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

2. 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.

3. 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.

4. 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.

5. 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.

6. 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”.

7. 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.

8. 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

9. 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

10. 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

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

12. 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.

13. 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

14. Non anticipativity constraints
Scenario weight
Non anticipativity constraints

15. Branching Time
First Stage
Second Stage

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

17. 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

18. 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%)

19. 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.

20. Stage 2
Thank you !

21. 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.

23. Stage 2

24. Stage 2

25. Stage 2