STATISTICAL BASED MODEL OF AGGREGATE AIR TRAFFIC FLOW. Trevor Owens UC Berkeley 2009
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1 STATISTIAL BASED MODEL OF AGGREGATE AIR TRAFFI FLOW Trevor Owens U Berkeley 2009
2 OUTLINE Moivaion Previous Work PDE Formulaion PDE Discreizaion ell Transmission Based Model Sochasic Process Descripion Daa Acquisiion and Program Archiecure Eperimenal Verificaion Fuure Work
3 MOTIVATION ongesed air raffic secors increase risk of operaor failure and decrease safey Build model o predic densiy and hus reroue planes if necessary urren Mehods use are oo compuaionally inense for real ime simulaion ombine effors o lessen compuaional cos Discreize PDE model Use links of ell Transmission Model TM Model enrances and eis ino links and secors sochasically
4 PREVIOUS WORK Work on several differen mehods has already been done. The TM PDE formulaion and a Menon Model have been used o creae a model and es is efficiency. [2] omparison of differen graph neworks showing he TM o run abou 10 imes faser han he second fases: PDE model PDE Formulaion Gives a high accuracy bu is compuaionally epensive TM Deerminisic Process Ineger Programming Problem ompuaionally Inense as well wihou relaaion Dynamic Sochasic Model Roy e. al. show ha he enrance and eis o secors is a sochasic process. Done by secor which may no be very accurae.
5 PDE FORMULATION Model he number of planes along a link firs is number of planes in [0] along link Using a conservaion of mass formulaion we have: Wih I and B: Where Equivalen form using densiy Taking parial w.r.. : I and B: is he inflow v is velociy Furhermore can formulae his by link. Assume m incoming links n ougoing
6 Allocaion mari: So require sum: Shown o be well posed wih unique soluion in [2] Minimize ime in secor: Perurb H and we use he Adjoin Mehod as shown in class or do we?
7 DISRETIZE PDE Firs So cancelling ou: Then: So subsiuing for wha hese quaniies are: Where we used: Mass Balance assuming he planes are moving in + direcion: This is he ell Transmission Model which is a discree form of he PDE lim lim 0 0 q v q v q 2 q in ou ou
8 ELL TRANSMISSION MODEL Discree equivalen of Mass Balance equaion Same number of planes enering a link mus also leave ha link Our fearless leader Professor arlos F. Daganzo Previously done for 1 minue cells now done for links 1 direced link for every 2 secors bordering secor of ineres
9 STOHASTI MODEL Idea: Travel ime on a link has a Gaussian Disribuion Model TM parameers on a link as a Poisson Process Find mean: Average number of deparures: So Probabiliy of secor coun decrease is: Then we can wrie he ell Transmission parameer as: Based on eperimenaion i appears we can model he oher TM parameers similarly
10 ADSI DATA There are a bunk load of planes ha fly over US every week 1 ener 7 Days 2 Secors ZOA34 and ZOA Flighs 11 Million Daum 5 Hours of processing per secor per week Daa for full year for whole U.S. is abou a Terrabye
11 PROGRAM ARHITETURE Raw Daa Processing Organize Daa by Fligh Info Finder Secor Enrance/Ei Times Travel Times by Link Plo Time Disribuion by Link Fligh Hisory Enrance Times Which Link Possible Links Time Hisogram Time In Link Remove Lis Repeiions
12 EXPERIMENTAL VERIFIATION Time of a plane in a secor is disribued in a roughly Gaussian fashion reaing a saisical model for each link proved difficul since no as many planes fly hough a link ZOA34 ZOA33 ZOA32 ZOA15 ZOA13 GND ZOA ZOA ZOA ZOA GND Travel Times hrough secor ZOA34 in one day
13 TIME DISTRIBUTIONS FOR SETOR ZOA34
14 TIME DISTRIBUTIONS FOR SETOR ZOA32
15 Hard o see a Gaussian Disribuion wih a small number of planes Top: ZOA34 Boom: ZOA32 Lef: Planes flying hrough secor Middle: Planes deparing from secor Righ: Planes landing in secor
16 FUTURE WORK I plan o use more daa o ge a beer saisically based link model This will likely require compiling he code and running on a faser compuer or cluser before a good model can be creaed Tesing he model for predicive capabiliies an be eended o oher secors across US
17 REFERENES
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