TRB Optimal Refueling Station Location and Supply Planning for Hurricane Evacuation

Transcription

1 TRB - 0 Optmal Refuelg Stato Locato ad Supply Plag for Hurrcae Evacuato Yag Gao, Y-Chag Chu*, Shuo Wag Departmet of Cvl Egeerg ad Egeerg Mechacs The Uversty of Arzoa, Tucso, Arzoa 1 Tel: (0) - E-mal: chu@emal.arzoa.edu *correspodg author Smge Küçükyavuz Departmet of Itegrated Systems Egeerg The Oho State Uversty, Columbus, Oho Emal: kucukyavuz.@osu.edu Words:, Fgures ad Tables: Total:, Fal Submttal for the publcato the Trasportato Research Record

2 1 1 Abstract The fuel supply shortage problem that has emerged the last few hurrcae evets uderscores the weakess of exstg emergecy logstcs plag processes. Cetral to the refuelg stato locato ad supply plag decso s a effectve modelg approach. Ths paper documets a research effort based o the smulato-optmzato framework tegratg a mxed teger program (MIP) formulato ad a mesoscopc smulato model. The mesoscopc smulato model was corporated wth decso rules to select refuelg statos, methods to model the mpact of stalled vehcles o traffc flow, ad formula to accumulate each vehcle s fuel cosumpto uder varous rug speed codtos. The mxed teger program formulato s amed at maxmzg the served demad by decdg o whch statos to operate ad how much fuel to supply gve lmted resources. The terplay betwee the smulato model ad the optmzato model cotues utl covergece. The proposed modelg approach s appled to a case study based o the terstate I- corrdor betwee Housto ad Dallas to hghlght the characterstcs of the proposed modelg approach INTRODUCTION The devastatg destructo potetal of a hurrcae ofte forces emergecy maagemet ageces to mplemet mass evacuato. Hurrcaes Rta ad Katra of 00 ot oly marked hstorcal evets, but also called for more effectve ad relable hurrcae evacuato plag ad operato practces, cludg logstcs maagemet. Accordg to a recet study for Hurrcae Rta, fuel supply was oe of the major ssues ecoutered Hurrcae Rta evacuato (1). Accouts dcated that durg Hurrcae Rta, may evacuees stalled e-route to ther destato ad evetually gave up o evacuato due to the lack of crtcal supples. Studes coducted after Hurrcae Rta also showed that the umber of evacuees raged from 1. to. mllo (1, ). I log-dstace tercty travel uder cogesto, evacuees are lkely to ru out of gas much faster tha uder ormal drvg codtos due to poorer fuel ecoomy (). Provdg suffcet fuel supply alog the evacuato route s also crucal from a traffc maagemet stadpot because stalled vehcles reduce roadway capacty, further dsturbg traffc flow ad aggravatg the severty of the cogesto. Such a cha reacto could set off a vcous crcle, resultg a rapd traffc breakdow of the etre evacuato corrdor. Therefore, a mproved refuelg strategy s eeded as part of the overall emergecy logstcs pla. To devse a optmal ad effectve refuelg strategy, oe promsg approach s to tackle the problem at strategc ad operatoal levels. Strategc level decsos requre a loger lead tme to pla ad execute. Oce plaed, the decso-makers ca choose whether to execute as plaed a evacuato evet. Operatoal decsos, o the other had, ca be refed ad adjusted real tme durg a evacuato operato. Both strategc ad operatoal decsos are eeded for a successful evacuato operato. The prmary focus of ths paper s o the strategc decsos o the plag of refuelg stato locatos ad capactes. These decsos are sought by formulatg ad solvg a locato-allocato (LA) problem that determes the optmal refuelg locatos satsfyg the set objectve subject to a umber of costrats. To ths extet, the ma research challeges le

