Impact of Probabilistic Road Capacity Constraints on the Spatial Distribution of Hurricane Evacuation Shelter Capacities

Transcription

1 Impac of Probablsc Road Capac Consrans on he Spaal Dsrbuon of Hurrcane Evacuaon Sheler Capaces Musafa Anl Yazc M.Sc. (Correspondng Auhor) Graduae Research Asssan Deparmen of Cvl and Envronmenal Engneerng Rugers he Sae Unvers of New Jerse. 623 Bowser Road Pscaawa NJ USA el: (732) Fa: (732) e-mal: azc@eden.rugers.edu Kaan Ozba Ph.D Assocae Professor Deparmen of Cvl and Envronmenal Engneerng Rugers he Sae Unvers of New Jerse 623 Bowser Road Pscaawa NJ USA el: (732) Fa: (732) e-mal: kaan@rc.rugers.edu Word coun: Fgures + 3 ables = 7494 Absrac: 24 Submsson Dae: Augus Paper Submed for Presenaon and Publcaon a he ransporaon Research Board s 86h Annual Meeng Washngon D.C RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal.

2 Yazc M.A. Ozba K. ABSRAC he sud s focused on deermnng he change n capac requremens and desrable shelers locaons as a resul of lnk capac changes durng evacuaon. A Cell ransmsson (CM) based ssem opmal dnamc raffc assgnmen (SODA) formulaon frs proposed b Zlaskopoulos(3) s eended b nroducng probablsc capac consrans. plep mehod frs proposed b Prekopa(8) s used o deal wh probablsc capac consrans of he proposed sochasc SODA model. he model capures he probablsc naure of lnk capaces due o he mpacs of evens such as hurrcanes and earhquakes ha can compleel or parall damage hghwa lnks. Frsl a smple sngle desnaon eample nework s suded o show he effecveness of he proposed model. hen he mpac of usng sochasc and deermnsc lnk capaces s also analzed usng a smplfed mulple-orgn mulple-desnaon verson of he Cape Ma nework. he desrable sheler locaons are evaluaed b leng sochasc SODA model o assgn flows ha generaes he mnmum ssem-wde ravel me. he resuls show ha nroducng probablsc lnk capaces can adus he overall flow n he nework as well as he sheler ulzaon. hus f he planners consder he predcons of he deermnsc model he ma face he rsk of no havng suffcen food medcne and oher emergenc suppl n shelers. hs paper suggess a more realsc approach o evacuaon plannng o avod he neffcen emergenc plannng ha creaed pos-dsaser problems n recen maor dsasers such as Karna and he sunam n Souh Eas Asa. RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal. 2

3 Yazc M.A. Ozba K. INRODUCION Sheler as defned n Oford Englsh dconar s -a place gvng proecon from bad weaher or danger. 2-a place provdng food and accommodaon for he homeless. 3-a shelded condon; proecon. Perods wh necessar use of shelers are as broad as he defnon: evacuaons n general bu especall hurrcane evacuaons earhquake response war condons refugee allocaon ec. hs paper sudes he locaon and effecveness of hurrcane evacuaon shelers wh a sochasc programmng model. he analss s focused on deermnng he desrable locaon and capac of shelers whch are less frequenl suded compared o her srucural and operaonal aspecs. A cell ransmsson model (CM) based ssem opmal dnamc raffc assgnmen (SODA) formulaon frs proposed b Zlaskopoulos(3) s emploed. An eample nework s suded wh possble sheler locaons. hs model s eended b nroducng sochasc cell capac consrans o capure he probablsc naure of lnk capaces due o he mpacs of evens such as hurrcanes and earhquakes ha can compleel or parall damage hghwa lnks. he sheler locaons are evaluaed b leng sochasc SODA model o assgn flows ha generaes he mnmum ssemwde ravel me. he number and locaon of he canddae shelers are assumed o be known a-pror. hen each possble sheler locaon s modeled as a desnaon node ha connecs o a super desnaon n order o be conssen wh he orgnal formulaon suggesed b Zlaskopoulos(3). he desnaons are evaluaed based on he flows he arac as a resul of SO assgnmen process. he mpac of sochasc and deermnsc lnk capaces n erms of he effecveness of shelers s also analzed usng a smplfed verson of he comple Cape Ma nework ha was recenl suded for varous realworld Hurrcane evacuaon scenaros. LIERAURE REVIEW Sudes and gudelnes abou shelers are mosl focused on srucural and operaonal ssues raher han allocaon and he defne sheler performance measures under hurrcane nduced loads(56). Operaonal sudes nvesgae he on-se problems such as frs ad food and waer suppl ec. here are few oher sudes ha address he effec of sheler locaons on he evacuaon performance. Sheral e.al.(4) are among he frs researchers o address he effec of locaon. he propose a locaonallocaon algorhm o deermne he bes sheler locaons among possble combnaons whch mnmze he congeson relaed oal evacuaon me. he proposed model s esed on Vrgna Beach nework. In Kongsomsaksakul e.al.(2) same problem s solved b emplong Sackelberg game o model he neracon beween he plannng auhor and he evacuees. he problem s modeled usng a b-level programmng formulaon. he plannng auhor deermnes he number and locaons of shelers ha mnmze he oal nework evacuaon me whereas he evacuees smulaneousl decde he sheler o go and he roue o ake whn he capac consrans and locaon of he sheler. Generc algorhm s used o solve he problem and he fndngs are appled on Logan nework n Uah. wo cases one beng nfne (no capac consran) and one beng lmed sheler capac s suded. For no capac consran case egh of oal 0 shelers are chosen for opmal performance. For lmed sheler capac case all he canddae shelers are chosen b he evacuees and oal ravel me naurall ncreases. For he hrd case vehcle occupanc s suded. I s shown ha hgher occupanc rae RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal. 3

