Safety of users in road evacuation: design of path choice models for emergency vehicles

Transcription

1 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury 803 Safety of users road evacuato: desg of path choce models for emergecy vehcles A. Vtetta, A. Quattroe & A. Polme Departmet of Computer Scece, Mathematcs, Electrocs ad Trasportato, Medterraea Uversty of Reggo Calabra, Italy Abstract Wth the framewor of the SICURO research project, the ma objectve of ths paper s to defe the procedures to be plaed ad actvated emergeces order to allow the evacuato of wea users (dsabled, old persos, etc.) from the area affected by a dsaster ad desg the optmal path for emergecy vehcles to reduce evacuato tmes. Specfcato, calbrato ad valdato of a path choce geerato model order to smulate the behavour of emergecy vehcle drvers at a urba level durg a evacuato s proposed. We specfy the factors that affect path choce behavour ad the two ma approaches: oe to oe ad may to oe. The frst regards the mmzato of geeralzed cost of a path that coects a org to a destato; the secod stead cosders the coecto of oe org to may destatos. We also report some expermetal results, obtaed the cotext of the SICURO Project, by applyg the proposed model to a real road trasport etwor at urba scale durg a smulato of a evacuato. Keywords: evacuato, path desg, emergecy vehcle. 1 Itroducto I ths paper we dscuss some results obtaed the SICURO research project carred out by the LAST-Laboratory for Trasport Systems Aalyss of the Medterraea Uversty of Reggo Calabra ad regardg path desg for emergecy vehcles. The ma objectve of ths paper s to defe the procedures to be plaed ad actvated emergecy cases order to allow the evacuato of wea users (dsabled, old persos, etc.) from the area affected by a dsaster ad desg the WIT Trasactos o The Bult Evromet, Vol 96, do: /ut070761

2 804 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury path for emergecy vehcles. It s worth otg that there s o geeral path choce model completely specfed ad calbrated for emergecy road trasport systems the evet of evacuato. Ths wor therefore proposes the specfcato, calbrato ad valdato of a path choce behavoural model at urba scale, o the bass of observato of a sample of emergecy vehcle drvers who used the road etwor of a small tow souther Italy durg a evacuato smulato. I the smulato ad desg of paths for emergecy vehcles, the path to follow ca be chose by two decso-maers: the drver or a exteral authorty. I the frst case the decso derves from the drver s experece ad/or from a GPS avgator. I the secod case the authorty forms the drver of the path to follow. I order to follow the best decso, the decso-maer has to be supported by a decso support system that receves real tme formato from the system, desgs the paths real tme, ad commucates t to the drver. To desg plag co-ordato of emergecy vehcles 'what to' models are cosdered [6]. The 'what to' approach s proposed order to defe optmal emergecy vehcle dstrbuto, terms of vehcle umber, wea users sequece to vst ad desg paths to mmze travel tme ad maxmze etwor relablty. 'What to' models allow tervetos o the supply (umber of vehcles, posto of the refuge areas), respectg some costrats (umber of persos to save ad stes to be left ). I partcular, we specfy the factors that affect path choce behavour ad the two ma approaches, oe to oe ad may to oe, that are commoly called, respectvely, the mmum path problem ad routg problem. The frst regards the mmzato of geeralzed cost of a path that coects a org to a destato; the secod stead cosders the coecto of oe org to may destatos. I both cases the problem s approached three phases: 1. paths ad travel tmes are geerated usg the models foud the lterature; 2. the paths effectvely chose by the emergecy vehcle drvers are aalyzed; 3. the model s calbrated order to maxmze the degree of cover of the chose path wth those geerated, each of whch s obtaed optmzg a fucto assocated to a certa crtero (mmum travel tme or maxmum etwor relablty). A cogested etwor s assumed: the system s a emergecy codto ad all the users use the etwor at the same tme. The paper s structured as follows: secto 2 the lterature o path choce geerato models s surveyed. Secto 3 treats the ma features of the proposed model terms of the oe to oe ad may to oe approaches; secto 4 gves the expermetal results, obtaed by applyg the proposed model to a real road trasport etwor at urba scale the specfc case of evacuato; secto 5 some coclusve cosderatos are reported. 2 Path choce geerato models Path choce geerato models ca be classfed by the umber of odes to coect ad the path betwee each org ad destato (Fgure 1). I the WIT Trasactos o The Bult Evromet, Vol 96,