3 how to create a approprate model formulato ad how to properly estmate the model puts ad parameters gve that the model eeds to be sestve to traffc dyamcs ad fuel cosumpto that s subject to cogesto levels. Addtoal factors that eed to be cosdered clude: (1) where vehcles ca be refueled (e.g. exstg gas statos, or eve rest areas resdg o the state rght of way premses), () the level of fuel demad at dfferet mleposts alog the route (e.g. umber of vehcles rug out of gas ad requrg refuelg), () total avalable fuel supply, ad () the maxmum umber of refuelg locatos that ca rema ope durg evacuato. Amog the factors above, the demad s perhaps the most dffcult to estmate accurately whe cosderg how fuel cosumpto may relate to rug speed, ad dfferet rug speeds may occur at dfferet locatos alog the evacuato route. It s documeted that the optmal fuel ecoomy remas the rage of 0 to 0 mph (). The overall fuel cosumpto patter s cocave. Whe rug speed s low (betwee 0 ad mph), the fuel ecoomy creases o-learly wth creasg speed. Whe speed exceeds 0 mph the fuel ecoomy decreases wth creasg speed. I ths paper, we propose a smulato-optmzato framework whch cludes the terplay betwee a mxed teger programmg (MIP) model ad a mesoscopc smulato model. The mesoscopc smulato model tracks fuel cosumpto of each dvdual vehcle ad the locatos where vehcles are rug low fuel to estmate the demad to each gas stato. The MIP problem optmzes the locato decsos: whch stato to ope ad how much capacty to allocate to each opeed locato for a gve estmate o fuel demad. The locato decso the feeds back to the smulato model to estmate the demad. The process cotues utl a stoppg crtero s met. Ths research provdes oe of the frst systematc treatmets to the plag of the refuelg stato locatos for hurrcae evacuato, allowg both researchers ad practtoers to further explore the opportutes to mprove fuel supply plag for hurrcae evacuato. The rest of ths paper s orgazed accordg to the followg structure. Secto revews the pror related lterature. The overall methodology s dscussed Chapter, followed by a case study based o the IH- corrdor betwee Housto ad Dallas usg data collected for Hurrcae Rta LITERATURE REVIEW Over the past decade, a umber of models have bee developed to assst emergecy evacuato plag ad operatos. However, the plag of refuelg stato locatos has ot bee wdely recogzed utl 00 Hurrcae Rta, whch a large umber of evacuato vehcles ecoutered the fuel shortage problem e route to ther teded safe destato. The problem of terest ca be modeled as a locato-allocato (LA) problem. The LA problem has attracted researchers from areas of operatos research, maagemet scece ad spatal aalyss. The topcs of terest clude allocatg dfferet types of facltes, such as emergecy facltes, schools, warehouses ad retal facltes. LA models etworks focus o locatg the optmal servce facltes as well as the assocated demad. Demad for faclty servce s ofte assumed to be geerated or could be expressed by a set of odes that covers the etre rego of terest. Uder ths assumpto, the goal of LA models s to locate facltes at odes to optmze a spatal fucto, usually the form of a weghted total dstace or tme to travel betwee demad odes