4 Yazc M.A. Ozba K. leads o less oal evacuaon me whch s also nuve. hus he propose promong hgh vehcle occupanc rae durng evacuaon. Margus e.al.() approach he sheler occupanc ssue as a more socal concep. he focus on he bus-dspachng scheme o deermne he opmal bus allocaon for specfc pck-up-pon-o-sheler roues whle mamzng he number of people evacuaed over a gven me perod. hs knd of scheme s epeced o resul n more effcen evacuaon as well as beng able o reach as man evacuees as possble ha do no have oher means of ransporaon. he evacuaon of people wh no means of ransporaon s proven b Hurrcane Karna o be a maor ssue. he sud assumes fed sheler locaons and formulaes he problem bu pons ou anoher dmenson whch can also be used for deermnng sheler locaons. Alhough proved oherwse n some hurrcane afermahs curren sud assumes ha all he evacuees evacuae b ndvdual vehcles and no modelng effor s pu o nclude effec of mass ransporaon n sheler allocaon. HE MODEL he evacuees are loaded ono he nework from dfferen orgns o reach he canddae sheler nodes. Ssem opmal assgnmen s used o deermne he evacuee flows o he shelers ha mnmze he oal ssem ravel me. No capac s assgned o he shelers and he capac need of each sheler o manan he mnmum oal evacuaon me s deermned a he end of evacuaon perod. he change n evacuaon performance measures such as average ravel me (A) clearance mes (C) are also found n case of closng ndvdual shelers. A can be consdered o be he perod durng whch he evacuee wll be eposed o rsk unl s/he reaches he desnaon (e.g. sheler). Snce C srongl depends on he loadng me of las evacuee ono he nework A can gve a beer dea abou he rsk eposure. hen he val/mporance of he sheler s deermned b nvesgang he mpac of s absence. In Sheral e.al.(4) a sngle perod model where volume orgnang from each zone s assumed o be dsspaed a a consan rae hroughou he evacuaon horzon s proposed. he gve a real-lfe eample wh consan loadng scheme bu as a fuure eenson he propose a mul perod formulaon ha can use dfferen loadng models such as S-curves. Lkewse Kongsomsaksakul e.al.(2) assgn producons ha are consan for each me sep o each evacuaon zone however he do no consder oher loadng models. Neverheless he address anoher mporan pon whch s he flood rsk durng evacuaon process. Floodng whch s lkel o occur as a resul of hurrcane surges durng evacuaon ma reduce he lnk capaces hus overall evacuaon performance. her sud does no nclude an analss for floodng condons bu he sugges usng CM based dnamc raffc assgnmen o capure he flood dnamcs. As suded n Ozba e.al.(6) he choce of demand model clearl affecs he evacuaon performance measures. In anoher sud b Ozba and Yazc(7) evacuaon demand model based on he popular S-curves s suded n deal. I s shown ha even when usng he same demand generaon scheme changes n model parameers have consderable affec on he evacuaon performance. In boh sudes(67) capac reducon due o eernal facors such as floodng s also analzed and he effec of capac reducon s shown o be an mporan facor for evacuaon sudes. o summarze n our sud a more realsc demand model n conuncon wh a model ha can capure he flood rsk (such as he fndngs of SLOSH(4)) s used. For RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal. 4