3 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury 805 specfc feld of emergecy vehcles, the problem of path choce ca be treated wth two ma approaches: 1. oe to oe, to geerate paths that coect oe org to oe destato; 2. may to oe for the coecto of oe org to may destatos. The may to oe problem s a exteso of the oe to oe problem because each par of odes to vst a oe to oe problem has to be solved. Hece the oe to oe problem s preseted frst. The may to oe problem s preseted later ad ca be cosdered the optmzato of a cha of oe to oe problems. Below we specfy the ma features of the oe to oe approach, dstgushg the two ma phases of geeratg the choce set ad choosg a alteratve (secto 2.1) ad may to oe approach (secto 2.2). Fgure 1: Approaches for path choce geerato models. 2.1 Oe to oe The oe to oe approach gves the probablty of every path beg chose, from those perceved as admssble, betwee each org to each destato. The problem of oe to oe path choce s complex due to the large umber of exstg alteratve (o,d) pars, also o small-sze etwors, ad ther overlappg. These dffcultes are treated varous studes whch complete model specfcato of path choce s artculated two phases: 1. geerato of the choce set, that s the possble alteratves [1, 3, 13, 15, 18]; 2. path choce amog the alteratves belogg to the choce set geerated [1, 3, 5, 7, 8, 16, 18]. Regardg the choce set geerato, there are dfferet approaches the lterature (fgure 2): a exhaustve approach, all the loopless aalytcal paths o the etwor are avalable ad belog to the sgle choce set for all users; a selectve approach, oly some avalable paths represet attractve choce alteratves. I the secod case, the geerato of avalable paths ca be obtaed followg three dfferet approaches: wth the moocrtero approach, determstc or probablstc mult-crtera approach. Regardg the moocrtero approach the avalable paths are obtaed by the satsfacto of a sgle crtero. I order to geerate the mmum path for the crtero t s ecessary to mmze trp dsutlty measured wth a sgle WIT Trasactos o The Bult Evromet, Vol 96,

4 806 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury attrbute (tme, dstace, etc.) or costruct a covered fucto of the crtero. The parameters of the covered fucto must be calbrated, maxmzg, for example, the overlappg factor betwee the geerated ad the observed paths. Alteratvely, t s possble to use the mult-crtera approach accordg to whch the avalable paths are obtaed by satsfyg some crtera calbrated by maxmzg the overlappg factor betwee the geerated ad observed paths, smlar to the moocrtero approach. Fgure 2: Approaches for choce set geerato. As regards path choce, most of the models proposed the lterature belog to the famly of Radom Utlty Models (RUMs). Based o assumptos o the radom resdual of the utlty perceved by users, the models ca have dfferet specfcatos, of whch those most commoly used for path choce are Multomal Logt, C/DC-Logt, Path Sze ad Probt [4, 8, 14, 15, 18, 19]. 2.2 May to oe Cocerg the may to oe approach the problem of path choce geerato ca be specfed as a routg problem. The routg problem regards the ecessty to vst a certa umber of odes (or ls) a gve sequece, leavg from a org ad returg to t, wth the respect of some costrats (.e. umber of users to vst ad ther localzato, umber of vehcles ad ther capacty, etc.) ad the am to optmze a Objectve Fucto OF. The OF ca deped o travel tme, moetary cost or umber of vehcles. The o routg problems are extesve, especally the freght trasport feld [9, 10, 21]. I the case of emergecy vehcles [12] the problem s treated uder the assumpto that a geeral vehcle covers a gve zoe, assgg to the vehcles a sequece of odes to vst accordg to the characterstcs of the users served. Araz et al. [2] study a emergecy system (ambulaces ad at-fre vehcles) so as to dmsh travel tme ad maxmze the area covered ad the umber of users saved. I the presece of a atural dsaster Taahash et al. [20] propose a model that smulates the varatos user path choce behavour whe, due to a calamtous WIT Trasactos o The Bult Evromet, Vol 96,