4 ad faclty odes. Three basc faclty LA models ca be foud lterature (, ). Hakm (, ) defed the p-meda ad p-ceter problems ad proposed correspodg soluto algorthms. The p-meda model detfes locatos for p facltes some space (such as the Eucldea pla or a road etwork) to serve demad pots so that the total weghted dstace (or cost) betwee the facltes ad the demad pots they serve s mmzed. The p-ceter problem addresses the problem by mmzg the maxmum dstace betwee where the demad orgates ad where the closest faclty s, gve a set of pre-determed facltes. Aother type of kow model s the maxmum coverg locato model (MCLP) by Church et al. (), whch locates p facltes wth dstace S, so as to cover the maxmum populato wth S. All the three basc LA models assume that demad occurs at odes, ad therefore ther goals are to optmze the weghted dstace, or the dstace of the drect path from ode to faclty. Hodgso (, ) ad Berma () proposed dfferet models that suggested that demad a etwork mght be expressed as flow passg through the faclty. Berma argued that retal busess, such as coveece stores, gasole statos, ad bakg maches, a creasg umber of servces were cosumed by customers who do t make a purposeful trp to the faclty. More lkely for these servces the customer s already o a pre-plaed trp, ad f (s)he passes the servce facltes o hs(her) preplaed route, (s)he may cosume that servce. Hodgso presets the Flow Capturg Locato Model (FCLM), amg at locatg facltes to serve as may of passg flows as possble. Ay flow that uses a path that passes through the locato of the faclty was cosdered to be captured. Hs model s also desged to prevet flow cabalzato: capturg flow more tha oce at the expese of flows elsewhere the etwork ot beg captured at all. Hodgso shows that the FCLM s a specal case of the Maxmal Coverg Locato Problem. Berma et al. () proposed a model smlar to FCLM, but they used the term dscretoary servce facltes to refer to facltes that capture passg flows. Cosderg demad the real world s ofte expressed as ether passg flows or cosumers cetered the resdetal areas, aggregated as odes, Hodgso ad Rosg () developed a hybrd model wth dual objectve (flow capturg ad p-meda) to serve both types of demad. Tradtoally, LA models for gas stato plag are used for frastructure ad/or ecoomc developmet purposes. Bapa et al. (1) developed a LA method for frastructure developmet for alteratve fuel. The mult-objectve formulato cosders three objectves such as cost mmzato, demad oretato, ad evrometal cocer. Ther model s called maxmum coverg/shortest spag sub-graph (MCSP) problem. Goodchld ad Noroha () proposed ther model for maxmzg market share based o two types of demad, smlar to Hodgso ad Rosg s model (). Kuby et al. () proposed a flow refuelg locato model (FRLM), based o FCLM, especally for the gas stato locato problem. The FRLM optmally locates p refuelg statos o a etwork so as to maxmze the total flow volume refueled. Kuby et al. argued that the FCLM caot be drectly appled to the refuelg problem, sce a sgle flow mght eed to be refueled more tha oce, whle FCLM was desged ot to double cout flows captured by more tha oe faclty alog ther path. I other words, FCLM, each drver s assumed to stop oly oce. The FRLM cosders a flow refueled oly f a adequate umber of statos are spaced approprately alog the path, ad uses feasble faclty combatos to refuel etwork paths. I ths research, we allow vehcles to demad fuel more tha oce, whch s ecessary as wll be llustrated our case study. Goodchld ad Noroha s model was appled to the problem of ratoalzg a compay s set of gasole statos after mergg wth aother compay o ecoomc value (). The FRLM ca hadle the multple refuelg stops eeded for paths loger tha the vehcle s rage, but the

5 demad s based o org-destato (O-D) flows. Uder a evacuato stuato, cosderg the upredcted umber of evacuees, t s hard to estmate the O-D flows uless a smulatobased approach s used. Besdes, the demad for gas uder the evacuato crcumstace would be qute challegg to estmate based o smple aalytcal methods because fuel ecoomy s affected by cogesto ad rug speed. Refuelg behavor eeds to be properly accouted for estmatg demad. For example, most of the travelers would refuel oly at the dowstream statos sce turaroud would be rsky or prohbtve uder a evacuato stuato. Therefore, drectly utlzg a p-meda, p-ceter or MCLP model to represet the refuel facltes allocato problem may ot be adequate. Other tha the statc optmzato problems, two-stage stochastc formulatos attracted cosderable atteto recet years. I a two-stage model, a decso s made wth complete formato before observg the realzato of some other stochastc factors. Subsequetly, a opportuty may be avalable for correctg the prelmary decso. The recourse acto may compesate for the complete formato the frst stage. Ths results a two-stage model whch formulates a prelmary plag problem the frst stage ad a recourse problem the secod stage (1). However, most of the stochastc programmg lterature assumes that the dstrbuto of the radom varable s depedet of the decsos made the frst stage. I our problem, however, the decsos the frst stage (amely the stato locatos ad capacty) affect the dstrbuto of the radom varable (demad for refuelg dfferet locatos). I cojucto wth optmzato models, smulato models allow to fd a good soluto to some decso problems, but also to observe a system uder dfferet sets of assumptos (1). I the past 0 years, smulato models have bee developed ad commoly used to evaluate the performace of emergecy respose systems. They also provde the possblty to test ew operatoal strateges such as dfferet ambulace locatos or dspatchg rules. I ths research, both smulato ad optmzato modeled tegrated to a ufed framework for the problem of terest MODELING FRAMEWORK AND SOLUTION PROCEDURE I geeral, the refuelg problem for evacuato falls to the LA problem class. However, the tradtoal LA problem falls short realstcally estmatg the model put such as the demad that s trscally sestve to cogesto. If a vehcle ca fd the earby gas stato wth suffcet supply, t ca cotue the jourey. If o gas stato ca be reached wth the remag fuel, the vehcle wll stall ad create dsturbace to traffc flow. Such a pheomeo ad the resultg traffc codto ad demad ca oly be realstcally estmated wth smulato. The objectve of ths paper s to propose a smulato-optmzato framework ad model formulato. Istead of estmatg refuelg demad from makg cosderable assumptos O-D flows or geerato odes, we use a smulato model to corporate the refuelg behavor, capture traffc cogesto pheomeo ad estmate fuel cosumpto based o tme-varyg rug speed. As show Fgure, the process starts from preparg ecessary dataset cludg etwork cofgurato, locatos of gas statos ad tal fuel level for every vehcle. The smulato model DyusT outputs the locato of each fuel requestg vehcle ad whether they could be served by the exstg locato ad capacty plag decso. The demad for each stato resulted from smulato s also outputted. More modelg detals DyusT are preseted Secto.1.