5 Yazc M.A. Ozba K. he raffc assgnmen CM based SODA formulaon proposed b Zlaskopoulos (3) s emploed. he ssem opmal naure of he assgnmen s assumed o represen he evacuaon condons accurael snce here wll be an offcal evacuaon plan mplemened b polce and oher auhores o ensure he mos effcen evacuaon mes. Alhough ma be clamed ha full user complance can never be acheved he SODA provdes he bes case scenaro for plannng purposes. o capure he probablsc naure of he floodng SODA formulaon gven n (3) s eended b usng probablsc capac consrans. CM Based SODA Model wh Probablsc Capac Consrans Orgnal sngle-desnaon LP formulaon of Zlaskopoulos(3) based on CM assumes deermnsc capac consrans. he complee LP problem consrucon wh dealed eplanaons can be found n (3). Brefl he obecve of he SODA problem s o mnmze he oal ravel me n he nework.e. he ravel me eperenced b all users of he nework. A an me nerval he ravel me eperenced b he users of cell equals oτ beng he number of vehcles n cell me. Accordng o he CM hese users have o sa n hs cell for he duraon of he me nerval. he ravel me eperenced b all users of he nework durng me nerval s τ because ζ / ζ no users are sored a he cell connecors. ζ / ζ s s he se of all cells ecep he snk cells because he snk cells do no conrbue o he oal ssem ravel me. hus he oal ssem ravel me durng he whole assgnmen perod s ζ ζ τ he SODA obecve s o mnmze he funcon () or s ζ ζ s s () (2) because τ was assumed o be one me un snce τ can ake an posve value whou affecng he soluon of he LP. he LP problem wh complee se of consrans whch s a drec eenson of he formulaon gven n (3) are gven below (Equaons 3-22) Mnmze τ ζ ζ s (3) Subec o: Conservaon for all cells ecep source (R) and snk cells (S): RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal. 5

6 Yazc M.A. Ozba K. 6 () () { } 0 S R k k = + Γ Γ ζ ζ ζ (4) Flow nequal consrans for source (R) and ordnar cells (O): ( ) 0 R O ξ ξ (5) ( ) R O Q ξ ξ (6) ( ) R O Q ξ ξ (7) ( ) + R O N ξ ξ δ δ (8) Flow nequal consrans for snk (S) cells: ( ) 0 S ξ (9) ( ) S Q ξ (0) Flow nequal consrans for dvergng (D): ( ) D Q ξ () ( ) + D N ξ δ δ (2) () 0 Γ D ζ (3) D Q ζ (4) Flow nequal consrans for mergng (M) cells: D 0 ζ (5) D Q ζ (6) ( ) Q M Γ ζ (7) ( ) N M + Γ ζ δ δ (8) Mass balance for source cells (R): ( ) ζ ζ = Γ = + d R 0 0 (9) Inal condons and non-negav consrans: ( ) ξ = 0 0 (20) RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal.

7 Yazc M.A. Ozba K. 0 ζ (2) ( ) 0 ξ (22) where; q : lnk flow q ma : mamum flow k : dens k : am dens v : lnk free flow speed w : backward proragaon speed ζ : se of cells; ordnar (O) dvergng (D) mergng (M) source (R) and snk (S). : se of dscree me nervals : number of vehcles n cell a me nerval N : mamum number of vehcles n cell a me nerval : number of vehcles movng from cell o cell a me nerval ξ : se of cell connecors; ordnar (O) dvergng (D) mergng (M) source (R) snk (S). Q : mamum number of vehcles ha can flow no or ou of cell durng me nerval δ : rao v/w for each cell and me nerval (Assumed δ = hroughou he analss) Γ () : se of successor cells o Γ () : se of predecessor cells o cell τ : dscrezaon me nerval d : demand (nflow) a cell n me nerval hs SODA formulaon presened n (3) can be smpl gven n he followng compac sandard form shown n equaon se (24). 7 RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal.

8 Yazc M.A. Ozba K. mn s.. Aυ b υ Q eq 0 A υ = b eq 0 ( ) ξ (23) where υ = s he vecor of ssem saes and Q s he deermnsc capac. A and A eq sands for he equal and nequal consrans of he orgnal formulaon wh correspondng rgh hand sdes b and b eq. hs sandard formulaon s bascall obaned b assgnng υ o represen he capac consrans equaons whch are equaons (7)- (9) ()-(3) (5) and (7)-(9). If cell flow and phscal capac are assumed o be probablsc he se of relevan consrans can be rewren as probablsc consrans for he capac as shown n (24). mn s.. A υ = b Aυ b υ Q eq ( υ φ ) P 2 0 eq p 0 ( ) ξ he problem formulaon shown n equaon-25 dffers from he sandard LP formulaon (equaon-) wh he flow consran P( 2 υ φ) p where φ s he random varable ha represens he probablsc capaces of he seleced cells. Noe ha ν n orgnal formulaon s separaed as ν and 2 ν o show ha boh deermnsc and probablsc capac consrans can be reaed smulaneousl. A dscree probabl dsrbuon s assgned for he capac and for he soluon of hs sochasc LP. Proposed soluon approach for sochasc SODA problem P-Level Effcen Pons (plep) mehod proposed b Prekopa (8) can be emploed o solve hs problem. Below we gve a bref descrpon of hs soluon echnque. P-Level Effcen Pons Defnon: A pon z Z p s called a p-level effcen pon (plep) of a probabl dsrbuon funcon F f F(z) p and here s no z <z such ha F() p where p[0 ]. pleps provde dscrezed se of pons whch gve he lower bound of a specfc probabl dsrbuon. For a scalar random varable ξ and for ever p (0 ) here s eacl one p-effcen pon namel he smalles z such ha F(z) p. he are used n he deermnsc equvalen of he probablsc consran and assure ha he consran wll sasf he gven relabl level p. Snce he defnon of pleps form a lower bound (24) RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal. 8

