals

\(LQ = \frac{\frac{M_{it}}{M_i}}{\frac{M_t}{M}}\)

\(LQ <1\): traffic of merchandise \(t\) in terminal \(i\) is under-represented compared to the same merchandise in all terminals

\(LQ = 1\) traffic of merchandise \(t\) in terminal \(i\) is proportional to its participation to total traffic

\(LQ > 1\) traffic of merchandise \(t\) in a terminal \(i\) is preponderant in total traffic.

Employment in manufacturing sector

Source: ONS

A spatial interaction is a realised movement of people, freight or information between an origin and a destination

It is a transport demand/supply relationship expressed over geographical space.

Conditions for spatial interaction to be materialised

Complementarity

Intervening opportunity

Transferability

Source: Rodrigue (2020)

Origin/destination matrices

Very large matrices

Missing data/0s

Estimation of flows

\(T_{ij} = f(V_i, W_j, S_{ij})\)

- Flows are a function of the attributes of the locations of origin, the attributes of the locations of destination and the friction of distance between the concerned origins and the destinations

\(T_{ij} = f(V_i, W_j, S_{ij})\)

\(T_{ij}\): Interaction between location \(i\) (origin) and location \(j\) (destination)

\(V_i\): Attributes of the location of origin \(i\) (e.g. population, number of jobs available, industrial output, GDP); push factors; the potential of origins

\(T_{ij} = f(V_i, W_j, S_{ij})\)

\(W_j\): Attributes of the location of destination \(j\), pull factors; attractiveness of destinations

\(S_{ij}\): Attributes of separation between \(i\) and \(j\) (e.g. distance, transport costs, or travel time); cost of overcoming the separation between origins and destinations

\(T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}\)

\(\beta\): transport friction parameter

\(\lambda\): Potential to generate movements

\(\alpha\): Potential to attract movements

\(T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}\)

Known: \(V\), \(W\), and \(d\)

Define: \(\lambda=1\), \(\alpha=1\), \(\beta=2\), and \(k=0.00001\)

These are some standard results from past empirical studies

Big unknown: \(T\)

Example from Tranos, Gheasi, and Nijkamp (2015)

Fairly good estimation of reality for such an oversimplified model, butâ€¦

â€¦ not good enough.

Known: \(T\), \(V\), \(W\), \(d\) and \(k\)

Estiamte: \(\lambda=1\), \(\alpha=1\), and \(\beta=2\)

*Why?*To understand the effect of distance, pull and push factorsHow? Regression

\(T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}\)

Look up properties of logarithms, e.g. here

\(T_{ij} = kV_i^\lambda W_j^\alpha d_{ij}^{-\beta}\)

\(ln T_{ij} = ln (kV_i^\lambda W_j^\alpha d_{ij}^{-\beta})\)

\(ln T_{ij} = lnk + lnV_i^\lambda + ln W_j^\alpha + lnd_{ij}^{-\beta}\)

\(\color{red}{ln T_{ij}} = \color{blue}{lnk} + \lambda \color{green}{lnV_i} + \alpha \color{orange}{ln W_j} -\beta \color{purple}{lnd_{ij}}\)

\(\color{red}{y} = \color{blue}{c} + \lambda \color{green}{x_1} + \alpha \color{orange}{x_2} + \beta \color{purple}{x_3}\)

Multivariate linear regression

\(c = lnk = 13.84\)

\(\lambda = lnV_i = 0.727\)

\(\alpha = lnW_j = 0.464\)

\(\beta = lnd_{ij} = -0.624\)

What did we learn?

How can we use these coefficients

The potential of opportunities for interaction

Ease of spatial interaction

Attractiveness of a node in a network taking into account the mass of other nodes and the costs to reach those nodes via the network

Different typologies (Holl 2007)

Network access

distance to access the network

travel opportunities

Travel cost measures

- network access + distance/time travelled on the network

Market potential accessibility

- destinations at greater distance provide diminishing opportunities

- \(Acc_{i} = \sum_j \frac{W_j}{d_{ij}^2}\)

Geographical indicator

Spatial structure (e.g. distance) and economic activities (e.g. population)

The potential for interaction

Opportunities

Bruinsma, Frank, and Pieter Rietveld. 1998. â€śThe Accessibility of European Cities: Theoretical Framework and Comparison of Approaches.â€ť *Environment and Planning A* 30 (3): 499â€“521.

Holl, Adelheid. 2007. â€śTwenty Years of Accessibility Improvements. The Case of the Spanish Motorway Building Programme.â€ť *Journal of Transport Geography* 15 (4): 286â€“97. https://doi.org/https://doi.org/10.1016/j.jtrangeo.2006.09.003.

Rodrigue, Jean-Paul. 2020. *The Geography of Transport Systems*. Routledge. https://transportgeography.org/.

Tranos, Emmanouil, Masood Gheasi, and Peter Nijkamp. 2015. â€śInternational Migration: A Global Complex Network.â€ť *Environment and Planning B: Planning and Design* 42 (1): 4â€“22.