A Multi-Airport Dynamic Network Flow Model with Capacity Uncertainty Paola Zuddas, Antonio Manca Department of Land Engineering, University of Cagliari, Italy zuddas@unica.it, amanca@unica.it A Multi-Airport Dynamic Network Flow Model with Capacity Uncertainty

In this presentation, we are going to show how to decompose tactical model based on dynamic networks applied to a set of airports of a total Air Traffic System under uncertainty on runway capacity in order to adapt it to GRID computing environment.

Under normal circumstances ATFM system: provides services to a certain volume of air traffic; satisfies the targeted high level of safety. maintain efficient the flow; Normally, the target (ATFM) is to enable aircraft operators to: meet both departure and arrival planned times; enable to carry out their planned flight operations with the minimum penalty.

bad weather conditions. It may require: runway closure; de-icing; cross-wind limitation. Air traffic delays occur for a variety of reasons technical/operational problems such us: customer service issues; air traffic control system decisions; equipment failures; airport congestion.

The flow management problem in ATFM occurs when flights at an airport must be delayed because: airport suffers of reduced capacity; demand for airport exceeds the capacity. When capacity is reduced, the goals of an ATFM are to: adapt the demands requests to the actual runway capacity. try to reduce congestion delay effects; allocate and optimize capacity; put in place penalties. Examples of operational penalties are: ground delay; assignment of a cruise level different from the optimum one; extra mileage; holding pattern.

optimize available air traffic resources (capacity); Our interest is in implement new tactical approaches extended to a network of airports in order to activate predictive strategies when: unpredictable events occur; We suggest an optimisation model for Air Traffic Flow Management based on: ground holding and holding pattern assignments; multi-period network model; scenario analysis to manage uncertainty in runway capacity. A tactical approach is a difficult process which requires: a practical implementation of great dimension instances. The solutions strictly depends on: uncertainty assigned to airport capacity by Decision Maker. The objectives are to: assign delays to balance delays among all airplanes; optimize available air traffic resources (capacity); plan the path of each airplane period for period; minimize the expected total cost of delay; domino effects; periods the airports works near the “hedge”.

The multi-period network structured model. Before to introduce the deterministic model, we assume: to study the system behaviour on a time horizon; to divide the time horizon T into sequential time steps called periods; also of variable length Δp; to describe airplane movements by dynamic direct graph G(N,A); a number K of airplanes are in competition among them for resource assignment; Q the set of airports of the considered Air Traffic System.

We model the graph by various types of arcs Periods Airport q Vertical arcs represent: (Resource waiting assignment) Holding pattern Ground holding A ar parking area 1 A a,q Admittance permission to runway 2 The model is structured in a manner to identify each airport through a double state-column of nodes representing sequentially different periods of time. t(i)=t(j) 3 i j 4 nodes at same levels are referred to the same period (t(i)=t(j)). 5 airplanes maintain the same state in the passage from a period to the successive, until the resource assignment. 6

Periods Airport q 1 slot assignment A p,q permission to occupy the runway 2 Diagonal arcs represent a change of state, from a waiting to an operational state. 3 A slot is assigned to airplane and it can occupy the runway. 4 The state change, it means a slot is assigned to a generic airplane and the runway is available (landing/take off). 5 6

Diagonal arcs type 2 Periods Airport q A r ,q is the set of arcs corresponding to the relocating activity. Mandatory procedures of routine done in parking area, foreseen before every new flight. 1 2 pre-flight operations 3 4 5 6

periods Airport 1 Airport 2 Airport 3 Airport 4 1 2 3 4 5 6

Airport 1 Airport 2 Airport 3 Airport 4 1 Av(1) 2 3 Ava(2) 4 5 6 7 8 A v, (q) and A va(q) are the sets of arcs representing flights connection for q.

periods Airport 1 Airport 2 Airport 3 Airport 4 1 b q slot assignment 2 c r d flight assignment 3 4 l 5 f competition 6 g 7 h m landing 8 n p

Non anticipativity constraints Scenario weight Non anticipativity constraints

Branching Time First Stage Second Stage

Stage 2 Stage 2 Sc 1 Stage 1 Sc 2 Equal Flow Constraints (linking costraints) Sc 1 Sc 2 Sc 3

Algorithm scheme Algorithm scheme New X New X New C New C λ λ MMCF 1 MMCF 1 New C New C Convex Function Optimization Convex Function Optimization MAIN MAIN MMCF 2 MMCF 2 λ λ MMCF 3 MMCF 3 MMCF 3 MMCF 3 NDO solvers Volume Cutting plane Bundle methods NDO solvers Volume Cutting plane Bundle methods MMCF 4 MMCF K+1

Waiting time for admissibility Preliminary results We generate instances solved by Cplex. Scenario Commodity Variables Constraints Waiting time for admissibility (seconds) Net-1 3 8 9624 7414 11.61 Net-2 4 12832 10090 13.53 Net-3 20 20172 13186 617 4,97% Net-4 26896 17927 797 14,79% Net-5 40 41750 28291 4486 (26.3%) Net-6 47424 29428 25301 (20.68%)

Stage 2 Conclusions and perspectives. We need to achieve an optimal/feasible solution but it is fundamental to take decision rapidly and with a consistent number of scenarios; Robust solvers in each cluster (numerical instability of open source MIP solvers); Methodology extension to other transport problems.

Stage 2 Thank you !

Conclusions. The increment of air traffic volume produces a great quantity of delay. It is interesting to distribute delays in a manner to optimize the available capacity.

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