9 Yazc M.A. Ozba K. o he gven probabl dsrbuon he smaller he p srcer s he assgnmen. p= gves he deermnsc equvalen for he capac consran. As p ges lower he plep pons form a lower bound resulng n smaller number o replace capac n he consran. In oher words small p value forces he assgnmen o ake less rsk n erms of no assgnng a capac ha wll be hgher han he predced. FIGURE shows he plep pons for a wo dmensonal case. Prekopa (9) proposes a recursve algorhm o enumerae he p-effcen pons for a muldmensonal dscree probabl dsrbuon. he resulng LP s easl solved b convenonal mehods afer subsung plep pons n he correspondng consran. FIGURE An Eample of he se Z p wh pleps v v 4 (Source: Dencheva (0)) A sraghforward soluon approach s o fnd all p-effcen pons and o process all LP problems. Le v () s he opmal soluon o he h LP problem wh consran () ( ) ( ) v z. If c v = mnc v hen v () s he opmal soluon. However for hghdmensonal random vecors he number of pleps can be ver large and enumeraon of hose pons ma no be effcen. For hs knd of suaons opmal bounds or usng a dual problem soluon as a sarng pon can be used o decrease he number of pleps. For our problem he nework s desgned o be racable wh sraghforward enumeraon of pleps however a dealed dscusson on dealng avodng numerous plep enumeraon can be found n (0). Deals of usng pleps for sochasc LP problems can be found n (9). he proposed model wh probablsc consrans are used n (3) and wh a smple nework and loadng scheme was shown ha probablsc reamen of roadwa capac reducon can affec he raffc flow consderabl. In curren sud hs fac wll be used o deermne he effec of hs approach on he sheler locaon and capac deermnaon. Neverheless a smple eample eraced from (3) s presened below o clarf he usage of he assgnmen. An Illusrave Eample for Probablsc DA Formulaon Consder he smple nework shown n FIGURE 2. Assume ha Cells #7 and #8 are subec o flood rsk. hese cells are assgned flood probables based on he predeermned probabl ha her ndvdual lanes wll be operaonal durng he evacuaon e.g. he probabl ha 2 or all lanes are operaonal. Praccall hs RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal. 9

10 Yazc M.A. Ozba K. knd of dscree approach s que approprae for hs problem snce paral use of a lane s an unrealsc assumpon. In oher words a lane s eher avalable or unavalable. hs knd of dscree approach also faclaes he use of plep mehod for he probablsc capac consran gven n equaon se-25. For calculang plep pons he on cumulave probabl s needed. he flood probabl for each cell s assumed o be ndependen whch ma sound o be an unrealsc assumpon frs snce hose cells represen consecuve roadwa porons and he ndependence assumpon can be quesoned. However hs assumpon causes no loss of general as far as he problem a hand s concerned. In case of a real applcaon hose probables wll anwa be deermned ndvduall usng ools lke SLOSH (Sea Lake and Overland Surges from Hurrcanes) whch s a compuerzed model run b he Naonal Hurrcane Cener (NHC) o esmae sorm surge heghs and wnds. In oher words hs ndependence assumpon whch s made o avod mahemacal complees nvolved whle fndng on probabl dsrbuons s n fac conssen wh he sae-of-pracce. Moreover he ndependence assumpon wll no mpac he meanng of our fndngs snce we are manl concerned wh he mpac of he sochasc lnk capaces on he evacuaon mes. For hs parcular nework cell#7 whch has 2 lanes are assgned probables for 0 and 2 lanes beng operaonal. Lkewse cell#8 whch has 4 lanes s assgned and 0.05 for and 4 lanes beng operaonal. he plep pons for on probabl dsrbuon of hose cells are calculaed for p=0.75. As menoned earler n hs work hese plep values are subsued for he capac values n he deermnsc equvalen of he capac consran and assure ha he probablsc capac consran wll hold a he gven p value. he resulng plep s found o be ( 3) whch means ha o assure p=0.75 he cell#7 s assgned o have operaonal lane and cell#8 o have 3 operaonal lanes. hen he nework s analzed wh boh deermnsc and probablsc consrans. I should be noed ha he plep pons smpl provde reduced capaces as gven above. Hence one can argue ha reduced capac assgnmen can be done regardless of usng mahemacall sophscaed mehod lke plep. However pleps enable he planner o deermne a relabl measure (p) for he gven reduced capac. For dfferen p values pleps ma sugges less or more reduced capaces can be used n LP however he relabl of graspng he real condons wh he ancpaed probables also changes. In oher words smaller he p value shows he less relabl perceved for he ancpaed probables or more cauous aude owards he oucomes of he probablsc even. FIGURE 2 Eample Nework (3) he resuls show ha emplong probablsc analss aduss all he flows n he nework. he flows on each roue are calculaed b choosng a cell unque o ha pah e.g. cell#9 for Roue- cell#7 for Roue-2 and Cell#3 for Roue-3 and summng up he RB 2007 Annual Meeng CD-ROM 0 Paper revsed from orgnal submal.