5 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury 807 evet, the road etwor has lmted accessblty. The model etals estmatg the varato costs curred by users who are forced to modfy ther path choce. Therefore, the routg problem regards the eed to vst a certa umber of odes (or ls) a gve sequece, leavg from a org ad returg to t, so as to optmze a objectve fucto OF. The OF ca deped o travel tme, moetary cost ad umber of vehcles. Routg problems ca be grouped to two dstct classes: ode routg problems ad l routg problems. Whereas the ode routg problem cossts vstg some odes leavg from a org, the l routg problem regards cover of some etwor ls. A further dstcto ca be made wth the classes defed above, partcular the case of ode routg: the vehcle routg problem (classcal or asymmetrc) ad salesma problem. I the case of l routg we ca dstgush the Chese postma problem (oreted or o-oreted) ad rural postma problem. Fgure 3: Approaches to the routg problem. 3 Proposed model The proposed model s used to aalyze the behavour of a sample of emergecy vehcle drvers terms of path choce o a road etwor at urba level the case of evacuato. The path choce geerato models are smulated wth two approaches: oe to oe ad may to oe. I both cases the paths geerated satsfy a fucto specfed o the bass of observato of emergecy vehcle drver behavour. Below we specfy the proposed model wth the oe to oe approach (secto 3.1) ad may to oe approach (secto 3.2). 3.1 Oe to oe Mas defes 1977 the probablty of a geerc path as the sum, o all the choce sets whch cota the alteratve, of the product betwee the probablty of the choce set ad the codtoal probablty of choosg path gve the choce set. WIT Trasactos o The Bult Evromet, Vol 96,

6 808 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury where p I p ( ) (/I p () ( I ) = p ( I ) p ( I ) / = p I I, probablty of the choce set, (1) I ), choce probablty of the geerc path Cocerg the geerato of the choce set, the selectve approach followed wth multcrtera, descrbed secto 2.1, s used to defe for every (o,d) par (refuge area - wea user resdece) a choce set that cossts of several paths, each of whch s geerated respect to a certa crtero. The crtera used deped o the factors that affect the emergecy vehcle drvers behavour. These crtera are: mmum travel tme ad maxmum etwor relablty. For both the crtera, relatve to every l j of the etwor, a covered fucto s defed. The fucto s depedet o travel tme ad uow parameters. The geeral structure characterzg the covered fuctos for every crtero h s: h ( j) = β R( j) tr( j) f the l j belogs to the reserved etwor (2) h ( j) = β NR( j) t NR( j) otherwse (3) where β R( j), β NR( j) are parameters calbrated for both crtera h t R( j), t NR( j) s travel tme o l j belogg to path ad respectvely to the reserved or o-reserved etwor. Table 1 reports the parameters relatve to the covered fuctos whch have the above geeral structure. Table 1: Parameters of the covered fuctos for the crtera. Crtero (h) β R(Ij) β NR(j) Mmum travel tme 1 1 Maxmum relablty 1 1/Φ j The etwor relablty Φ j of l j, relatve to the tme terval T, s defed as the codtoal probablty that vehcle speed does ot decrease durg T to the pot where the desty lmt s reached, gve that the level at stat zero s equal to the average speed correspodg to the flow rate stable flow codtos [11]. 3.2 May to oe Cocerg the may to oe approach the vehcle routg problem, descrbed secto 2.2, s used to defe a choce set that cossts of several paths, each of whch optmzes a objectve fucto ad coects oe org (refuge area) to may destatos (wea user resdeces). WIT Trasactos o The Bult Evromet, Vol 96,

