Study on Traffic Synchronization
Claus Gwiggner
Masato Fujita
Yutaka Fukuda
Sakae Nagaoka
Electronic Navigation Research InstituteTokyo
EIWAC, Tokyo, November, 2010.

1

Contents
1. Traffic Synchronization
2. Delay propagation
3. Delay absorption
4. Conclusions2

1. Traffic
Synchronization

Airspace Congestion

Gates

Tokyo
Terminal
Area
Figure: Inefficient arrival flow to Tokyo Int'l Airport

Top of descent

En-route sector

Delay● Fuel consumption● Controller workload●3

1. Traffic
Synchronization

Airspace Congestion

Gates

Tokyo
Terminal
Area

Traffic Synchronization
Speedcontrolcontrol
Speed
DynamicQueuesqueues
DynamicBalance
ground / enroute ground andBalancedelays delays
en-route

Figure: Inefficient arrival flow to Tokyo Int'l Airport

Definition: “Tactical establishment andof orderly andEn-route
maintenance of aTop
safe,efficientsector
flow of air traffic.”descent[ICAO]
Benefits:●

Less delay●Less fuel consumption●Less controller workload [ICAO 2005, SESAR, NextGen]41. Traffic
Synchronization

Concept of Operations“Controlled time of arrival” (CTA)[i][CTAiTarget precision:+/- 10 seci+1]

CTAi1

Window size:[cta-x, cta+x] sec

Traffic Window

Current precision:+/- 30 sec
Traffic Window

SectorFlight Trials:
CTA/ATC system integration
studies (CASSIS)

Window position:●between sectors●on waypoints●on merge-points●(...)

Simulation studies:
Contract-based
Air Transportation
System project (CATS)
5[CASSIS 09, CATS 08]

1. Traffic
Synchronization

Concept of Operations“Controlled time of arrival” (CTA)[i][CTAii+1]

CTAi1Open questions
Target precision:+/- 10 sec

Traffic Window

Feasibility ?
Currentprecision:● Number of constraints ?
+/- 30 sec● Impact of uncertainty

Window size:[cta-x, cta+x] sec●

Traffic WindowSector

Flight Trials:
CTA/ATC system integration
studies (CASSIS)

Window position:●between sectors●on waypoints●on merge-points●(...)

Simulation studies:
Contract-based
Air Transportation
System project (CATS)
6[CASSIS 09, CATS 08]

2. Delay
Propagation

Delay Propagation
under uncertainties

dimi−1
eta D eta Cd i1=max d i −a imi ,0
Follower
LeaderHeavy

Mid/Small

Heavy

90

120

Mid/Small6060

A i rc ra ft e ta
A1 2 :0 1B
1 2 :0 2
D1 2 :0 4C
1 2 :0 5

Queueing Delays[Erzberger 95, Bayen 06, Balakrishnan 09]

s ta d ela y
1 2 :0 10
1 2 :0 3
1
1 2 :0 5
1
1 2 :0 7
27

2. Delay
Propagation

Delay Propagation
under uncertainties

hHigh altitude
delay absorption(fuel efficient)Top of descent(TOD)1− d i

d i :queueing delay of aircraft i : absorption coefficient01ch ,c l : delay absorption costsc h c l , [min−1 ]Optimaldescent

Low altitude
delay absorption(fuel inefficient)gate dixProfile plotdimi−1eta D eta Cd i1=max d i −a imi ,0Follower
LeaderHeavy

Mid/SmallHeavy

90

120

Mid/Small60

60

A i rc ra ft e ta
A
1 2 :0 1B
1 2 :0 2D
1 2 :0 4C
1 2 :0 5

Queueing Delays[Erzberger 95, Bayen 06, Balakrishnan 09]

s ta d ela y
1 2 :0 10
1 2 :0 3
1
1 2 :0 5
1
1 2 :0 7
28

2. Delay
Propagation

Delay Propagation
under uncertainties

hHigh altitude
delay absorption(fuel efficient)Top of descent(TOD)1− d id i :queueing delay of aircraft i : absorption coefficient01ch ,c l : delay absorption costsc h c l , [min−1 ]Optimaldescent
Remaining delay on
low altitude

Delayed arrivalat TOD

Low altitude
delay absorption(fuel inefficient)

gate

 dix

Profile plot

Actual time of arrivalat TODhigh altitude
delay absorption

Scheduled time of arrivalat TOD

low altitude
delay absorption
atasta

cost:

cost:

1− d i dichtclc i=[1−c h  c l ]d i

Delay absorption
costTime plotdimi−1
eta D eta Cd i1=max d i −a imi ,0Follower
LeaderHeavy

Mid/SmallHeavy

90

120

Mid/Small60

60

A i rc ra ft eta
A
1 2 :0 1B
1 2 :0 2D
1 2 :0 4C
1 2 :0 5Queueing Delays[Erzberger 95, Bayen 06, Balakrishnan 09]

s ta d ela y
1 2 :0 10
1 2 :0 3
1
1 2 :0 5
1
1 2 :0 729

2. Delay
Propagation

Delay Propagation
under uncertainties

hHigh altitude
delay absorption(fuel efficient)Top of descent(TOD)1− d i

d i :queueing delay of aircraft i : absorption coefficient01ch ,c l : delay absorption costsc h c l , [min−1 ]Optimaldescent
Remaining delay on
low altitude