11 Yazc M.A. Ozba K. flow hrough hose cells. he percenage of overall flow hrough Roue- ncreases from 44% o 5%. On he oher hand flow on Roue-2 decreases from 24% o 7% whereas flow on Roue-3 sas he same a 32%. hese resuls show ha usng probablsc consrans alers he flows hroughou he nework whch ma hreaen people s lves n case of an evacuaon. NUMERICAL EXAMPLE CAPE MAY COUNY EVACUAION NEWORK Caegor-4 Cape Ma Hurrcane n 82 s he las maor hurrcane o make a drec landfall n New Jerse. Accordng o hsorcal records snce 82 New Jerse s que safe compared o souhern saes. However recen changes n world clmae and emperaure rse warnng b scenss ncrease he mporance of evacuaon plans for coasal areas. Hence hs sud analzes Cape Ma Coun whch s one of he mos vulnerable counes of New Jerse. FIGURE 3 shows he offcal evacuaon roues for Cape Ma and FIGURE 4 shows he smplfed cell represenaon of he Cape Ma evacuaon nework. FIGURE 3 Cape Ma Evacuaon Roues (Source (7)) RB 2007 Annual Meeng CD-ROM Paper revsed from orgnal submal.

12 Yazc M.A. Ozba K. FIGURE 4 Smplfed Cell Represenaon of Cape Ma Evacuaon Nework he analzed nework s a mul-orgn mul-desnaon nework each desnaon beng a sheler locaon. However he orgnal SO-DA formulaon s based on sngle desnaon. Kalafaas and Peea () sugges ha n he evacuaon problem where all desnaons are equvalen a sngle super-desnaon cell can be added and conneced o all desnaon cells. Desnaon cells and he connecors o superdesnaon are assgned nfne capac so ha here wll be no congeson a he desnaon cells. hs suggeson s adoped n he curren work. Durng evacuaon he vehcles canno manan everda free-flow veloc because of ver heav congeson hus hroughou he analss he average evacuaon speeds of he vehcles are assumed o be 30 mph. he cell lengh s se o be 5 mles. Followng he requremen of he CM ha a vehcle can raverse a mos one cell n one me nerval he me nerval s se o be 0 mnues and loadng s also performed for each 0 mnue nerval. Followng he Hghwa Capac Manual he mamum flow rae s se o be 260 vehcles per hour per lane and abou 50 vehcles are assumed o f mle road segmen. he cells on Garden Sae Parkwa (cell# ) have 4 lanes whereas he oher roads have 3 lanes. Overall nework feaures and cell phscal properes are shown n ABLE. ABLE Phscal Cell Properes of he Eample Nework Cell# # of Lanes Ma Flow (veh/τ * /ln) Phscal Capac N Cell Lengh Speed (mph) (veh / mle) (mles) * τ : me nerval = 0 mnues For nework loadng S-curve s used followng sae-of-he-pracce n evacuaon modelng. Mahemacal represenaon of S-curve s as follows: P () = { + ep[ α ( H )]} (25) RB 2007 Annual Meeng CD-ROM 2 Paper revsed from orgnal submal.

