complexworld ws3 | air transport network | timetable centrality

Timetable Centrality and Efficiency of Connections in Air-Rail Intermodal Hubs

ComplexWorld Workshop 3: “Air Transport Network: an Integrated View”

Barcelona, September 20th, 2013

Fabio [email protected] | www.timenetwork.org | @fblamanna

venerdì 20 settembre 2013

http://www.timenetwork.org


Something about me

I’m a Transportation Civil Engineer

I’ve been working as freelance (mainly on traffic management, transportation networks modelization, simulation and visualization)

I’ve been interested in Complex Networks theories applied on Transportation Systems since my Ph.D. (2008)


So, why dealing with intermodality?

Some months ago I discovered railway traffic data(I thought it would be a good topic to be investigated)

Focus on Railway Networks Dynamics as an “integrated view” of such systems


Overview

‣ Introduction‣ Methodology (Layers and Spaces) + Graph Definition‣ Centrality Measures‣ Efficiency of Connections‣ test case: Frankfurt Am Main Intermodal Hub‣ Results + Work in Progress + Outlook


We’re focusing on (lack of) connections:

“[...] Connections issues have been highlighted as one of the major improvements wished by passengers in Intermodal journeys [...]”

“[...] it appears that connections issues are the main obstacle for intermodal passengers [...]”.

(IATA - Air/ Rail Intermodality Study - Air Transport Consultancy Services, 2003)

Introduction


Introducing a Complex Network Approach to:

Find the dynamics based on the variation in time of the timetable structure(that can cause missing connections at Hubs)

Provide information on the connecting role of Hubs(efficiency in linking two or more transportation systems together)

Introduction


Methodology: Layers and Spaces

Modelling Networks from Timetable and Services point of view(Kurant and Thiran, 2006)

Capture scheduled information and connections properties (in a better way than the classical graph structures can do)

Methodology - Layers and Spaces


Layers

Transportation Systems having one (or more) nodes in common



Spaces

Graph structures related to services

‣ Space of Stops: information on the availability of connections between nodes‣ Space of Changes: focus on the direct reachability of destinations



Spaces


Space of Stops Space of Changes

shortcut


Graph Definition

Weighted MultiDiGraph

Suitable weights to edges: delayij

(Variability of timetable structure for on-time and delayed services)

Reduction to a Weighted Direct Graph(performing shortest paths algorithms)

Methodology - Graph Definition


Graph Definition

Adjacency Matrix A(aij) + Weighted Matrix W(wij)

Methodology - Graph Definition

wij = delayij wij = delayij

single delays mean delay


Centrality Measures

Relative importance of a node within the system(fits well with the purposes of this study!)

Extended definitions are needed(to capture the dynamics occurring in weighted networks analysis)

Centrality Measures


Timetable Centrality

”How much the Hub is ”central”, within each transportation system, with respect to the scheduled and delay timetable structure?”

It’s a sort of a Weighted Betweenness Centrality

Centrality Measures: Timetable Centrality

wij = delayij


Hub Strength

Generalization of degree for weighted networks(catch the amount of delayed services starting or arriving on a particular node)

Centrality Measures: Hub Strength


Efficiency

Communications among nodes in the network (disconnected as well!)(Latora and Marchiori, 2001)

Efficiency of Connections


Timetable Efficiency

Taking into account the scheduled and delay timetable information(how efficient the real communication among nodes in a network can be)

Global Measure(i.e. referred to the whole system dynamics)

Efficiency of Connections: Timetable Efficiency

Normalized by on-time conditions


Hub Efficiency

Role of the Hub in the communications through each Layer(the subgraph of all reachable nodes from and to node i)

Local Measure(i.e. referred to single node dynamics)

Efficiency of Connections: Hub Efficiency


Frankfurt Am Main Flughafen Fernbahnhof

test case

test case: Frankfurt Am Main Intermodal Hub


Frankfurt Am Main Flughafen Fernbahnhof

common node (Intermodal Hub) between the following Layers:

Layer 1: the Deutsche Bahn Railway Network

Layer 2: the European / Worldwide Airport Network



Layer 1 | Deutsche Bahn Railway Network

656 stations (nodes)

around 800 long-distance trains running each day(IC, EC, ICE, TGV, Thalys, RailJet, CNL)

test case: Frankfurt Am Main Intermodal Hub - Layer 1


Layer 1 | Railway Traffic Data Management

OpenDataCity - Zugmonitor Project (zugmonitor.sueddeutsche.de)

Completely free (for no-commercial use) API of daily German railway operations(.json data format)

Python self-developed codes and public packages(numpy, matplotlib, networkx...)



Deutsche Bahn Network - Space of Stops


N = 656E = 1457


Deutsche Bahn Network - Space of Changes


N = 656E = 24473


Layer 1 | Analysis and Results

Analysis on every single day in 2012(in both Spaces, focus on node “Frankfurt Am Main Flughafen”)

24h of railway operations(but the time period of analysis can be fixed differently)



Daily Trends, Space of Stops and Space of Changes




Timetable Centrality vs Betweenness Centrality


Layer 1 | The Meaning of Gaps (Tc - Bc):

(Tc - Bc) > 0: the most efficient / scheduled paths are passing through the node

(Tc - Bc) = 0: on-time services

(Tc - Bc) < 0: presence of delays in the neighbours of the node




Layer 1 | Hub Performance indices on Frankfurt node


Layer 2 | Airport Network

Topology of direct connections between airports (but no travel information)(openflights.org)



Worldwide Airport Network of direct connections



Layer 2 | Working on Travel Data

Flightstats database API and hystorical data are on the way(www.flightstats.com)

“delay index”(a forecast of departure disruption at the airport)



http://www.flightstats.com

http://www.flightstats.com

Outlook | Connections among Layers

Apply this framework to each Layer

How to join dynamics of BOTH networks to capture the role of the Hub?(this is the challenge!)

Starting from some recent approaches on Multiplex?Cardillo et al. 2013 | Gomez et al. 2013 | Nicosia et al. 2013 ...

test case: Frankfurt Am Main Intermodal Hub - Outlook on Connections


Summary

We talked about connections issues in transportation systems (in general related to delays)

We suggested a simple complex network approach to investigate Intermodality issues by means of scheduled and delayed dynamics on nodes

Timetable Centrality + Efficiency(seems a good way to define how much a node is involved in the delay dynamics)

Looking for an extended methodology to join dynamics of multiple networks


Thanks for your [email protected] | www.timenetwork.org | @fblamanna


mailto:[email protected]

mailto:[email protected]



complexworld ws3 | air transport network | timetable centrality

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