Flötteröd, Gunnar

Infoscience - École polytechnique fédérale de Lausanne

Disaggregate simulation and some impliations foralibrationGunnar FlötterödJune 28, 20111 / 19An appeal for a more disaggregate perspetive•ommon sense is to keep things simple•inreased disaggregation looks more at the distributed side of a simulation may appear as if one was not keeping things simple•this talk indiates relevane and feasibility of disaggregation2 / 19One argument: alibration priniples stay lear•alibration problem statement:P(X | Y) ∝ P(Y | X)P(X)•naive simulation of the solution:E{X | Y} ∝ˆXP(Y | X)P(X)dX≈1RR∑r=1XrP(Y | Xr ); Xr ∼ P(X)•It is possible to do things like this for very large systems!3 / 19OutlineRelevane: truthful modeling of unertaintyDoability: avoiding to drown in detailsSummary4 / 19OutlineRelevane: truthful modeling of unertaintyDoability: avoiding to drown in detailsSummary5 / 19Explaining deviations from reality•when alibrating a (ompliated) mirosimulation... one needs some kind of alibration model this model must explain all deviations from reality•essentially two approahes:1. use a deterministi alibration model1and add random slak2. expliitly use a stohasti model to represent unertainty1assignment matrix, OD matrix, linear dynamis, response surfae, ...6 / 19Deterministi alibration model + random slak?•(typial) measurement equation:Y = F (X1) + ε(X2)•two extreme ases1. analyst really knows what is going on: Y = F (X1)2. analyst does not get the ausality right: Y = ε(X2)•in transportation, one seems to deal more with ase 2...7 / 19Example: hoie set unertainties•(simulated) travel behavior with unertain hoie sets:Pn(i) =∑Cn∈CPn(i | Cn)Pn(Cn)•operational version:Pn(i) = Pn(i | C)•not allowing for all alternatives an lead to inonsistenies well known in hoie modeling have never seen this in OD matrix estimation8 / 19Things an go wrong in the simplest aseap=2000 ap=1000 ap=2000ap=1000•senario: peak hour demand of 1500 exeeds eah route alone ongestion builds up upstream of the diverge9 / 19Things an go wrong in the simplest aseap=2000 ap=1000 ap=2000ap=1000•senario: peak hour demand of 1500 exeeds eah route alone ongestion builds up upstream of the diverge•best-response hoie set generation never nds the detour•even with a stohasti hoie model, no one takes the detour•eet on OD/path ow estimation when using random slaks?!9 / 19Metropolis-Hastings sampling of paths (1/2)•approah give every path i ∈ C a weight b(i) > 0 sampling probability q(i) shall be ∝ b(i)•diret sampling from q(i) requires path enumerationq(i) =b(i)∑j∈Cb(j)•MH does the job based on pair-wise omparisons onlyq(i)q(j)=b(i)b(j)10 / 19Metropolis-Hastings sampling of paths (2/2)[[movie℄℄22Flötteröd & Bierlaire (submitted).transp-or.epfl.h/douments/tehnialReports/FloeBier11.pdf11 / 19OutlineRelevane: truthful modeling of unertaintyDoability: avoiding to drown in detailsSummary12 / 19Where this is going•this talks suggests to simulate and alibrate more details•here: an idea of how a gradual enrihment is possible rst, introdue disaggregation without additional modeling seond, exploit the resulting struture whenever onvenient13 / 19Example: dynami OD matrix estimation•well-known to be utterly underspeied•marosopi approahes to deal with this: non-negativity onstraints stay lose to an (arbitrary) prior assume (linear) dynamis14 / 19Example: dynami OD matrix estimation•well-known to be utterly underspeied•marosopi approahes to deal with this: non-negativity onstraints stay lose to an (arbitrary) prior assume (linear) dynamis•problems arise when faing: rigorous mass onservation truthful representation of demand utuations more than a handful of ommodities14 / 19Autoregressive OD matrix dynamis•autoregressive model for OD ows (simplied):xs(k + 1) =∑rars(k)xr(k) + εs(k)15 / 19Autoregressive OD matrix dynamis•autoregressive model for OD ows (simplied):xs(k + 1) =∑rars(k)xr(k) + εs(k)•expeted OD ows are sums of hoie probabilities:∑nPn(s|k + 1) =∑rars(k)∑nPn(r |k)15 / 19Autoregressive OD matrix dynamis•autoregressive model for OD ows (simplied):xs(k + 1) =∑rars(k)xr(k) + εs(k)•expeted OD ows are sums of hoie probabilities:∑nPn(s|k + 1) =∑rars(k)∑nPn(r |k)•looking bak at the original problem:⇐ ∀n : Pn(s|k + 1) =∑rars(k)Pn(r |k)15 / 19Really more omplex than the AR model?k − 1rksk + 1ars(k)•Markovian trip making dynamis at individual level•truthful representation of original AR model•but...16 / 19Added value of traveler disaggregation•onstraints beome simple in the disaggregate approah: rigorous mass onservation truthful representation of demand utuations more than a handful of ommodities•in addition, one an add any behavioral model of trip haining•in this partiular example, all of this is already possible33Flötteröd & al. (2011). Transp. Siene.17 / 19OutlineRelevane: truthful modeling of unertaintyDoability: avoiding to drown in detailsSummary18 / 19Summary•disaggregate simulation & alibration modeling apture unertainty where it ours ontribute to unbiased alibration•model omplexity does not neessarily explode in the 1st instane, only add physially existing struture in the 2nd instane, add more omplex model struture•(very subjetive) onlusion alibration models benet from inreased disaggregation possible without jumping right on ativity-based models19 / 19

Disaggregate simulation and some implications for calibration

http://infoscience.epfl.ch/record/167453/files/FloeMULTITUDE2011.pdf

Disaggregate simulation and some implications for calibration

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