13 Yazc M.A. Ozba K. where P() s he cumulave percenage of he oal rps generaed a me. he α parameer represens he response of he publc o he dsaser and alers he slope of he cumulave raffc-loadng curve. H s he half loadng me; he me a whch half of he vehcles n he ssem have been loaded ono he hghwa nework. H defnes he mdpon of he loadng curve and can be vared b he planner accordng o dsaser characerscs. he loadng parameer choce aduss he overall performance hus he parameers are kep fed durng all analses. Specfcall loadng parameers are se as α=0.0 and H=6. Accordng o census daa here are 4248 households n Cape Ma area and assumng deparure from each household appromael half of he evacuaons (2000) are generaed from 3 concenraed sources represenng he resden and ours populaon along he shore. Case Sudes here are 2 basc ssues ha are suded. Frs ssue s he esence/necess of a sheler a one of he desnaons. Second ssue s he effec of flood probabl whch ma cause decrease n roadwa capac and evenuall change he favorable sheler locaons. In boh cases capac of he shelers are under consderaon snce decdng he locaon of a sheler s no enough whou knowng he number of people ha ma use ha sheler. Mananng a sheler s furher complcaed because of emergenc suppl and response personnel requremens. Le he problem be he elmnaon of one sheler ou of hree shown n FIGURE 4 because of suppl logscs and possble problems n fndng a suffcen number emergenc response personnel ha can saff all hree shelers. However le s also assume ha here s a flood rsk n he area especall near he shore whch ma cause a specfc lnk o lose par or all of s capac and consequenl aler he selecon sheler plan. Frs cell capaces are assumed o be deermnsc and consan. hen he nework s analzed for all possble couples of shelers b elmnang he hrd one a each eraon. Same procedure s emploed bu hs me wh capac loss probables for specfcall chosen lnks. he ndependence of flood probables of cells s agan assumed usng reasonng saed above when solvng he smple nework probablsc assgnmen problem. Case- For hs case Cells #20 #2 and #22 represen he roadwa whch s near he shore and covered wh waer creeks ha can be vsuall seen from aeral phoos. Probables of he number of lanes ha are operaonal are se o be for 0 2 and 3 lanes respecvel for cell#20 and #2. hs dsrbuon represens a severe floodng where he full operaonal and lane loss probables onl sum up o Cell#22 s assgned probables of and 0.05 for 0 2 and 3 operaonal lanes whch represen less severe floodng condons compared o oher cells wh flood rsk. hese cells were chosen snce he road segmens ha are represened wh hese cells are close o he shore and le n a waer-rch area as well. All oher cells are assgned fed deermnsc capaces hroughou he evacuaon. Frs a complee analss wh all shelers s performed o compare he average evacuaon ravel me and needed sheler capaces under bes condons. hen each sheler shown n FIGURE 4 are elmnaed one-b-one and he ncrease ravel mes and RB 2007 Annual Meeng CD-ROM 3 Paper revsed from orgnal submal.

14 Yazc M.A. Ozba K. sheler capac requremens are compared wh he complee nework where all he shelers are operaonal. he same procedure s appled for probablsc road capac formulaon and resuls are gven n ABLE 2. Please noe ha for he probablsc assgnmen p s se o be hs p value resuls n pleps whch correspond o lane floodng (n oher words 2 operaonal lanes) for all cells wh flood rsk. Also noe ha he base scenaro s chosen o be he deermnsc case and all oher performance values are compared wh he base scenaro. Abandoned Sheler All Operaonal ABLE 2 he Resuls for Deermnsc Case and Case- A * (mns) A Change Needed Capac De. Prob. De. Prob. Deermnsc Probablsc S# = 6943 S# = (C ** n/a 24% S#2 = 7000 S#2 = 7744 =440) (C=450) S#3 = 7057 S#3 = 567 S# (C=550) (C=640) 92% 56% S# (C=550) (C=640) 9% 56% S# (C=550) (C=550) 94% 94% * A: Average ravel me ** C: Clearance me S#2 = 0469 S#3 = 053 S# =0369 S#3 =063 S# = 038 S#2 = 0682 S#2 = 2426 S#3 = 8574 S# =3399 S#3 =760 S# =0280 S#2 =0720 As seen n ABLE 2 for he deermnsc case all he shelers as appear o be equal n erms of overall evacuaon performance and capac requremens. he ncreases n clearance mes average ravel mes and capaces are equal or ver close. However when he analss s done wh predeermned flood probables he absence of sheler# makes a bg dfference n evacuaon performance. Average ravel me ncreases b 56% whereas he ncrease n deermnsc case s 92%. Also compared o absence of oher shelers sheler# s dsngushed as he mos val sheler. here s also anoher pon ha s of mporance oher han he locaon or absence of he sheler. Even f one assumes ha all shelers wll reman open probablsc analss suggess dfferen capaces for shelers. Resuls show ha he number of evacuees n he shelers wll dffer b 6% 0% -20% for sheler# #2 and #3 respecvel. hese changes are equal up o 386 evacuees for nsance for sheler 3. If he sheler manenance aspecs are consdered e.g. food-waer suppl medcal facles hs dfference can change evacuaon plans. Case-2 For Case- should be noed ha he cells whch have flood rsk are he ones near he shore and affec onl he evacuees ha ravel from orgn#3 o sheler#3. However he resuls are sll sgnfcan n erms of he mpac of he probablsc analss on he overall pcure. For Case-2 same analss ha s presened n ABLE 2 s repeaed b assgnng a flood probabl o an addonal cell. One can also hnk of hs proposed probablsc capac decrease as a resul of he probabl of an accden on he road nsead of possble floodng. hs perspecve ma lead us o use probablsc analss for lnks ha do no have a maor flood rsk bu hgh ncden rsks nsead. For RB 2007 Annual Meeng CD-ROM 4 Paper revsed from orgnal submal.