Delayed arrivalat TOD

Low altitude
delay absorption(fuel inefficient)Actual time of arrivalat TODhigh altitude
delay absorption

 di



low altitude
delay absorption
atasta

cost:

cost:

1− d i dichgate

Scheduled time of arrivalat TODclc i=[1−c h  c l ]d i

Delay absorption
costTime plotx

Profile plottmi a idimi−1sta g(scheduled)eta D eta Cd i1=max d i −a imi ,0Follower
LeaderHeavy

Mid/SmallHeavy

90

120

Mid/Small60

60

A i rc ra ft eta
A
1 2 :0 1B
1 2 :0 2D
1 2 :0 4C
1 2 :0 5Queueing Delays[Erzberger 95, Bayen 06, Balakrishnan 09]td is ta d ela y
1 2 :0 1
01 2 :0 3
1
1 2 :0 5
1
1 2 :0 7210

2. Delay
Propagation

Delay Propagation
under uncertainties

hHigh altitude
delay absorption(fuel efficient)Top of descent(TOD)1− d id i :queueing delay of aircraft i : absorption coefficient01ch ,c l : delay absorption costsc h c l , [min−1 ]Optimaldescent
Remaining delay on
low altitude

Delayed arrivalat TOD

Low altitude
delay absorption(fuel inefficient)Actual time of arrivalat TODhigh altitude
delay absorption

 di

low altitude
delay absorption
ata

sta

cost:

cost:

1− d i dichgate

Scheduled time of arrivalat TODcl

Delay absorption
cost

c i=[1−c h  c l ]d i

Time plotx

Profile plottmi a idimi−1sta g(scheduled)teta D eta Cd i1=max d i −a imi ,0Follower
LeaderHeavy

Mid/Small

Heavy

90

120

Mid/Small60

60

A i rc ra ft eta
A
1 2 :0 1B
1 2 :0 2D
1 2 :0 4C
1 2 :0 5

Queueing Delays[Erzberger 95, Bayen 06, Balakrishnan 09]

ata gs ta d ela y
1 2 :0 101 2 :0 3
1
1 2 :0 5
1
1 2 :0 72(actual)

d ixx
i11

2. Delay
Propagation

Delay Propagation
under uncertainties

hHigh altitude
delay absorption(fuel efficient)Top of descent(TOD)1− d i

d i :queueing delay of aircraft i : absorption coefficient01ch ,c l : delay absorption costsc h c l , [min−1 ]Optimaldescent
Remaining delay on
low altitude

Delayed arrivalat TOD

Low altitude
delay absorption(fuel inefficient)Actual time of arrivalat TODhigh altitude
delay absorption

Scheduled time of arrivalat TOD

low altitude
delay absorption
ata

cost:

cost:

1− d i dichgate

 distacl

Delay absorption
cost

c i=[1−c h  c l ]d i

Time plotxProfile plottmi a idimi−1sta g(scheduled)teta D eta Cd i1=max d i −a imi ,0Follower
LeaderHeavy

Mid/SmallHeavy

90

120

Mid/Small60

60

A i rc ra ft e ta
A
1 2 :0 1B
1 2 :0 2D
1 2 :0 4C
1 2 :0 5

d i

ata gs ta d ela y
1 2 :0 1
0
1 2 :0 3
1
1 2 :0 5
1
1 2 :0 7
2x(actual)ista g '
re-scheduledxi −aix

 − dimi  ai −i iQueueing Delays[Erzberger 95, Bayen 06, Balakrishnan 09]x

Delay propagation

122. Delay
Propagation

Delay Propagation
under uncertainties

hHigh altitude
delay absorption(fuel efficient)Top of descent(TOD)1− d i

d i :queueing delay of aircraft i : absorption coefficient01ch ,c l : delay absorption costsc h c l , [min−1 ]Actual time of arrivalat TODhigh altitude
delay absorption

low altitude
delay absorption
ataOptimaldescent
Remaining delay on
low altitude

Delayed arrivalat TOD

Scheduled time of arrivalat TOD

cost:stachcl

Traffic Synchronization Problem

Low altitude
delay absorption(fuel inefficient)gate

1− ddGiven :dc =[1−c  c ]dFlow of pre-scheduled aircraft sta 1 sta 2 ...stan withplot
Profile plot queueing delaysx d i and trajectory prediction errors Timei.
iii

di

mi−1

hFollower
LeaderHeavy

Mid/Small

Heavy

90

120

Mid/Small6060

A i rc ra ft e ta
A
1 2 :0 1B
1 2 :0 2D
1 2 :0 4C
1 2 :0 5sta gFind :Optimal delayabsorption strategy.
(scheduled)tx(actual)xista g 're-scheduledx
i −aix