7 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury 809 Gve the followg otato: L = {(,j),, j N}, l set; f j, ordary vehcle flows; δ, amplfyg factor; e j, emergecy vehcle flows; r, demad o ode ; v, emergecy vehcle; NV ={1, 2,, NV}, umber of emergecy vehcles; b, emergecy vehcle capacty; x jv, varable that s equal to 1 f the l j s used by vehcle v, zero otherwse; y v, varable that s equal to 1 f the ode s already vsted by vehcle v, zero otherwse; Φ j, relablty o l j (see secto 3.1); the vehcle routg problem ca be expressed wth the followg geeral optmum problem. Objectve Fucto: Mmzg: ( j + ej ) (,j) L NV h j f δ x jv (4) varable: x jv (,j) L; v = 1,2,,NV subject to: NV y 1 Z, = 1,2,, (5) v= 1 j Z v = j NV v= 1 y 0v = NV v= 1 (6) r y b v = 1,2,,NV (7) v y v { 0,1} N (8) x jv { 0,1} N; (,j) L (9) x jv x = Z, v = 1,2,,NV (10) jv j Z where cocerg mmum travel tme: h j = tj, travel tme o l j dstgushg reserved or o-reserved etwors; cocerg maxmum relablty: h j = t(f j )/ Φ(f j), rato betwee travel tme ad relablty o l j, both depedg o l ordary flow f j. 4 Expermetato The proposed model, descrbed the prevous secto, was specfed, calbrated ad valdated for a emergecy system, studed wth regard to path choce o a road trasport etwor at urba scale. The model was calbrated o the bass of emergecy vehcle drver motorg durg a smulato of evacuato, carred out by the Trasport System Aalyss Laboratory (LAST) Melto Porto Salvo WIT Trasactos o The Bult Evromet, Vol 96,

8 810 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury (Calabra, souther Italy) wth the ambt of the SICURO Project. The paths chose by the drver sample were motored usg a GPS (Global Postog System) o board emergecy vehcles ad vdeo cameras deployed o the etwor. The etwor cossts of all the ma roads (37 odes ad 66 ls). As regards geerato of the choce set, the uow parameters of covered ad objectve fuctos were calbrated by maxmzg the degree of overlappg of the chose paths by the sample wth the geerated paths. Fgure 4: Melto Porto Salvo road etwor wth localzato of wea users ad the refuge area. Gve oe org cocdg wth the refuge area (RA) ad the resdece localzato of fve (A, B, C, D, E) wea users to rescue (Fgure 4), we aalyzed the observed paths. The drvers chose two routg paths wth oly oe emergecy vehcle: the frst routg two wea users were rescued the secod three. The total evacuato tme observed was approxmately 47 mutes. We the smulated wth the proposed model the observed path, obtag almost the same results. Ths demostrates the model s goodess-of-ft. We also desged the optmal path wth the proposed model, cosderg both the approaches prevously specfed, Oe to oe ad May to oe, assumg dfferet scearos terms of umber of emergecy vehcles ad ther capacty. Wth the oe to oe scearo, assumg oly oe emergecy vehcle order to rescue oe wea user at a tme, we obtaed a reducto evacuato tme of about 15%. The same result was acheved wth the may to oe approach, assumg oly oe emergecy vehcle wth a greater capacty order to rescue all fve users at a tme. Uder aother hypothess (two emergecy vehcles that move at the same tme ad rescue all wea users wth two may to oe routgs) the total evacuato tme s reduced approxmately by 20%. 5 Cocluso I ths paper some results of the SICURO research project are gve ad partcular the problem of emergecy vehcle drvers path choce at urba scale durg a evacuato are treated. Path choce geerato behavoural models WIT Trasactos o The Bult Evromet, Vol 96,

