Terminal Airspace Traffic Complexity
Fedja NetjasovUniversity of Belgrade
Faculty of Traffic and Transport EngineeringDivision of Airports and Air Traffic Safety
.
Why Terminal Airspace?
• Terminal airspace (TMA) represents transitional airspace between airports and ATC sectors;
• The TMA contains a high concentration of arrival trajectories converging on the airport as well as departure trajectories diverging from the airport.
Why Complexity?
• Mix of aircraft types resulting in different separation rules;
• Aircraft traverse the TMA at a broad range of speeds.
Definition of Complexity
• complexity presents a measure of quantity as well as quality of the interactions between the aircraft which are to be controlled (managed) by one air traffic controller.
Concept of Complexity
airlinecosts
airport andsector trafficcomplexity
traffic
situation
noise level and air pollution
influenceon
quality ofpassengers
service
controller workload
Basic assumptions
Complexity depends on two groups of factors:
• static factors: TMA geometry;
• dynamic factors: traffic demand characteristics, distribution of traffic in TMA, etc.
Causes of Complexity (1)
In the case of arrival, traffic complexity could be generated because of:
• existence of traffic on trajectories (C’ARR);
• potential catching-up situations (C’’ARR);
• potential conflict at trajectory merging points
(C’’’ARR) ;
• demand exceeding trajectory capacity (C’’’’ARR)
Ts
1
34
2
Ts
1
34
21
34
21
34
2
Tr
Tr
Catching-up situation
Conflict at trajectory merging point
Causes of Complexity (2)
In the case of departure, traffic complexity could be generated because of:
• existence of traffic on trajectories (C’DEP);
• potential catching-up situations (C’’DEP);
Index of Complexity
The concept of measuring complexity is based on a no-dimensional variable named “Index of complexity”. It is assumed that the Index of traffic complexity (C) consists of two components:
• Index of static complexity (Cs ) and
• Index of dynamic complexity (Cd ).
Index of Static Complexity - Cs
Depends on airspace geometry, i.e. number of trajectories and their length, number of runways, number of entry and exit points, etc.
Nm1)Nm(P
d)kn(d)mn(
C2
mn
1i
kn
1j
DEPj
ARRi
s
Index of Dynamic Complexity - Cd
Presents the sum of two elements:
• Index of dinamic complexity in case of arrival traffic - Cd
ARR and
• Index of dinamic complexity in case of departure traffic - Cd
DEP
Index of Dynamic Complexity in case of arrival traffic - Cd
ARR
Presents the sum of four elements:
CdARR = CARR
’ + CARR’’ + CARR
’’’ + CARR’’’’
ARR
ARR
p
Pp
maxp
)t(D
1r faf
rfaf
Pp
maxppp
)t(A
1s
spp
pARR N
TTT
)t(zN)t(N)t(gT
TT)t(y)t(N
)t(B)t(C
C’ C’’ C’’’C’’’’
Index of Dynamic Complexity in case of departure traffic - Cd
DEP
Presents the sum of two elements:
CdDEP = CDEP
’ + CDEP’’
DEP
DEP
r
Rr
maxr
R
)t(A
1s
srr
rDEP N
TTT
)t(y)t(N
)t(B)t(C
C’ C’’
Index of Complexity (rèsumè)
DEP
DEP
r
ARR
ARR
p
Rr
maxr
R
)t(A
1s
srr
r
Pp
maxp
)t(D
1r faf
rfaf
Pp
maxppp
)t(A
1s
spp
p
mn
1i
kn
1j
DEPj
ARRi
DEPARRsds
N
TTT
)t(y)t(N
)t(B
N
TTT
)t(zN)t(N)t(gT
TT)t(y)t(N
)t(B
P
d)kn(d)mn(
)t(C)t(C)t(C)t(C)t(C)t(C
Experiments (1)
Characteristics:
• TMA contains two arrival and two
departure trajectories (generic case);
• hypothetical traffic;
• simulation of traffic in TMA
Experiments (2)
• Changes in the number of trajectories in the TMA - the purpose of which is to determine what influence changes in the number of trajectories have on the value of the Index of complexity; and
• Changes of traffic volume - the purpose of which is to determine what influence change in traffic volume has on the value of the Index of complexity.
