COMPARISION OF POTENTIAL PATHS SELECTED BY A MALICIOUS ENTITY WITH HAZARDOUS MATERIALS : MINIMIZATION OF TIME VS. MINIMIZATION OF DISTANCE

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1 Proceedngs of the 2007 Wnter Smulaton Conference S. G. Henderson, B. Bller, M.-H. Hseh, J. Shortle, J. D. Tew, and R. R. Barton, eds. COMPARISION OF POTENTIAL PATHS SELECTED BY A MALICIOUS ENTITY WITH HAZARDOUS MATERIALS : MINIMIZATION OF TIME VS. MINIMIZATION OF DISTANCE Rakesh Nune Pamela Murray-Tute Vrgna Polytechnc Insttute and State Unversty 7054 Haycock Road Falls Church, VA 22043,USA ABSTRACT Securty of hazardous materals (hazmat) shpments s a growng concern for many governments and prvate companes due to ther potental use as weapons. Ths paper dentfes a methodology for obtanng the paths taken by a malcous entty when he/she hjacks a hazmat truck based on condtonal consequence and a measure of cost (ether dstance or travel tme). The work compares the routes obtaned by travel tme and dstance for a sample network and suggests the need for travel tme to be consdered n urban areas, especally n peak hours. 1 INTRODUCTION Hazardous materals (hazmat) are generally substances requred for ndustral producton or a byproduct of the same. These materals should be safely transported to and from the ndustral areas owng to ther potental hazardous behavor. For example, n 1977 alone, the Unted States transported 2.8 mllon tons of ammona by hghway over 476 mllon ton-mles (Brown et al. 2001). Thus, hazmat routng s a source of concern for government and prvate agences. The major concern about hazmat transportaton s the potental damage done to socety and the envronment when accdents or splls occur (Taboada et al. 2006). Hence, there s consderable pressure on authortes to formulate gudelnes for routng hazmats. Such dangerous shpments pose rsk both at ndvdual and socetal levels and was calculated by prevous authors (Saccomanno and Shortreed 1993). The probablty of occurrence of such accdents s generally very low, but when they do occur, they could cause wde-spread damage to both human lves and nfrastructure. Such behavor classfes these events n to a low probablty and hgh consequence (lphc) group. Thus, the paths chosen by the hazmat trucks should mnmze the possble consequences and also mnmze the dstance traveled n order to reduce shpments costs. These shpments could become targets for terrorsts and other malcous enttes and could be used as weapons. Terrorst-related rsk nvolved n hazmat transportaton s very dffcult to calculate, due to ts low probablty of occurrence and potental hgh consequence. Rsk s generally estmated wth probablty and consequence of the event as a whole (Volpe Center 2003; Hames 2004). Consequence s measured n terms of causaltes or economc loss (Bush 2003; Crowther and Hames 2005). Prevous authors (Huang and Fery 2005; Huang et al. 2004) have worked on the ntegraton of hazmat routng and securty concerns but dd not consder the decsons hjackers mght make to reach ther targets. 1.1 Travel Tme and Smulaton Changng traffc condtons and congeston patterns actually force the general commuters and hazmat vehcle owners to choose routes accordng to travel tme rather than the dstance (Haghan and Jung 2005). Chang and Mahmassan (1998) descrbed a heurstc rule wth whch daly commuters recall the travel tmes under lmted nformaton and ther cumulatve experence for choosng the best routes to reach ther destnaton. Wunderlch (1998) conducted a study by smulatng route gudance under varable network congeston condtons and concluded that gudance actually mproves the travel by 8-26% n peak tme. The same rule apples to hazmat vehcle owners and more mportantly for the malcous enttes. Prevous work(murray-tute et al. 2006) focused on developng routes taken by the hazmat drver and also the possble routes taken by the malcous enttes. The present work consders travel tme, rather than dstance, n route determnaton. The travel tme coupled wth possble consequence on network lnks s used for the estmatng the multple paths of the malcous enttes n ths work. The /07/$ IEEE 1161