15 Yazc M.A. Ozba K. hs purpose cell#23 s assgned a capac decrease probabl. Cell#23 connecs sheler# o all orgns and s an mporan cell. he probabl dsrbuon whch s same as cell#22 ( and 0.05 for 0 2 and 3 operaonal lanes respecvel) s assgned o cell#23. he resuls of Case- and Case-2 are gven n ABLE 3. Noe ha all he ncrease/decrease comparsons are based on he deermnsc base scenaro n whch all cell capaces are deermnsc and all shelers are operaonal. Same p value as n case-2 s used (0.75) and hs agan corresponds o lane closure for all cells wh flood rsk. Abandoned Sheler All Operaonal 3 Flooded Cells ABLE 3 Resuls for Case- and Case-2 A * (mns) 78 (C ** =450) 4 Flooded Cells 96 (C=490) 3 Flooded Cells A Change 4 Flooded Cells 24% 45% S# (C=640) (C=640) 56% 56% S# (C=640) (C=800) 56% 254% S# (C=550) (C=640) 94% 58% * A: Average ravel me ** C: Clearance me 3 Flooded Cells S# = 7585 S#2 = 7744 S#3 = 567 S#2 = 2426 S#3 = 8574 S# =3399 S#3 =760 S# =0280 S#2 =0720 Needed Capac 4 Flooded Cells S# = 6006 S#2 = 8703 S#3 = 629 S#2 = 2430 S#3 = 8570 S# =0370 S#3 =0630 S# =835 S#2 =2685 As seen n ABLE 3 addon of anoher cell wh flood probabl alers he overall nework performance. For eample he requred sheler capaces when all shelers are operaonal change wh respec o boh deermnsc case and Case-. Sheler#2 receves 959 more evacuees han dd n Case- and 703 more compared o he deermnsc case. Demand for sheler#3 ncreases b 620 compared o Case- neverheless sll sas under he deermnsc case demand. For Case-2 sheler# demand drops below deermnsc case b 937 whch was above he deermnsc capac predcon b 642 n Case-. hs shows ha no onl probablsc approach changes he overall resuls bu also a complee probabl esmaes of floodng for all he cells n he nework s essenal. Snce he nework capaces are full ulzed durng he evacuaon an change n capac especall a mergng cells can aler he flows consderabl. he addon of a new flood rsk cell also changes he mporance rankng of he shelers. In he deermnsc case absence of an of he shelers resuls more or less n he same overall consequence. In Case- shelers # and #2 are found o affec he performance of evacuaon more han sheler#3. In Case-2 sheler#2 s found o be he mos val sheler and he absence of shelers # and #3 are found o have almos he same mpac on A. In erms of capac requremens n case of an abandoned sheler he needed capac for a sheler can be up o 3029 evacuees. hs change s equal o relocang of almos 5% of he oal evacuees n Cape Ma Coun o operaonal shelers. RB 2007 Annual Meeng CD-ROM 5 Paper revsed from orgnal submal.

