Transcript Presentazione di PowerPoint

Paola Zuddas, Antonio Manca
Department of Land Engineering,
University of Cagliari, Italy
[email protected], [email protected]
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:
Air traffic delays occur
for a variety of reasons
•
•
•
runway closure;
de-icing;
cross-wind limitation.
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.
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.
PeriodsWe model
Airportthe
q graph by various types of arcs
a (q)
b (q)
1
Vertical arcs represent:
(Resource waiting assignment)
Holding pattern
Ground holding
A a,q
Admittance 2
permission
to runway
t(i)=t(j)
3
4
5
6
A ar parking area
i
j
The model is structured in a manner
to identify each airport through
a double state-column of nodes
representing sequentially different
periods of time.
nodes at same levels are referred
to the same period (t(i)=t(j)).
airplanes maintain the same state
in the passage from a period to the
successive, until the resource
assignment.
Periods
Airport q
a (q)
b (q)
1
slot assignment
A p,q
permission 2
to occupy the
runway
3
4
5
6
Diagonal arcs represent a change of state,
from a waiting to an operational state.
A slot is assigned to airplane and it can
occupy the runway.
The state change, it means a slot is
assigned to a generic airplane and the
runway is available (landing/take off).
Diagonal arcs type 2
Periods
Airport q
a (q)
1
b (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.
2
3
pre-flight operations
4
5
6
periods
Airport 1
a (1)
1
2
3
4
5
6
b (1)
Airport 2
a (2)
b (2)
Airport 3
a (3)
b (3)
Airport 4
a (4)
b (4)
Airport 1
a (1)
b (1)
Airport 2
a (2)
Airport 3
b (2)
a (3)
b (3)
Airport 4
a (4)
b (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
a (1)
1
b (1)
Airport 2
a (2)
a (3)
Airport 4
a (4)
b (4)
q
slot
assignment
c
d
3
flight
assignment
l
4
f
5
competition
g
h
7
m
landing
8
b (3)
b
2
6
b (2)
Airport 3
n
p
r
Scenario
weight
minx
  c
hk hk
k ij ij
( i , j )A h kK
x
i:(i , j )A
hk
ij
x
hK
hk
ij

x
hk
ij
j:( j ,i )A
 uijk ,
hk
ij
( i , j )Ar , q :t ( j )t ( f )

( i , j )Ava , q
x

x

x
hk
rs
( r , s )Ava , q :t ( s )t ( f )
( r , s )Ar , q
hk
ij
( i , j )Ar , q :t ( j )t ( f )
xijhk 0,1,
i  N , h  K ,k  
(s, t )  S12 , h  1,.., K 1, k  
x
hk
ij
 bihk ,
(s, t )  S1 , h  1,.., K  1, k  
xsthk  xsthk 1 ,
x
k 
(i, j )  A, k  
xsthk  xsthk 1 ,

x
hk
rs

x
hk
up
( u , p )Av , q :t ( f )t ( u )
 1, h  K , f  b (q), q  Q, k  
 0, h  K , q  Q, k  
x
hk
rs
( r , s )Ava , q :t ( q )t ( f )
 x hkfg  0, h  K , ( f , g )  Aar ,q
(i, j)  A, h  K , k  
Non anticipativity
constraints
Branching Time
First Stage
Second Stage
Stage 2
Stage 2
Stage 1
Sc 1
Sc 2
Equal Flow Constraints
(linking costraints)
Sc 3
Algorithm scheme
MMCF
1
New X
New C
MMCF
2
MAIN
Convex Function
Optimization
λ
MMCF
3
MMCF
3
MMCF
MMCF
4
K+1
NDO solvers
Volume
Cutting plane
Bundle methods
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
8
12832
10090
13.53
Net-3
3
20
20172
13186
617
4,97%
Net-4
4
20
26896
17927
797
14,79%
Net-5
3
40
41750
28291
4486
(26.3%)
Net-6
4
40
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.
Stage 2
Stage 2
Stage 2