6 The optmzato model s a mxed teger program (MIP) that decdes o whch gas statos to operate ad how much fuel supply to provde to each stato (more detals are dscussed Secto.). After verfyg the covergece by comparg demad wth demad from last smulato terato, the algorthm termates or the soluto s fed back to DyusT for aother smulato ru to re-estmate demad. Ths process repeats utl the stoppg codto s met. FIGURE 1 HERE Mesoscopc Vehcular Smulato for Fuel Cosumpto ad Fuel Supply The smulato model appled to ths research s Dyamc Urba Systems for Trasportato (DyusT). DyusT s a mesoscopc dyamc traffc smulato (1) ad assgmet model (1) that has bee developed for years ad has bee appled to varous rego-wde traffc smulato modelg applcatos cludg mass evacuato (1, 1-1). As show Fgure, wth DyusT the traffc assgmet process volves the terplay of the smulato model ad the tme-depedet shortest path ad flow redstrbuto compoet. DyusT ca be used to compute the equlbrated route selecto for travelers departg at dfferet tmes. Ths capablty s prmarly used to assg the evacuees to the evacuato etwork. The modeler ca choose to perform oe-shot smulato or smulatoassgmet procedure depedg o the modelg requremet. Durg the teratve computatoal process, the tme-depedet lk travel tme ad tersecto delays are put to the tme-depedet shortest path algorthm. Based o the shortest path results, the ew flow dstrbuto ad routg polces are computed a tme-depedet traffc assgmet procedure based o the Method of Isochroal Vehcle Assgmet (MIVA) (, ). The vehcles wth updated routes are the put to the traffc smulator to assess the performace. The process s repeated utl some covergece crtera are satsfed or the maxmum umber of teratos s reached. FIGURE HERE The vehcle smulato mechasm follows the asotropc mesoscopc smulato (AMS) logc (1) that dvdual vehcles are geerated wth dvdual attrbutes such as departure tme, org, destato, occupacy, vehcle types, ad the route that each vehcle s takg for evacuato. Durg the smulato, a vehcle s movemet follows a speed-desty relatoshp a wdely kow relato betwee speed ad desty that descrbes the traffc flow to esure that as a vast amout of vehcles are smulated, they exhbt realstc traffc flow characterstcs at the macroscopc level. Furthermore, dvdual vehcles have decso rules respose to traffc codtos as well as formato (1). For ths research, addtoal fuel cosumpto logcs were bult alogsde wth the AMS smulato method order to properly capture fuel cosumpto uder varous cogesto stuatos. Ths permts a more detaled estmato of fuel cosumpto tha tradtoal statc or aalytcal approaches. At each smulato stace t for each vehcle, the fuel cosumpto s expressed as:

7 f t 1 t ( u ) t ( u ) (1) k t where s the smulato terval, u s the rug speed of vehcle at tme stace t t, ( u ) s the mle-per-gallo (mpg) fuel ecoomy for vehcle fuel ecoomy type k at rug k speed t u. The term ( u ) meas the dstace traveled by vehcle at tme stace t at t t t t rug speed u. The fuel ecoomy at rug speed u s k( u), thereby the fuel cosumpto at tme stace t over the smulato terval ca be calculated by Equato (1). The vehcle fuel ecoomy type k correspods to a specfc fuel ecoomy-speed profle that ca be appled to passeger cars, lght-duty trucks, heavy duty trucks or eve traler trucks. The umber of vehcle fuel ecoomy types that ca be cluded the modelg also depeds o the avalable data vehcle stream composto ad the fuel ecoomy data. As show Fgure, for a typcal vehcle at low speed, the fuel ecoomy s at mpg. The fuel ecoomy creases to 0 mpg whe speed s the rage of to mles per hour (mph). The fuel ecoomy however starts to decrease at a lear rate whe speed exceeds mph. The fuel ecoomy curve clearly dcates that fuel ecoomy s sestve to rug speed; as such, t becomes clear that severe cogesto durg evacuato ca quckly deplete a evacuee vehcle s fuel tak. FIGURE HERE The applcato of Equato (1) to smulato cosderg other related mplemetato ssues are brefly dscussed hereafter. At the begg of smulato, each vehcle (assumg 0 0 vehcle type s kow) s assged wth a radom tal fuel level F. F ca be assumed to follow varous dstrbutos. Oe would assume that whe evacuees set off ther trps ther fuel level may be close to full. As they travel a certa dstace ad arrve at the boudary of the study area, ther remag fuel level becomes radom as ths depeds o ther org ad traffc codto alog the way. The research fuel level dstrbuto s out of the scope of ths research. To ths extet, we assume that the dstrbuto follows a ormal N(, ) dstrbuto wth modeler-specfed mea ad stadard devato parameters. Bouds for mmal ad maxmum fuel levels also eed to be specfed. To crcumvet ths ssue a log-ormal dstrbuto ca be also be used. A uform dstrbuto ca also be cosdered, f approprate. For each vehcle, the remag fuel at each smulato tme stace t ca be t t 1 t t m calculated as F F f. Vehcle s marked as a fuel requestg vehcle whe F F, m m where F s the mmal fuel level threshold for vehcle. F s also assumed a radom varable. Modelg multple vehcle types ca be pursued by applyg dfferet tal fuel level dstrbutos Nk (, ) for each vehcle type k. The fuel ecoomy for each vehcle type k also eeds to be specfed, but oce t s specfed Equato (1) s applcable to all vehcles regardless of ther vehcle type. Whe a vehcle s eed for fuel (.e. F t F m, t would search for fuel at the mmedate dowstream refuelg locato. If ths locato has suffcet fuel (e.g. c 0 ) whe

8 the vehcle requests fuel, the the remag fuel for that stato c s reduced by the fuel tak capacty of that vehcle utl the stato rus out of fuel. The demad for the stato b s cremeted by oe ut. For a vehcle, f the earest stato has o fuel, the vehcle wll look for the d earest stato dowstream alog the travel drecto utl t s refueled or t rus out of fuel. I the evet that a vehcle rus out of fuel, t becomes a stalled vehcle. A certa roadway capacty reducto (% as a example) s appled for each stalled vehcle. The reduced roadway capacty wll tur affect the traffc codto at the ste startg whe the vehcle s stalled ad oward. I other words, the stalled vehcle could decrease the roadway capacty ad further aggravate the cogesto stuato. The reduced capacty ca be partally restored at a later tme to cosder the stuato of movg the stalled vehcles out of the traffc lae Optmzato Model The Optmal Refuelg Stato Locato ad Capacty Plag problem s formulated as a mxed-teger program (MIP). The problem s formulated as follows. Data: I Set of potetal refuelg statos Subscrpt for refuelg stato, I Average vehcle fuel tak capacty (gallos) C Total avalable fuel supply (gallos) N Maxmum umber of statos that ca be operated b Decso varables: Model The umber of vehcles whch demad fuel from stato estmated by smulato. x (Bary) x 1 f stato s operated durg evacuato, x 0 otherwse y Subject to: Fracto of stato demad met Amout of fuel supply provded to stato max Z by (1) 0 y 1, () y x, ()