2 paper compares the results between the routes of the malcous enttes by consderng travel dstance and travel tme. The remander of ths paper conssts of three sectons. Frst, the problem s defned and the mathematcal model s descrbed. Second, the model s appled to a sample network and the smulaton s descrbed. Fnally, conclusons are presented. 2 PROBLEM DEFINITION Ths paper dentfes possble paths taken by the hjacker once he/she captures the hazmat truck at any pont n ts normal route. Snce the malcous entty s target s often located n an urban area and the objectve s often to cause the maxmum damage, the entty s assumed to tme a hazmat release durng or near the peak traffc hours. The hjacker s further assumed to elmnate paths wth hgh congeston levels to reduce hs/her travel tme. The network on whch he/she hjacks the truck and causes damage s denoted by G (N, A) whch conssts of a set of nodes N and drected arcs A. Each lnk has the attrbutes of law enforcement ntercepton probablty P, consequence C, dstance d, and travel tme t. The malcous entty ntercepts the truck at node O and moves towards target T. Table 1 summarzes the notaton used n the paper. The path chosen by the hjacker should maxmze consequence wth consderaton of the probablty of beng ntercepted by authortes and mnmze travel tme. The route taken by the malcous entty may be determned by the dstance traveled (Murray-Tute et al. 2006), but n urban areas, travel tmes are not necessarly proportonal to dstance due to congeston. 2.1 Procedure The magntude of the probablty of an accdent on any partcular lnk s suffcently small that the probablty of accdent along a path can be approxmated as n equaton (1) (Sheral et al. 1997). P p x (1) AQ A Where P AQ s the probablty of accdent on path Q p a s the probablty of accdent on a partcular lnk x s the varable denotng lnk whose value becomes 1 f lnk s chosen and 0 f not. The expresson can be smlarly extended to probablty of hjack snce the probablty of hjack s also comparatvely very low whch gves rse to equaton (2) P p x (2) Q A Where P Q s the probablty of hjack along path Q a p s probablty of ntercepton by law authortes on lnk x s the varable denotng lnk whose value becomes 1 f lnk s chosen and 0 f not. Table 1: Notaton summary Notaton Interpretaton Sets and Indces G(N,A) Road network consstng of a set N of nodes and set A of drected arcs A Set of drected arcs, ndexed by a N Set of nodes, ndexed by j O Orgn node of the malcous entty s path T Possble target for the malcous entty Parameters C Consequence of a hazmat ncdent on lnk D Length of lnk P hj Probablty of a successful hjack at node j Probablty of ntercepton by law enforcement Weght assocated wth condtonal expected consequence t mn Mnmum tme for the malcous entty s path t max Maxmum tme for the malcous entty s path v mn Mnmum condtonal expected consequence for the malcous entty s path v max Maxmum condtonal expected consequence for the malcous entty s path w mn Mnmum condtonal expected consequence for orgnal path w max Maxmum condtonal expected consequence for orgnal path t x z 1 z 2 Travel tme on a lnk Varables Bnary nteger decson varable takng the value 1 f the lnk s chosen by the hjacker and 0 otherwse Value of objectve functon for malcous entty s path selecton usng dstance of the network Value of objectve functon for malcous entty s path selecton usng travel tme of the network The methodology developed n the followng sectons for dentfyng the most lkely paths taken by the malcous enttes s based on a few assumptons. Frst, t s certan that a hjackng wll occur somewhere n the network. Sec- 1162