 − dimi  ai −i iQueueing Delays[Erzberger 95, Bayen 06, Balakrishnan 09]

Delay absorption
costi

d i

ata gs ta d ela y
1 2 :0 101 2 :0 3
1
1 2 :0 5
1
1 2 :0 72li

mi a ieta D eta Cd i1=max d i −a imi ,0t

cost:

Delay propagation

13

2. Delay
Propagation

Main Results
1
Analytical model

Monte Carlosimulation

Averagepropagateddelay(normalized)
Flown distance with
reduced speed
00x j0 −lx i0selv ik i vi
with  j : speed control delay for aircraft jw i : metering delay for aircraft i = j-1
 j wi−

0.2

0.4

0.8

1.0u/ ∞∞k=0

u=0 v=0E D i =∑ k 1 ∫ ∫ u− v P k | u , v f u gv dvdu
withf , g: probability density function of  , d
P : distribution of length of propagation[Gwiggner et al. 09, 10]

0.6

14

2. Delay
Propagation

Main Results
In words:1
Analytical model

Speed control itself causes no delay
propagation.
Average

Monte Carlosimulation

propagateddelay(normalized)

The reason for delay propagation:
Flown distance with
reduced speed
trajectory
prediction errors
00x j0 −lx i0se
lv i
k i viwith  j : speed control delay for aircraft j
w i : metering delay for aircraft i = j-1
 j wi−

0.2

0.4

0.8

1.0u/ ∞∞k=0u=0 v=0E D i =∑ k 1 ∫ ∫ u− v P k | u , v f u gv dvdu
withf , g: probability density function of  , dP : distribution of length of propagation[Gwiggner et al. 09, 10]

0.615

3. Delayabsorption

Delay absorption strategy●Delay absorption strategy
Trade-off●High altitude
High propagated delay

total cost
全体コスト
additional delay
追加遅延時間baseline cost
燃料コスト

High altitude Fraction of metering delay absorbed in low altitude Low altitude
only
only
低高度での滞留時間の割合
高高度のみ
低高度のみ

c =[c L c H 1−]d d  =d 0d p  ,average delay+
propagation

wherec L ≫c H :cost of delay absorbtion (kg/min)
d 0 :average queueing delayd p : propagated delay●Fuel efficiency●Workload sharing

Low altitude
High fuel consumption

Consequences:●●

Even in the future, there is aneed for radar vectoring.
Sequencing strategies under
uncertainties should be studied.

16

4. Conclusions●Conclusions

Traffic Synchronization●●

Delay Propagation●●

Tactical management of queues of aircraft
Delay propagation due to trajectory prediction
errorsDelay absorption strategy●●

Trade-off between high altitude (fuel efficient) and
low altitude (fuel inefficient)
Even when the objective is to minimize fuel (!)
17

4. Conclusions●Future work

Fundamental Research●●●Conditions for existence of minimum
Delay propagation in transportation
networks

Operational Concept●Ground delay vs. en-route delays●Delay management strategies

18Thank you.
claus@enri.go.jp

19Traffic Synchronization
Tactical phase

Global ATM Concept (ICAO)

Demand/Capacity
Balancing
需要／容量均衡化

Traffic Synchronization● Departure● Arrival● Interaction

Traffic Management Coordinator(TMC)
航空交通管理管制官

Conflict Management
コンフリクト管理

Air Traffic Controller(ATCo)
航空管制官[ICAO 2005, ATM Masterplan]20

Aircraft sequencing
AdiCB
mi−1
eta D eta CDd i1=max d i −a i mi ,0 

Basic Operations●

A ir c r a ft
ABDCSequencing●●●Queueing DelayFirst-come-first-served(FCSF)
Constrained position shifting(CPS)

Metering●

Flow control with separation
constraints mimi mi−1

FCFS delay:
CPS delay:mi

Follower

LeaderHeavy

Mid/Small

Heavy

90

120

Mid/Small

60

60

eta
1 2 :0 1
1 2 :0 2
1 2 :0 4
1 2 :0 5sta
1 2 :0 1
1 2 :0 3
1 2 :0 5
1 2 :0 7

d e la y01
124 min
3.2 min21[Erzberger 95, Bayen 06, Balakrishnan 09]

2. Delaypropagation

Delay propagation

Condition for delay propagation:

Delay triggered by aircraft i:
kD p ,i=[ k  i −ai −k−1ai1 −...−a ik ]− ∑ d ij 1

i  d i
i −a i  d i1...

(2)

j=0k

k

=k i− ∑ k− j a i j − ∑ d i j1

 
j=0k

i −a i −∑ a ij  d ik1(3)

(1)

j=0

≈0

j=1

≈k  d iwhere k is smallest number, such that (1) is smaller thand kPropagation approximation (high-congestion):D p ,i ≈{n−i i − d i , i  d i
0, elseExpectation:∞(4)u/ E D p ,i =n−i  ∫ ∫ u− v f u g v dvdu(5)

u=0 v =0

= ddwith
f , g: probability density function of  , d22