9 1 by 0, C () x N () The objectve fucto (1) maxmzes the total umber of vehcles that ca be refueled wth a maxmum of N opeed statos. The maxmum umber of opeed statos ca be determed by the emergecy maagemet agecy cosderg the staffg ad cotract ssues wth the gas statos. Costrats () restrct y to be a fracto of demad met by stato. Costrats () force y to zero uless x s ozero. If x s zero, stato wll ot be operated, so y has to be zero. I other words, f x 1, y ca be ozero. Costrats () dcate that the assged fuel supply for stato dvded by average vehcle fuel tak capacty, gve by, eeds to be greater or equal to the total amout of fuel requestg vehcles, gve by by. Costrats () requre that the total stato supply ot exceed the total avalable fuel supply C. The total fuel supply C ca be estmated from the petroleum termal operators based o the umber ad capacty of gasole termals a feasble dstace to the study area. Costrats () boud the maxmum umber of statos to operate. () Covergece Crtero The overall model covergece crtero could be set based o objectve fucto or estmated demad. The algorthm wll termate oce the chage objectve fucto value Z or the chage demad b s less tha a pre-set threshold. The reaso that we choose ot to use the soluto per se as the stoppg crtero s because ths MIP problem may ot have a uque soluto; the model may be oscllatg betwee two dfferet solutos wth the same objectve fucto value. 1 NUMERICAL EXAMPLE 0.1 Network Descrptos ad Model Setup Ths secto provdes a llustratve example to hghlght the performace of the proposed modelg approach. The etwork s a 00-mle secto of terstate from North Housto to South Dallas. Ths etwork s extracted from a cetral Texas regoal etwork wth all the lae geometry cofgurato carefully coded as part of a pror modelg effort DyusT (1). All evacuato vehcles were extracted from the same study to form ew trajectores pertag to the extracted etwork show Fgure 1. A total of about 0,000 evacuato vehcles were geerated over the perod of hours. The tal fuel level follows the ormal dstrbuto N(,). The mea fuel level appears to be seemgly less tha what a typcal passeger car ca

10 1 hold. Ths s because vehcles actual org s outsde the modeled etwork. After drvg for a certa dstace, ther fuel level upo arrval at the etwork should be lower tha the actual capacty. Therefore, gallo was chose as the mea startg fuel level. The average travel dstace s 0. mles ad average travel tme s mutes, equvalet to a average speed 1. mph. FIGURE HERE Ffty three refuelg statos were detfed usg Google map. These stes are prmarly the exstg gas statos. Exstg rest areas o state rght of way ca also be cluded. Fgure - llustrate selected stes alog the I- corrdor. I ths case study, the average vehcle fuel tak capacty s assumed to be 0 gallos. The total fuel supply for all the ope statos C, s assumed to be 1. mllo gallos for all the statos ad the maxmum umber of opeed statos N, s assumed to be Results ad Aalyss The frst step of the aalyss s to exame the covergece of the soluto procedure. As prevously explaed, the overall algorthmc procedure vokes teratve terplay betwee the smulato ad the optmzato model. Fgure dcates that tally, oly 00 vehcles are served. The umber creases to 00 at the d terato. The umber remas the same at the rd terato, suggestg the covergece of the soluto procedure. FIGURE HERE The demad b obtaed from DyusT at covergece s depcted Fgure. Oe ca see that alog the I- corrdor, a large porto of demad cocetrates betwee Housto to Madsovlle, partcularly the area before reachg Coroe. These locatos have demad exceedg,000 vehcles over the -hour perod. The smulato results also dcate severe traffc cogesto occurrg the same area due to lae droppg from laes to laes at Coroe. The secodary demad cocetrato locato s at the vcty of Farfeld, about 0 mles south of Dallas. FIGURE HERE The soluto obtaed by the optmzato model, as show Fgure 1, dcate a cocetrated allocato of fuel supply to statos located betwee Housto ad Coroe. The eeded fuel would be as hgh as k gallos. Others rage betwee 0k to 0k gallos. The fuel supply would gradually decrease after passg Coroe. Statos the vcty of Farfeld are also allocated wth fuel the rage of,000 gallos. The 1. mllo gallos of gasole that s set as the costrat s foud to be bdg, meag that there may be userved vehcles. FIGURE HERE