9 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury 811 were specfed ad calbrated for the road trasport system of a Itala tow based o motorg evacuato procedures of some wea users durg a smulato. These calbratos suppled some vald results ad provde soud dcatos o the emergecy vehcle drver path decsoal process the urba cotext ad the specfc feld of a evacuato whe a dsaster occurs. Prelmary calbratos for the Itala urba etwor also show that sgfcat mprovemets terms of evacuato tme savg ca be obtaed by desgg emergecy vehcle paths ad defg the ma characterstcs of the supply system for the wea users such as the umber of vehcles ad ther capacty. I the future, the model should be further aalyzed through the use of a more extesve etwor ad database, ad dfferet scearos should be proposed by also varyg the refuge area umber ad localzato. Refereces [1] Atosse, R. W., Daly, A. J., ad Be Ava, M., Hghway assgmet method based o behavoural models of car drver s route choce, Trasportato Research Record (1220), pp 1-11, [2] Araz, C., Selm, S., Ozaraha, I., A fuzzy mult-objectve coverg-based vehcle locato model for emergecy servces. I Computers & Operatos Research 34, pp , [3] Be Ava, M., Bergma M. J., Daly A. J., Ramaswamy, R., Modellg terurba route choce behavour, Proceedgs of the 9 th Iteratoal Symposum o Trasportato ad Traffc Theory, VNU Scece Press, pp , [4] Be Ava, M., Lerma, S. R., Dscrete choce aalyss: theory ad applcato to travel demad, MIT Press, Cambrdge, Mass, [5] Be-Ava, M. ad Berlare, M., Dscrete choce methods ad ther applcatos to short term travel decsos, Chapter for the Trasportato Scece Hadboo, Prelmary Draft, [6] Catarella, G. E., Vtetta, A., The mult-crtera road etwor desg problem a urba area. Trasportato, vol. 33, pp , [7] Cascetta, E., Nuzzolo, A., Bggero, L., Aalyss ad modellg of commuters departure tme ad route choces urba etwors, Proceedgs of the 2 d Iteratoal Semar o Urba Traffc Networ, Capr, Italy, [8] Cascetta, E., Nuzzolo, A., Russo, F., Vtetta, A., A ew route choce logt model overcomg IIA problems: specfcato ad some calbrato results for terurba etwors, Proceedgs of the 13 th Iteratoal Symposum o Trasportato Traffc Theory, Jea-Baptste Lesort ed., Pergamo Press, [9] Cho, Y.J., Wag, S.D., A threshold acceptg meta-heurstc for the vehcle routg problem wth bachauls ad tme wdows. I Joural of the Easter Asa Socety for Trasportato Studes, V 6, pp , WIT Trasactos o The Bult Evromet, Vol 96,

10 812 Urba Trasport XIII: Urba Trasport ad the Evromet the 21st Cetury [10] Chou, Sw, Itegratg the vetory maagemet ad Vehcle Routg Problems For Cogested Urba Logstcs Networ. I Joural of the Easter Asa Socety for Trasportato Studes, V 6, pp , [11] Ferrar, P., The traffc cotrol o motorways. I Proceedgs of semar Traffc mage processg - State of developmet ad possblty of utlzato, Agosto Nuzzolo (ed.), [12] Yag, S., Hamed, M., Haga, A., Ole Dspatchg ad Routg Model for Emergecy Vehcles wth Area Coverage Costrats. I Trasportato Research Record: Joural of the Trasportato Research Board Issue Number 1923, 2005 [13] Morawa, T., A hybrd probablstc choce set model wth compesatory ad o compesatory ruler, Proceedgs of the 7 th WCTR, Sydey, Australa, [14] Ortuzar, J. d. D. ad Wllumse, L. G., Modellg trasport, Wley ad Sos, Eglad, [15] Russo, F. ad Vtetta, A., Networs ad assgmet models for the Itala atoal trasportato system, Proceedgs of the 7 th WCTR, Sydey, Australa, [16] Russo, F. ad Vtetta, A., A assgmet model wth modfed Logt, whch obvates eumerato ad overlappg problems, Trasportato 30, pp , [17] Russo, F. ad Vtetta, A., La rcerca d percors ua rete: Algortm d mmo costo ed esteso, Fraco Agel, Mla, Italy, [18] F. Russo, A. Vtetta, A. Quattroe, Route choce modellg for freght trasport at atoal level. Proceedgs of the Europea Trasport Coferece, Strasbourg, [19] Sheffy, Y., Urba trasportato etwors, Pretce Hall, Eglewood Clff, NJ, [20] Taahash et al, Dsaster mpact aalyss of lmted access through traffc etwor model: the case of mt. Usu erupto. I Proceedgs of the Easter Asa Socety for Trasportato Studes, V. 5, pp , [21] Taguch, E., Ado, N., A expermetal aalyss o probablstc vehcle routg ad schedulg wth ts. I Joural of the Easter Asa Socety for Trasportato Studes, Vol. 6, pp , WIT Trasactos o The Bult Evromet, Vol 96,