Airspace Occupancy Model (AOM)
• Mathematical NAS representation
• 20 centers each divided into sectors
• Flight plans processed to determine sector occupancy
time intervals
• Occupancy data used:
– To characterize sector occupancy workloads
– As pre-processing data for PAEM conflict analysis
Airspace Occupancy Model (AOM)
Probabilistic Aircraft Encounter Model
(PAEM)
•
Proximity Shell Around Each Focal Aircraft
δz
traj
rcraft
i
a
l
a
foc
ectory
δy
δx
• Moves with aircraft as it traverses its flight trajectory
• Conflict occurs when another aircraft pierces the proximity
shell
Probabilistic Aircraft Encounter Model
(PAEM)
• Aircraft Position & Trajectory Not Known With
Certainty
– Weather Effects
– Navigation System Inaccuracy
– Pilot Error
planned trajectory
actual trajectory
Airspace Planning and
Collaborative Decision Model (APCDM)
• Flight Plan Selection
– For each flight, select one flight-plan from among
alternatives
– Minimize Flight Costs (Objective Function)
– Subject to Considerations (Penalty Terms in
Objective Function):
• Sector Workload
• Safety (Conflict Resolution)
• Decision Equity
Model APCDM
F
min ∑ ∑ c
fp
x fp +
f =1 p∈P f 0
subj to: ∑ x
F
∑c
f0
xf 0 +
f =1
fp
ns
S
∑∑µ
y sn + µ x + µ
e
sn
e
α
D
∑ϖ
α
[1 − Eα ( x)] + µ
e
max
E
e
max
+
α =1
s =1 n = 0
S
∑ γ w +∑ϕ
s
s
PQ
s =1
= 1 ∀f = 1,..., F
p∈Pf 0
Conflict Resolution
Constraints
Workload Constraints
CDM Constraints
Dmax
ns ≤ ns
ns
∑y
n =0
sn
Eα ( x ) =
∀s = 1,..., S
= 1 ∀s = 1,..., S
ns
ns − ws = ∑ nysn
∑
( f , p )∈Csi
∑
( f , p )∈Ω s
x fp ≤ ns
s
fp
t x fp
∀s = 1,..., S
∀i = 1,..., I s , s = 1,..., S
z( PQ ) ≤ rs xP , ∀P ∈ N sk
s.t. J sk ( P) ≥ rs + 1, ∀( s, k )
xP + xQ ≤ 1 ∀ ( P, Q ) ∈ FC
xP + xQ − z PQ ≤ 1 ∀( P, Q ) ∈ A
∑
f
*
f
−
( Dmax − 1)
∑ ∑w c
f
fp
x fp
f ∈ Aα p∈P f
∑w c
f
*
f
∀ α = 1,..., α
f ∈ Aα
∀s = 1,..., S
n =0
1
ws =
H
∑
j∈J sk ( P )
∑w c
f ∈ Aα
( P ,Q )∈M sk
z PQ ≤ rs , ∀( s, k )
Eα ( x ) ≥ 0 ∀α = 1,..., α
⎛ α
⎞
Eαe ( x) = Eα ( x) − ⎜ ∑ ωα Eα ( x) ⎟ ∀α = 1,...,α
⎝ α =1
⎠
e
e
wα Eα ( x) ≥ − Emax ∀ α = 1,..., α
α
∑w v
α α
= xe ≤ ve
α =1
vα ≥ − Eαe ( x) and vα ≥ Eαe ( x) ∀ α = 1,..., α
z PQ
Research Directions
• Development of a dynamic/stochastic TDSP
algorithm to consider uncertainties in severe
weather pattern.
• Application of the APCDM in concert with AOM
and PAEM to scenario based on ETMS data in
order to evaluate the quality of the resulting
solutions under alternative conditions:
– a bad weather day or
– a space launch day.
• Resectorization strategies, resource allocation
schemes, effects of FAA/NASA policy guidelines,
and incorporation of SATS into NAS can also be
studies by the model.