11 The amout of userved vehcles are foud to be rather uformly dstrbuted alog the corrdor, o the average less tha 0 vehcles per gas stato, except for stato wth more tha 0 userved vehcles (see Fgure ). FIGURE HERE SUMMARIES AND CONCLUDING REMARKS Ths paper documets a research effort based o the smulato-optmzato framework tegratg a mxed teger programmg (MIP) formulato ad a mesoscopc smulato model. The mesoscopc smulato model corporates realstc refuelg stato selecto decso for evacuees ad stalled vehcles mpact o traffc flow. The MIP formulato s amed at maxmzg the served demad by decdg o whch statos to operate ad how much fuel to supply gve the set costrats. The terplay betwee the smulato ad optmzato models cotues utl covergece. The case study dcates the potetal of the proposed modelg approach. Further refemet of both smulato ad optmzato models ca be pursued to mprove the realsm of the model. Frst, the mpact of the stalled vehcles was assumed ths paper, but t ca be more realstcally estmated from feld data. The gas stato searchg behavor s assumed to be stataeous, that s, there s o delay assocated wth refuelg ad vehcles are reloaded to the etwork wthout delay. The optmzato model s a statc model, whch does ot accout for the tme-varyg demad that ca be aturally output from smulato. Ths would lead to tme-varyg fuel supply decsos, whch may requre addtoal gas taker fleet routg decsos ad fuel termal operato costrats. 0 1 REFERENCES [1] Hek, R. H., Ballard, A. J., Robdeau, R. L., Peacock, W. G., Maghelal, P., Ldell, M. K., Prater, C. S., Loftus-Otway, L., Segesmud, P., Harrso, R., Lasdo, L., Chu, Y.- C., Zheg, H., Perks, J., Lews, C., ad Boxll, S., Dsaster Preparedess Texas Fal Report, Texas Trasportato Isttute, College Stato00. [] Eskovtz, J., Evacuato Plag Texas: Before ad After Hurrcae Rta, Iterm News00 ed. vol. th Legslature, Texas: HOUSE RESEARCH ORGANIZATION, 00. [] Fuel Ecoomy Gov, Fuel Ecoomy versus Speed, 00 ed. vol. 00: Fuel Ecoomy Gov, 00. [] Curret, J., Dask, M., ad Schllg, D., Basc Faclty Locato Models, Faclty Locato: Applcato ad Theory00 ed, H. W. H. Zv Drezer, Ed.: Sprger, 00. [] Plastra, F., Cotuous Coverg Locato Problems, Faclty Locato: Applcato ad Theory00 ed, H. W. H. Zv Drezer, Ed.: Sprger, 00. [] Hakm, S. L., Optmum Locatos of Swtchg Ceters ad the Absolute Ceters ad Medas of a Graph, Operatos Research, vol. 1, pp. 0-,.

