Capacity Utilization Metrics
Revisited: Delay Weighting vs
Demand Weighting
Mark Hansen
Chieh-Yu Hsiao
University of California, Berkeley
01/29/04
1
Outline
‰ Introduction
‰ Existing metrics examination
‰ Proposed metrics
‰ Comparisons: existing vs. proposed
scores
‰ Remarks
2
Introduction
‰ Airport Performance
¾Assessment of the use of the airport’s
capacity, taking into account the relative
importance of meeting arrival and depart
demand in each time period (FAA (1999),
Documentation for airport utilization metrics)
¾Meeting demand is considered by
“utilization”
¾Relative importance is accounted by
“weight” (demand)
3
Existing metrics examination
‰ Utilization Formula (Applied to Arrivals)
Arrival _ Utilizationt =
Actual _ Arrivalst
Min( Arrival _ Demandt , Arrival _ Ratet )
¾ Actual Arrivals: Arrival count for 15-minute time period t
(based on wheels-on time)
¾ Arrival Demand: estimated number of arriving flights
“available” in 15-minute time period t, based on flight plan
or actual arrival time
¾ Arrival Rate: Airport Acceptance Rate for period t
¾ Get full score when the service meets all demand or AAR
¾ Utilization score is taken as the minimum of the formula
result and 1 (no credit for exceeding AAR)
4
Existing metrics examination
‰ Arrival Score Formula
∑ Arrival _ Utilization * Arrival _ Demand
Arrival _ Score =
∑ Arrival _ Demand
t
t
t
t
t
¾Utilization to capture the missed slots of
each period
¾Arrival Demand to represent the relative
importance (missed slot effects) of each
period
5
Existing metrics examination
‰ Graph representation
CDemand t = CDemand t −1 + Arrival _ Demand t
Oct.3, 2003 (DTW Arrivals)
− (CDemand t −1 − CArrivals t −1 )
CDemand
70
CArrival
= CArrivals t −1 + Arrival _ Demand t
No Missed Slot CArrival (NCArrival)
C um ulative count
60
50
Miss 3 slots
Delay caused by
missed slots
NCArrivalt = Min{CDmand t , NCArrivalt −1 + Min
Miss 3 slots
40
CArrivals t = CArrivals t −1 + Actual _ Arrival t
( Arrival _ Demandt , Arrival _ Ratet )}
30
Miss 1 slots
20
Miss 3 slots
10
0
19.2
19.3
19.4
20.1
20.2
20.3
Time
6
Existing metrics examination
‰ Major Drawback: Arrival Demand may not
appropriately reflect the relative importance
(missed slot effects) of each period
¾ Some periods, although their demands are low,
are important because if we miss slots in these
period there will be huge delays
¾ In contrast, some high demand periods are not so
important because the impacts of missed slots
can be recovered very soon
7
Proposed metrics
‰ Basic Idea
¾Keep “Utilization”: account for missed
slots
¾Find another weighting factor, which better
reflects the impacts of missed slots
9 For each period, consider the delay caused by a missed
slot ( What is the extra delay if we miss one additional
slot?) –- the effect may propagate for several periods
9 Economic explanation: employ the marginal costs (extra
delays) as the weights
8
Proposed metrics
‰ example:
Oct.3, 2003 (DTW Arrivals)
CDemand
CArrival
No Missed Slot CArrival (NCArrival)
Carrival'
70
60
60
50
50
Cumulative count
Cumulative count
70
Oct.3, 2003 (DTW Arrivals)
40
Delay caused by
the missed slot
= 60 min
30
20
10
CDemand
CArrival
No Missed Slot CArrival (NCArrival)
Carrival''
Delay caused by
the missed slot
= 45 min
40
30
Miss 1 slot
20
10
Miss 1 slot
0
0
19.2
19.3
19.4
20.1
20.2
19.2
20.3
19.3
19.4
20.1
20.2
20.3
Time
Time
Miss Slot Period
3rd qrt, 7p.m.
4th qrt, 7p.m.
Arrival Demand t
21
<
34
Delay per missed slot t
60
>
45
9
Proposed metrics
‰ New Arrival Score Formula
∑ Arrival _ Utilization * Marginal _ Delay
New _ Arrival _ Score =
∑ Marginal _ Delay
t
t
t
t
t
¾ Utilization to capture the missed slots of each
period
¾ Marginal Delay to represent the relative
importance (missed slot effects) of each period: It
is the area between original and hypothetical
(assuming one additional missed slot) cumulative
arrival curves
10
Comparisons:
existing vs. proposed scores
‰ Data
¾ ASPM Airport Quart Hour Data
¾ 32 DOT Airports, from 1/1/00 to 11/17/03, except
some days in which their data with “daylight
saving changes” problem
‰ Comparisons
¾ Different length of time: daily and monthly scores
¾ Given airports, investigate the time trends
¾ Given time periods, examine the differences
between airports
11
Comparisons:
existing vs. proposed scores
‰
All Data:
¾ Highly (positively) correlated
¾ Correlation is less for low scores
¾ Daily scores have higher correlation than monthly scores
12
Comparisons:
existing vs. proposed scores
‰ Given Airport (each point is a monthly score):
¾ Positively correlated, but differences among airports
¾ The proposed metrics may get lower (MSP) or higher (MCO)
scores
13
Comparisons:
existing vs. proposed scores
‰ Given Time (each point is an airport monthly score):
¾ Positively correlated, but differences among time periods
¾ More airports get lower scores in this two periods by the
proposed metrics
14
Comparisons:
existing vs. proposed scores
‰ Airports change over
times (each point is an airport
monthly score):
10
8
6
New Score Change
¾ Scores differences
between 10/2000 and
10/2003
¾ For most airports the
measures are
consistent: (+,+) or (-,-)
--better or worse
¾ 4 airports inconsistent:
(+,-)
Scores Change Over time
4
2
0
-4
-2
-2
0
2
4
6
8
10
LAX
-4
-6
-8
Old Score Change
15
Comparisons:
existing vs. proposed scores
‰ Airport Ranks: (Based
Airport Ranks (Based on whole period scores)
on whole period scores)
28
LAX
STL
24
New Score Ranks
¾ For top and bottom
ranking airports,
ranks are similar
¾ For medium
ranking airports,
ranks may change
more
32
20
16
12
8
SLC
4
DEN
0
0
4
8
12
16
20
24
28
32
Old Score Ranks
16
Comparisons:
existing vs. proposed scores
‰ Correlation between Airport Traffic and Scores (All
Data)
¾ For the both metrics, an airport with high traffic has a little
higher possibility get lower score
¾ If we consider specific airport, the correlation may change
to positive
Corr. Coeff.
Daily Traffic
Monthly Traffic
Old Score
-0.02
-0.17
New Score
-0.03
-0.24
17
Remarks
‰ Alternative ways of determining
marginal delay
¾One less missed slot instead of one more
¾Cases when demand<AAR—missed slot
may be filled or unfilled
‰ Utilization compensation:
¾Both metrics set utilization <=1 : no credit
for exceeding AAR
¾Modest proposal: don’t truncate!
18
Remarks
‰ Other meaningful
metrics:
CDemand
70
CArrival
No Missed Slot CArrival (NCArrival)
60
Cumulative count
¾Total Delay caused
by missed slots
¾Average delay per
missed slot
Oct.3, 2003 (DTW Arrivals)
50
40
Delay caused by
missed slots
30
20
10
0
19.2
19.3
19.4
20.1
20.2
20.3
Time
19
Questions?
20