3 ond, once a truck s hjacked, t s drectly moved towards the target. Multple paths are estmated for a sngle target gven the most possble hjack node. The method n the present work obtans routes based on the trade off between consequence and estmated travel tme. Prevous works have consdered use of dstance as cost, but travel tme mght be a better measure durng peak hours. Snce congeston causes consderable changes n travel tme, t s often necessary to recalculate the paths, especally estmatng the paths taken by malcous enttes. 2.2 Preferred Paths By The Malcous Entty The dfferent paths preferred paths by the malcous entty are obtaned from the formulaton gves from equatons (3-5) pc x A vmn x d x umn A A mn z1 1 (1 1 ) (3) v v u u max mn Subject to 1 f j = O' x x 1 f j = T (4) F ( j) H ( j) 0 Otherwse x 0, A 1 the objectve functon n equaton 3 should be mnmzed for dfferent values of 1. Equaton 4 represents the contnuty of the flow n the network and equaton 5 ensures the nteger constrant of the varables. C x a a a a vmn axa t x a A 2 2 (1 2 ) vmaxvmn tmax z max t mn mn mn (5) (6) t Equaton 6 s obtaned by replacng the travel dstance term wth travel tme t n equaton (3). The methodology for obtanng the values of obtanng v max, vmn, tmax, tmn and procedure for solvng s used as descrbed by (Murray- Tute et al. 2006) 3 SAMPLE APPLICATION The above descred routng methodology s appled to a network based on Reston, Vrgna. The network, shown n Fgure 1, has 354 lnks and 147 nodes and s dvded nto 14 zones. Reston has populaton of 56,407 accordng to the 2000 US Census (Ctydata.com 2000). In addton to the resdents, people move through Reston gong to/ comng from Washngton, DC. The network has both freeways and arterals, ncludng Route 7 and the Dulles Toll Road ndcated by arrows n Fgure 1. Approxmately 60,000 total vehcles were loaded on the network n 120 mnutes, wth an ncremental ncrease up to 75 mnutes followed by a gradual reducton n new demand. The exact demand for any partcular ffteen mnute ncrement was based on a random number and a base orgn-destnaton matrx. The travel tme was found by smulatng the gven envronment wth the traffc assgnment-smulaton tool DYNASMART-P verson 1.2. Traffc was assgned accordng to user equlbrum. Smulaton tme was set to 1000 mnutes and 50 teratons were performed. The parameters used for the smulaton are gven n Table 2. Consequences were generated randomly and dstrbuted among the zones dependng on the zone characterstcs. The areas nsde Reston wth resdental areas and offce space were gven hgh consequence values and zones contanng only routes and freeways were gven lower values. The probablty of capture by law authortes was also randomly generated and dstrbuted dfferently n resdental areas and hghways, as t s easer to be caught n arterals due to lower capacty, low speeds and hgher densty of law agences. The hazmat truck was assumed to be hjacked at the northern most pont n Fgure 1 on Route 7. The hjacker then proceeds towards the arport, whch s the selected target. Hjack pont Target Route 7 Dulles toll road Fgure 1: The map of Reston used for smulaton The traffc condton smulated was the peak hour, whch s when heavy congeston s experenced and when the malcous entty mght prefer to attack so that he/she can cause maxmum damage. Congeston and queues can be observed from the smulaton software outputs for the frst 400 mnutes whch can be observed from the Fgures

4 Table 2: Parameters used for smulaton Total number of vehcles Max Smulaton Tme (mn) 1000 Number of Nodes 147 Number of Lnks 354 Total number of teratons 20 Start Tme n Whch Vehcle Statstcs are Collected 30 End Tme n Whch Vehcle Statstcs are Collected 1000 Fgure 4: Queue length at traffc sgnals after 90 mn. Fgure 2: Queue length at traffc sgnals after 30 mn. Fgure 5: Queue length at traffc sgnals after 120 mn. Fgure 3: Queue length at traffc sgnals after 60 mn. Fgure 6: Queue length at traffc sgnals after 150 mn. 1164

5 Fgure 7: Queue length at traffc sgnals after 180 mn. The darker lnes on the lnks ndcate the length of the queues and the blue dots ndcate the traffc sgnals. Mean travel tme for frst 180 mnutes s consdered startng from 30 mnutes. Ths represents the peak tme of loadng and whch s of prmary nterest here. 3.1 Dfferent Preferred Paths Fgure 9: Path obtaned when = 0.5 for dstance Usng the descrbed optmzaton formulaton n equatons (3-6) varous paths were calculated for dfferent values of. The dfferent paths can be observed n the Fgures 8-10 when dstance s consdered and n Fgures when travel tme s consdered. The hghlghted lne ndcates the path taken by the malcous enttes. Fgure 10: Path obtaned when = 0.9 for dstance 3.2 Results Fgure 11: Path obtaned when = 0.1 for travel tme Fgure 8: Path obtaned when = 0.1 for dstance 1165

