A linear programming approach to maximum flow estimation on the - - PowerPoint PPT Presentation

▶
a linear programming approach to
SMART_READER_LITE
LIVE PREVIEW

A linear programming approach to maximum flow estimation on the - - PowerPoint PPT Presentation

Nov 24, 2023 232 likes •513 views

ROC Air Force A linear programming approach to maximum flow estimation on the European air traffic network ICRAT 2014 Kuang-Chang Pien k.pien11@imperial.ac.uk Curriculum Vitae Air Force Officer in Taiwan (1999-2003, 2005-2011) BA

slide-1
SLIDE 1

A linear programming approach to maximum flow estimation on the European air traffic network

ICRAT 2014

Kuang-Chang Pien

k.pien11@imperial.ac.uk ROC Air Force
slide-2
SLIDE 2

Curriculum Vitae

  • Air Force Officer in Taiwan (1999-2003, 2005-2011)
  • BA in Engineering and System Science, National Tsing Hua University, Taiwan.
  • Logistics and Intelligence officer in ROC (Taiwan) Air Force.
  • MSc. in Advanced Engineering (2003-2004)
  • Warwick University (UK)
  • Sponsored by the ROC (Taiwan) Air Force Academy
  • Thesis: Numerical simulation of mass transport in a WVF
  • MRes. in Engineering (2004-2005)
  • Warwick University (UK)
  • Sponsored by the ROC (Taiwan) Air Force Academy
  • Thesis: Structure function analysis of QuikSCAT measured near-surface winds
  • ver the Pacific Ocean from 40S to 40N
  • Ph.D. Student in Air Traffic Management (2011-2015)
  • Imperial College London (UK)
  • Sponsored by the ROC (Taiwan) Air Force Academy and the LRF
slide-3
SLIDE 3

Presentation Plan

  • Introduction
  • Background
  • Methodology
  • Results and discussion
  • Findings
  • Limitation and future work
  • Conclusion
slide-4
SLIDE 4

Introduction

  • In Europe, the number of flights doubled between 1999

and 2008 and is forecast to grow with a compound annual growth rate of 0.6% between 2013 and 2019.

  • Although traffic growth has flattened and the performance
  • f the European air traffic network has improved, the

congestion at busy airports and in Area Control Centres (ACCs) still remains severe.

  • In order to cope with the need to satisfy the increasing

demand for air travel, the Single European Sky (SES) Air Traffic Management (ATM) Research programme (SESAR)in Europe have been launched.

slide-5
SLIDE 5 Gate Taxiing Take-off Climb Cruise Decent Landing Taxiing Gate Ground ATCO Runway ATCO Terminal ATCO Plannig ATCO Tactical ATCO TWR (Supervisor) ACC (Supervisor) TWR (Supervisor) Ground Handler Airport (Operator) Slot Coordinator Aircraft Operator FMP FMP FMP Airport Operator Slot Coordinator Aircraft Operator ATFM CFMU AOM Capacity Management Conflict Management Terminal ATCO Runway ATCO Ground ATCO Ground Handler Departure Management Surface Management Arrival Management Surface Management Turnaround Turnaround Slot Management Slot Management Slot Management Slot Management Flight Plan Demand Management Flight Plan Demand Management Terminal Control Terminal Control

Introduction-Current ATM

Airport Capacity Airspace Capacity Airport Capacity
slide-6
SLIDE 6

Introduction-Future ATM

An Air Transport Network

Network Capacity Estimation

slide-7
SLIDE 7

Introduction-Research Problem

The research problem is : How to measure the network capacity of an air transport system? The aim of this research is : To develop a method to estimate the network capacity that is flexible and accommodates the new ConOps.

slide-8
SLIDE 8

Background

  • European air traffic network
  • Network capacity
  • Maximum flow
  • Capacity factors
slide-9
SLIDE 9

European Air Traffic Network

  • European Air Traffic Network

The European air traffic network can be displayed as a graph, the nodes represent airports and ACCs. A critical notion is connectivity, which can be defined as a binary state that exists between any two nodes in the network, and takes value 1 if the two nodes are connected by a link and 0 otherwise.

850 nodes+4,431 links
slide-10
SLIDE 10

Background-Network Capacity

  • EUROCONTROL: Network capacity is the network throughput

taking traffic demand patterns and the network effect of airports and airspace into account.