16 Yazc M.A. Ozba K. DISCUSSION AND CONCLUSION In hs sud he mpacs of ncorporang flood probabl of cells on sheler locaons/mporance/capac are suded. plep mehod frs proposed b Prekopa (8) s used o deal wh probablsc capac consrans of he proposed sochasc SODA model. he applcaon of he mehod s frs llusraed hrough a smple eample. hen an eample nework whch s a smplfed cell ransmsson model of he comple NJ Cape Ma Coun s suded. A sae-of-pracce loadng paern (S-curve) s used. Our fndngs show ha accounng for flood probables even for lnks ha are no used b all evacuees can change he ssem-opmal flows and performance measures as well as he favorable sheler locaons and capac requremens. Neverheless wo case sudes show ha a complee flood rsk analss s also necessar because an new flood probabl assgnmen o a lnk n an alread congesed nework alers he evacuaon paern consderabl. Snce sheler allocaon s no onl buldng he sheler bu also mananng hese knds of sheler allocaon and capac deermnaon models are no suffcen on her own. Oher emergenc managemen ssues such as medcal equpmen and personnel food and waer suppl energ suppl ec. should also be consdered. However hese ssues can be deal effcenl onl f planners emplo realsc models such as he sochasc SODA model proposed n hs paper whch no onl capures me-dependen raffc flows bu also varous sochasces due he evens causng he emergenc suaon. As shown n hs paper when floodng rsk of ceran lnks are ncorporaed no he model he demand for shelers changed consderabl (hghes change beng a sheler#2) compared wh he predcons of he deermnsc model. hus f he planners consder he predcons of he deermnsc model he face he rsk of no havng suffcen food medcne and oher emergenc suppl n sheler#2. hs knd of neffcen emergenc plannng has alread creaed pos-dsaser problems n case of maor dsasers such as Karna and sunam n Souh Eas Asa. hese recen dsasers and pos dsaser condons have onl ncreased he need for beer and more realsc plannng models along he possble mprovemens suggesed n hs paper. REFERENCES. Leandro Marguls Pablo Charosk Juan Fernandez. Hurrcane Evacuaon Decson- Suppor Model for Bus Dspach. ORMS omorrow Undergraduae Paper. Avalable: hp://ormsomorrow.nforms.org/paper_compeon_runner.doc Accessed: Jul Kongsomsaksakul S. Yang C. Chen A. Sheler Locaon-Allocaon Model for Flood Evacuaon Plannng Journal of he Easern Asa Soce for ransporaon Sudes Vol pp Ahanasos K. Zlaskopoulos A Lnear Programmng Model for he Sngle Desnaon Ssem Opmum Dnamc raffc Assgnmen Problem ransporaon Scence Vol.34 No pp Sheral H. D. Carer. B. and Hobeka A. G. A Locaon-Allocaon Model and Algorhm for Evacuaon Plannng under Hurrcane/Flood Condons ransporaon Research Par B Vol. 25(6) 99 pp RB 2007 Annual Meeng CD-ROM 6 Paper revsed from orgnal submal.

17 Yazc M.A. Ozba K. 5. ElDessouk W. M. Some Developmens n ransporaon Nework Analss and Desgn wh Applcaon o Emergenc Managemen Problems. Ph.D. Dsseraon Norh Carolna Sae Unvers Ozba K. Yazc M.A. and Chen S. I-J. Sud Of he Nework-Wde Impac Of Varous Demand Generaon Mehods Under Hurrcane Evacuaon Condons. Presened a 85 h Annual Meeng of he ransporaon Research Board Washngon D.C Ozba K. and Yazc M.A. Analss of Nework-wde Impacs of Behavoral Response Curves for Evacuaon Condons o appear n IEEE ISC 2006 Conference Prekopa A. Dual Mehod for a One-sage Sochasc Programmng Problem wh Random RHS Obeng a Dscree Probabl Dsrbuon Z. Oper. Res. Vol pp Prekopa A. Probablsc programmng n: A. Ruszcz'nsk and A. Shapro eds. Handbooks n operaons research and managemen scence Vol. 0 (Elsever New York) 2003 pp Dencheva D. Prékopa A. Ruszcznsk A. Concav and effcen pons of dscree dsrbuons n probablsc programmng Mahemacal Programmng Ser. A Vol.89: pp Kalafaas G. And Peea S. A Graph-Based Formulaon for he Sngle Desnaon Dnamc raffc Assgnmen Problem. Presened a Frs Inernaonal Smposum on Dnamc raffc Assgnmen Unvers of Leeds L Y. Waller S.. Zlaskopoulos A. A Decomposon Scheme for Ssem Opmal Dnamc raffc Assgnmen Models Neworks and Spaal Economcs Vol pp Ozba K. And Yazc M.A. Handlng Demand and Capac Unceranes Durng Maor Evacuaons Proceedngs Of EWG 2006 Jon Inernaonal Conference Bar Ial Comprehensve Hurrcane Daa Preparedness Sud Web Se Federal Emergenc Managemen Agenc & Arm Corps of Engneers Avalable: hp://chps.sam.usace.arm.ml/ushesdaa/heshome.hm Accessed Jul We Y and Lne Ozdamar A dnamc logscs coordnaon model for evacuaon and suppor n dsaser response acves European Journal of Operaonal Research Arcle n Press Mulparameer Assessmen Gude for Emergenc Shelers: Dsaser Relef Applcaons Journal of Performance of Consruced Facles Vol. 9 No. 2 (2005) pp NJ Offce of Emergenc Managemen hp:// Accessed Jul RB 2007 Annual Meeng CD-ROM 7 Paper revsed from orgnal submal.