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

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 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 over 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

Presentation Plan • Introduction • Background • Methodology • Results and discussion • Findings • Limitation and future work • Conclusion

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 of 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.

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

Introduction-Future ATM An Air Transport Network Network Capacity Estimation

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.

Background  European air traffic network  Network capacity  Maximum flow  Capacity factors

European Air Traffic Network  European Air Traffic Network 850 nodes+4,431 links 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.

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.

Background-Maximum Flow  Conventional approach In graph theory, network capacity is the maximum flow in a transport network. Source node Node 1 Node 2 Node 3 Intermediate nodes Node 4 Node 5 Sink Node 6 node

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.

Background-Capacity Factors

Background-Capacity Factors

Background-Capacity Factors

Methodology  Linear Programming

Methodology Objective function: Subject to

Results and Discussion 10000 6000 EMF EMF=0.6*TMF-142 9000 TMF 5000 8000 Flights and Operations 4000 7000 6000 3000 EMF 5000 2000 4000 3000 1000 2000 0 1000 0 -1000 0 50 100 150 200 0 2000 4000 6000 8000 10000 ACCs and Airports TMF EMF and TMF in the network. Left: Correlation between TMF and EMF =0.96; Right: EMF=0.6xTMF−142.

Results and Discussion 2000 1600 EMF EMF=0.65*TMF-65 1800 TMF 1400 1600 1200 1400 1000 1200 Operations 800 EMF 1000 600 800 400 600 200 400 0 200 0 -200 0 20 40 60 80 0 500 1000 1500 2000 Busy Airports TMF EMF and TMF at 67 busy airports . Left: Correlation between TMF and EMF =0.79; Right: EMF=0.65TMF−65 .

Results and Discussion 4000 1200 EMF TMF 3500 1000 EMF=0.25*TMF+38 3000 800 2500 Operations EMF 2000 600 1500 400 1000 200 500 0 0 0 20 40 60 80 0 1000 2000 3000 4000 TMF Aggregated Airports EMF and TMF at 64 aggregated airports. Left: Correlation between TMF and EMF =0.74; Right: EMF=0.25TMF+38.

Results and Discussion 10000 6000 EMF TMF EMF=0.63*TMF-191 9000 Capacity baseline 5000 8000 7000 4000 6000 Flights EMF 5000 3000 4000 2000 3000 2000 1000 1000 0 0 0 10 20 30 40 50 60 70 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 ACCs TMF 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. •

Results and Discussion 6 50 Little’s Law Theoretical Prediction 5 45 𝜍 Queue length at Airport 1 − 𝜍 𝑀𝑡 = 𝑋𝑟 × 𝜈 = Queueing Delay Queue length in ACC 40 4 35 Where System Queue Length Ls :system queue length 30 3 Wq :waiting time 25 μ : service rate 20 2 ρ :utilization rate 15 =arrival rate/service rate 10 1 In the case of an air traffic 5 network 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Utilization Rate Waiting time=ATFM delays ATFM Delay Comparison between the Service rate=Capacity empirical queue lengths and Arrival rate=Traffic the theoretical predictions.

Findings • Validation of the LP model • Influences of capacity factors • Quantification of capacity factors

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 operational improvements to capacity factors.

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.

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