Capacity Utilization Metrics Revisited: Delay Weighting vs Demand Weighting. Mark Hansen Chieh-Yu Hsiao University of California, Berkeley 01/29/04

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1 Capaciy Uilizaion Merics Revisied: Delay Weighing vs Demand Weighing Mark Hansen Chieh-Yu Hsiao Universiy of California, Berkeley 01/29/04 1

2 Ouline Inroducion Exising merics examinaion Proposed merics Comparisons: exising vs. proposed scores Remarks 2

3 Inroducion Airpor Performance Assessmen of he use of he airpor s capaciy, aking ino accoun he relaive imporance of meeing arrival and depar demand in each ime period (FAA (1999), Documenaion for airpor uilizaion merics) Meeing demand is considered by uilizaion Relaive imporance is accouned by weigh (demand) 3

4 Exising merics examinaion Uilizaion Formula (Applied o Arrivals) Arrival _ Uilizaion = Acual _ Arrivals Min( Arrival _ Demand, Arrival _ Rae ) Acual Arrivals: Arrival coun for 15-minue ime period (based on wheels-on ime) Arrival Demand: esimaed number of arriving flighs available in 15-minue ime period, based on fligh plan or acual arrival ime Arrival Rae: Airpor Accepance Rae for period Ge full score when he service mees all demand or AAR Uilizaion score is aken as he minimum of he formula resul and 1 (no credi for exceeding AAR) 4

5 Exising merics examinaion Arrival Score Formula Arrival _ Score = Arrival _ Uilizaion Uilizaion o capure he missed slos of each period Arrival Demand o represen he relaive imporance (missed slo effecs) of each period Arrival _ Demand * Arrival _ Demand 5

6 Exising merics examinaion Graph represenaion Cumulaive coun CDemand CArrival Oc.3, 2003 (DTW Arrivals) No Missed Slo CArrival (NCArrival) Delay caused by missed slos Miss 1 slos Miss 3 slos Miss 3 slos CDemand CArrivals = CDemand = CArrivals 1 ( CDemand Arrival _ Demand CArrivals 1 + Arrival _ Demand = CArrivals 1 + Acual _ ) Arrival NCArrival = Min{ CDmand, NCArrival 1 + Min ( Arrival _ Demand, Arrival _ Rae )} 10 Miss 3 slos Time 6

7 Exising merics examinaion Major Drawback: Arrival Demand may no appropriaely reflec he relaive imporance (missed slo effecs) of each period Some periods, alhough heir demands are low, are imporan because if we miss slos in hese period here will be huge delays In conras, some high demand periods are no so imporan because he impacs of missed slos can be recovered very soon 7

8 Proposed merics Basic Idea Keep Uilizaion : accoun for missed slos Find anoher weighing facor, which beer reflecs he impacs of missed slos For each period, consider he delay caused by a missed slo ( Wha is he exra delay if we miss one addiional slo?) - he effec may propagae for several periods Economic explanaion: employ he marginal coss (exra delays) as he weighs 8

9 example: Oc.3, 2003 (DTW Arrivals) Proposed merics Oc.3, 2003 (DTW Arrivals) CDemand CArrival No Missed Slo CArrival (NCArrival) Carrival' CDemand CArrival No Missed Slo CArrival (NCArrival) Carrival'' Cumulaive coun Delay caused by he missed slo = 60 min Cumulaive coun Miss 1 slo Delay caused by he missed slo = 45 min 10 Miss 1 slo Time Time Miss Slo Period 3 rd qr, 7p.m. 4h qr, 7p.m. Arrival Demand 21 < 34 Delay per missed slo 60 > 45 9

10 Proposed merics New Arrival Score Formula New _ Arrival _ Score = Arrival _ Uilizaion * Marginal _ Delay Uilizaion o capure he missed slos of each period Marginal Delay o represen he relaive imporance (missed slo effecs) of each period: I is he area beween original and hypoheical (assuming one addiional missed slo) cumulaive arrival curves Marginal _ Delay 10

11 Comparisons: exising vs. proposed scores Daa ASPM Airpor Quar Hour Daa 32 DOT Airpors, from 1/1/00 o 11/17/03, excep some days in which heir daa wih dayligh saving changes problem Comparisons Differen lengh of ime: daily and monhly scores Given airpors, invesigae he ime rends Given ime periods, examine he differences beween airpors 11

12 Comparisons: exising vs. proposed scores All Daa: Highly (posiively) correlaed Correlaion is less for low scores Daily scores have higher correlaion han monhly scores 12

13 Comparisons: exising vs. proposed scores Given Airpor (each poin is a monhly score): Posiively correlaed, bu differences among airpors The proposed merics may ge lower (MSP) or higher (MCO) scores 13

14 Comparisons: exising vs. proposed scores Given Time (each poin is an airpor monhly score): Posiively correlaed, bu differences among ime periods More airpors ge lower scores in his wo periods by he proposed merics 14

15 Comparisons: exising vs. proposed scores Airpors change over imes (each poin is an airpor monhly score): Scores differences beween 10/2000 and 10/2003 For mos airpors he measures are consisen: (+,+) or (-,-) --beer or worse 4 airpors inconsisen: (+,-) New Score Change Scores Change Over ime LAX Old Score Change 15

16 Comparisons: exising vs. proposed scores Airpor Ranks: (Based on whole period scores) For op and boom ranking airpors, ranks are similar For medium ranking airpors, ranks may change more New Score Ranks Airpor Ranks (Based on whole period scores) STL LAX SLC DEN Old Score Ranks 16

17 Comparisons: exising vs. proposed scores Correlaion beween Airpor Traffic and Scores (All Daa) For he boh merics, an airpor wih high raffic has a lile higher possibiliy ge lower score If we consider specific airpor, he correlaion may change o posiive Corr. Coeff. Old Score New Score Daily Traffic Monhly Traffic

18 Remarks Alernaive ways of deermining marginal delay One less missed slo insead of one more Cases when demand<aar missed slo may be filled or unfilled Uilizaion compensaion: Boh merics se uilizaion <=1 : no credi for exceeding AAR Modes proposal: don runcae! 18

19 Remarks Oher meaningful merics: CDemand CArrival Oc.3, 2003 (DTW Arrivals) No Missed Slo CArrival (NCArrival) Toal Delay caused by missed slos Average delay per missed slo Cumulaive coun Delay caused by missed slos Time 19

20 Quesions? 20