Changes in the number of trajectories in the TMA (1)
01
23
456
78
91011
1213
1415
1
121
241
361
481
601
721
841
961
1081
1201
1321
1441
1561
1681
1801
1921
2041
2161
2281
2401
2521
2641
2761
2881
3001
3121
3241
3361
3481
3601
Time (sec)
Num
ber
of a
ircr
aft
C(t)
0
1
2
3
4
5
6
7
8
9
10
1
115
229
343
457
571
685
799
913
1027
1141
1255
1369
1483
1597
1711
1825
1939
2053
2167
2281
2395
2509
2623
2737
2851
2965
3079
3193
3307
3421
3535
T ime (sec)
Inde
x of
com
plex
ity2
C(t)
0
1
2
3
4
5
6
7
8
9
10
1
116
231
346
461
576
691
806
921
1036
1151
1266
1381
1496
1611
1726
1841
1956
2071
2186
2301
2416
2531
2646
2761
2876
2991
3106
3221
3336
3451
3566
T ime (sec)In
dex
of c
ompl
exit
y3
C(t)
0
1
2
3
4
5
6
7
8
9
10
1
128
255
382
509
636
763
890
1017
1144
1271
1398
1525
1652
1779
1906
2033
2160
2287
2414
2541
2668
2795
2922
3049
3176
3303
3430
3557
Time (sec)
Inde
x of
com
plex
ity
4
24 op/h
Changes in the number of trajectories in the TMA (2)
0
1
2
3
4
5
6
7
8
9
10
1
134
267
400
533
666
799
932
1065
1198
1331
1464
1597
1730
1863
1996
2129
2262
2395
2528
2661
2794
2927
3060
3193
3326
3459
3592
Duration (sec)
Inde
x of
com
plex
ity
twothreefour
≈ 800 ≈ 2100 ≈ 3200
Changes of traffic volume (1) N1(t) + N2(t)
0
12
34
5
67
89
10
1112
1314
15
1
114
227
340
453
566
679
792
905
1018
1131
1244
1357
1470
1583
1696
1809
1922
2035
2148
2261
2374
2487
2600
2713
2826
2939
3052
3165
3278
3391
3504
T ime (sec)
Num
ber
of a
ircr
aft
C(t)
0
1
2
3
4
5
6
7
8
9
10
1
115
229
343
457
571
685
799
913
1027
1141
1255
1369
1483
1597
1711
1825
1939
2053
2167
2281
2395
2509
2623
2737
2851
2965
3079
3193
3307
3421
3535
T ime (sec)
Inde
x of
com
plex
ity
18
N1(t) + N2(t)
0123456789
101112131415
1
115
229
343
457
571
685
799
913
1027
1141
1255
1369
1483
1597
1711
1825
1939
2053
2167
2281
2395
2509
2623
2737
2851
2965
3079
3193
3307
3421
3535
T ime (sec)
Num
ber
of a
ircr
aft
C(t)
0123456789
101112131415
1
115
229
343
457
571
685
799
913
1027
1141
1255
1369
1483
1597
1711
1825
1939
2053
2167
2281
2395
2509
2623
2737
2851
2965
3079
3193
3307
3421
3535
T ime (sec)
Inde
x of
com
plex
ity
24
N1(t) + N2(t)
0123456789
101112131415
1
120
239
358
477
596
715
834
953
1072
1191
1310
1429
1548
1667
1786
1905
2024
2143
2262
2381
2500
2619
2738
2857
2976
3095
3214
3333
3452
3571
T ime (sec)
Num
ber
of a
ircr
aft
C(t)
0
1
2
3
4
5
6
7
8
9
101
117
233
349
465
581
697
813
929
1045
1161
1277
1393
1509
1625
1741
1857
1973
2089
2205
2321
2437
2553
2669
2785
2901
3017
3133
3249
3365
3481
3597
T ime (sec)
Inde
x of
com
plex
ity
30
Changes of traffic volume (2)
0
1
2
3
4
5
6
7
8
9
10
1
155
309
463
617
771
925
1079
1233
1387
1541
1695
1849
2003
2157
2311
2465
2619
2773
2927
3081
3235
3389
3543
Duration (sec)
Inde
x of
com
plex
ity
18 aircraft
24 aircraft
30 aircraft
≈ 130 ≈ 700 ≈ 2400
The main result of this research is the development of a model for the Index of complexity, of general use.
This model could be used:
• for evaluation of current and novel organisational solutions for the TMA containing one single runway airport, or
• for estimation of effects of implementing new arrival and departure trajectories, on traffic in a TMA.
Conclusion
• Consideration of irregular situations such as
missed-approaches;
• Consideration of influences of the meteorological
situation on traffic;
• Analysis of traffic complexity for airports
with multiple runways;
• Usage of weight factors;
• Consideration of heterogeneous aircraft fleet, etc.
Further research
University of Belgrade Faculty of Transport and Traffic Engineering
Department of Air TransportDivision of Airports and Air Traffic Safety
http://apatc.sf.bg.ac.yu Vojvode Stepe 305, 11000 Belgrade
Serbia and Montenegrotel: +381 11 3091 352fax: + 381 11 466 294
Thank you for
your attention