12 [] Hakm, S. L., Optmum Dstrbuto of Swtchg Ceters a Commucato Network ad Some Related Graph Theoretc Problems, Operatos Research, vol., pp. -, 1. [] Church, R. ad ReVelle, C., The maxmal coverg locato problem, Papers Regoal Scece, vol., pp. 1-,. [] Hodgso, M. J., Developmets Flow-Based Locato-Allocato Models, Ecoometrc Advaces Spatal Modelg ad Methodology, ed, C. G. A. Dael. A. Grffth, Jea-Mare Hurot, Ed.: Sprger, 1. [] Hodgso, M. J. ad Rosg, K. E., A etwork locato-allocato model tradg off flow capturg ad p-meda objectves, Aals of Operatos Research, vol. 0, pp. -0, 1. [] Berma, O., Larso, R. C., ad Fouska, N., Optmal Locato of Dscretoary Servce Facltes, Trasportato Scece, vol., 1. [1] Bapa, R., Thakur, L. S., ad Nar, S. K., Ifrastructure developmet for coverso to evrometally fredly fuel, Europea Joural of Operatoal Research, vol., pp. 0-, 00. [] Goodchld, M. F. ad Noroha, V. T., Locato-allocato ad mpulsve shoppg: the case of gasole retalg, Spatal Aalyss ad Locato-Allocato Models1 ed, A. G. a. G. Rushto, Ed., New York: Va Nostrad Rehold, pp. 11-, 1. [] Kuby, M. ad Lm, S., The flow-refuelg locato problem for alteratve-fuel vehcles, Soco-Ecoomcs Plag Sceces, vol., pp. 1-, 00. [1] Brge, J. ad Louveaux, F. (1). Itroducto to Stochastc Programmg. Sprger- Verlag. [1] Hagha, A. ad Yag, S.,Real-tme Emergecy Respose Fleet Deploymet: Cocepts, Systems, Smulato ad Case Studes, Dyamc Fleet Maagemet, 1 ed, C. D. T. Vasleos Zempeks, George M. Gagls, Ioas Ms, Ed.: Sprger, 00. [1] Chu, Y.-C., Zhou, L., ad Sog, H., Developmet ad Calbrato of Asotropc Mesoscopc Smulato Model for Uterrupted Flow Facltes, Trasportato Research Part B, vol. forthcomg, 00. [1] Chu, Y.-C. ad Bustllos, B., A Gap Fucto Vehcle-Based Soluto Procedure for Cosstet ad Robust Smulato-Based Dyamc Traffc Assgmet, The th Aual Meetg of Trasportato Research Board, Washgto, D.C., 00. [1] Noh, H., Chu, Y.-C., Zheg, H., Hckma, M., ad Mrchada, P., A Approach to Modelg Demad ad Supply for a Short-Notce Evacuato, Trasportato Research Record, vol. Forthcomg, 00. [0] Chu, Y.-C., Zheg, H., Vllalobos, J. A., Hek, R., ad Peacock, W., Evaluatg Regoal Cotra-Flow ad Phased Evacuato Strateges for Cetral Texas Usg a Large-Scale Dyamc Traffc Smulato ad Assgmet Approach, Joural of Homelad Securty ad Emergecy Maagemet, vol., 00. [1] Chu, Y.-C. ad Mrchada, P. B., Ole Behavor-Robust Feedback Iformato Routg Strategy for Mass Evacuato, IEEE Trasacto o Itellget Trasportato Systems, vol., pp. -, 00. 1

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14 Lst of fgures: Fgure 1 Research Framework Fgure Geeral Algorthm Structure of the DyusT Model Fgure Relatoshp of vehcle speed ad fuel cosumpto Fgure Case study etwork Fgure Objectve Fucto Value (Served Demad) Over Iteratos Fgure Demad Spatal Dstrbuto Fgure Plaed supply (model soluto) for each stato Fgure Userved demad by stato

15 START Read Data* DyusT smulato ad fuel cosumpto calculato algorthm Smulato TDSP Refuelg Stato Decsos Demad NO Optmzato Check Covergecy* Optmzato Model Yes (*Data cludes etwork cofgurato, locatos of gas stato ad tal fuel level for every vehcle. *Covergece crtera clude ether demad or objectve fucto value.) STOP Fgure Research Framework 1

16 Evacuato Flow at each ode r Set Target Evacuato TmeTˆ Tme-Depedet Lk Destes, Travel Tmes Asotropc Traffc Smulato Mmal Exposure Shortest Path Algorthm Set Ital evacuato temporal demad profle r Drver Choce Behavor Model * Partcpato Rate * Route * Departure Tme Traffc Assgmet updated r, k No Yes Stop Coverged? Fgure Geeral Algorthm Structure of the DyusT Model (1) 1

17 Fgure Relatoshp of vehcle speed ad fuel cosumpto () 1

18 Fgure 1 Case study etwork 1

19 Vehcle (#) 000 Demad Served terato 0 Demad Served terato 1 Demad Served terato Iterato Fgure Objectve Fucto Value (Served Demad) Over Iteratos 1

20 Stato ID 1 1 Farfeld Vehcle (#) Fgure Demad Spatal Dstrbuto 0

21 Stato ID Supply (gallo) Fgure 1 Plaed supply (model soluto) for each stato 1

22 Userved Demad 1 Farfeld Stato ID 1 Fgure 1 Userved demad by stato