  • This definition does not capture the influences of all factors that

affect capacity i.e. capacity factors.

  • Traditionally, the maximum network flow is the theoretical

maximum amount of traffic.

  • We argue that the gap between theoretical and empirical

maximum network flow is caused by the inefficiencies in the capacity factors.

slide-11
SLIDE 11

Background-Maximum Flow

  • Conventional approach

In graph theory, network capacity is the maximum flow in a transport network.

Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Source node Sink node Intermediate nodes
slide-12
SLIDE 12

Background-Maximum Flow

 Max-flow and min-cut theory The renowned max-flow min-cut theory is commonly used to calculate the maximum flow and identify the bottlenecks within a transport network.

slide-13
SLIDE 13

Background-Capacity Factors

slide-14
SLIDE 14

Background-Capacity Factors

slide-15
SLIDE 15

Background-Capacity Factors

slide-16
SLIDE 16

Methodology

  • Linear Programming
slide-17
SLIDE 17

Methodology

Objective function: Subject to

slide-18
SLIDE 18

Results and Discussion

50 100 150 200 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 ACCs and Airports Flights and Operations EMF TMF 2000 4000 6000 8000 10000
  • 1000
1000 2000 3000 4000 5000 6000 TMF EMF EMF=0.6*TMF-142 EMF and TMF in the network. Left: Correlation between TMF and EMF =0.96; Right: EMF=0.6xTMF−142.
slide-19
SLIDE 19

Results and Discussion

20 40 60 80 200 400 600 800 1000 1200 1400 1600 1800 2000 Busy Airports Operations EMF TMF 500 1000 1500 2000
  • 200
200 400 600 800 1000 1200 1400 1600 TMF EMF EMF=0.65*TMF-65 EMF and TMF at 67 busy airports . Left: Correlation between TMF and EMF =0.79; Right: EMF=0.65TMF−65.
slide-20
SLIDE 20

Results and Discussion

20 40 60 80 500 1000 1500 2000 2500 3000 3500 4000 Aggregated Airports Operations EMF TMF 1000 2000 3000 4000 200 400 600 800 1000 1200 TMF EMF EMF=0.25*TMF+38 EMF and TMF at 64 aggregated airports. Left: Correlation between TMF and EMF =0.74; Right: EMF=0.25TMF+38.
slide-21
SLIDE 21

Results and Discussion

EMF and TMF in 64 ACCs.
  • Left: Correlation
between TMF and EMF =0.98; between capacity baselines and EMF = 0.94.
  • Right: EMF=0.63TMF−191.
10 20 30 40 50 60 70 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 ACCs Flights EMF TMF Capacity baseline 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 1000 2000 3000 4000 5000 6000 TMF EMF EMF=0.63*TMF-191
slide-22
SLIDE 22

Results and Discussion

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5 10 15 20 25 30 35 40 45 50 Utilization Rate System Queue Length Theoretical Prediction Queue length at Airport Queue length in ACC Comparison between the empirical queue lengths and the theoretical predictions. Little’s Law 𝑀𝑡 = 𝑋𝑟 × 𝜈 = 𝜍 1 − 𝜍 Where Ls :system queue length Wq :waiting time μ : service rate ρ:utilization rate =arrival rate/service rate In the case of an air traffic network Waiting time=ATFM delays Service rate=Capacity Arrival rate=Traffic 0.5 1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4 5 6 ATFM Delay Queueing Delay
slide-23
SLIDE 23

Findings

  • Validation of the LP model
  • Influences of capacity factors
  • Quantification of capacity factors
slide-24
SLIDE 24

Limitation and Future Work

  • Inherent limitations
  • Capacities
  • Static nature
  • Traffic demand pattern
  • Future work
  • Overcome the limitations
  • Quantify the capacity factors.
  • Assess the contribution of SESAR by mapping new
  • perational improvements to capacity factors.
slide-25
SLIDE 25

Conclusion

  • We have developed, for the first time, a linear

programming to estimate maximum flows in the European air traffic network. The results suggest that this LP approach is relatively capable to model the air traffic in Europe.

  • In addition, the influence of the capacity factors can

be assessed by using regression analysis to quantify these parameters.

  • Finally, ATFM delays and queuing theory can

potentially be used to quantify capacity factors.

slide-26
SLIDE 26

???

Questions