6 Fgure 12: Path obtaned when = 0.5 for travel tme tme, he/she mght not prefer the path through Reston because of hgh travel tme unless and untl he/she gves a very hgh preference to only the damage factor. Fgures 10 and 13 obtaned at =0.9 are smlar except n the last few lnks of the routes because the dstance and travel tme factor s reduced to a small amount. Usng dstance for determnng the routes taken by the malcous enttes after hjackng mght not gve the correct estmate of the path especally n networks whch are coupled wth freeways and toll roads. The travel tme factor domnates more n peak hours when congeston s very hgh and hence could gve dfferent answers f travel tme s not used. The travel tme mght be proportonal to dstance at off peak hours and n areas where all the lnks face smlar knds of congeston. The present results are specfc to networks when there s surroundng freeways whch provde a relatvely low travel tme at peak hours. The selected hjackng pont and target also nfluence the potental varablty n routng. Future work wll nclude the larger networks. In the present work consequence s consdered from the resdental and offce space, the consequence actually changes wth ncreases n traffc and queue length as the damage at that pont could take more lves; ncludng ths crteron would further ncrease the results accuracy. REFERENCES Fgure 13: Path obtaned when = 0.9 for travel tme 4 CONCLUSIONS As Reston s both a resdental and workng area the consequence to human lves and prvate property that can be caused by any possble hazmat ncdent n those areas s relatvely hgh compared to more open roadways. But from the queung pctures t can observed that these areas also have relatvely hgh congeston and hence hgh travel tme. Thus we can see that for =0.1 whch would gve preference (greatest weght) to shortest travel dstance or tme, the routes obtaned by dstance and travel tme crtera are the same whereas at = 0.5 (fgure 9 and 12) dfferences exst. The tme crtera yelds a path travelng on the hghway (Farfax County Parkway) where there s less congeston whereas the dstance crtera gves a path through Reston whch has hgher consequences snce the dstance factor and consequence factor are now gven equal weght and the dstance factor s not as domnatng as the travel tme factor whch s very hgh n the Reston area durng the peak hour. Ths mples that though the malcous entty mght want to travel n a path where he/she can also cause a hgh degree of damage and also lower travel Brown, D. F., S. Hwang, J. O. Steen, A. J. Polcastro, and W. E. Dunn A rsk assessment for natonal transportaton of selected hazardous materals. 80th Annual Meetng of the Transportaton Research Board, Washngton, D.C., Transportaton Research Board. Bush, G. W Homeland Securty Presdental Drectve / HSPD-7. The Whte House, Offce of the Press Secretary. Ctydata.com. (2000). Reston, Vrgna. Retreved 2 Aprl, 2007, from < /cty/reston-vrgna.html#top>. Crowther, K. G. and Y. Y. Hames Applcaton of the noperablty nput-output model (IIM) for systemc rsk assessment and management of nterdependent nfrastructures. Systems Engneerng 8(4): Saccomanno, F. F. and J. H. Shortreed Hazmat transport rsks: socetal and ndvdual perspectves. ASCE Journal of Transportaton Engneerng 119(2): 11. Chang, G.L., and H. S. Mahmassan Travel tme predcton and departure tme adjustment behavor dynamcs n a congested traffc system. Transportaton Research 22B(3): Haghan, A. and S. Jung A dynamc vehcle routng problem wth tme-dependent travel tmes Computers & Operatons Research 32:

7 Hames, Y. Y Rsk modelng, assessment, and management of terrorsm. Rsk Modelng, Assessment, and Management. John Wley & Sons. Hoboken, John Wley & Sons, Inc: Huang, B. and P. Fery Adng route decson for hazardous materal transportaton. Transportaton Research Board. Huang, B., C. R. Long and Y. S. Lew GIS and genetc algorthms for HAZMAT route plannng wth securty consderatons. Internatonal Journal of Geographcal Informaton Scence 18(8): Murray-Tute, P., R. H. Garrdo and R. Nune Path predcton methodology for hazardous materals transported by malcous enttes. In 11th World Conference on Transport Research Berkeley, Calforna. Sheral, H. D., L. D. Brzedne, T. S. Glckman and S. Subramanan Low probablty-hgh consequence consderatons n routng hazardous materal shpments. Transportaton Scence 31:14. Taboada, J., J. M. Matas, A. Saavedra, C. Ordonez and R. Martnez-Algera Rsk communcaton: around the world neural networks models for assessng road sutablty for dangerous goods transport. Human and Ecologcal Rsk Assessment 12:17. Volpe Center. (2003). Rsk assessment and prortzaton. Retreved July 14, 2006, from < urnal/2003/chap1.html>. Wunderlch, K A smulaton-based assessment of route gudance benefts under varable network congeston condtons. Mathematcal and Computer Modelng 27(9-11): AUTHOR BIOGRAPHIES RAKESH NUNE s a graduate research assstants presently pursung hs masters from Vrgna teach n transportaton engneerng. He has completed hs undergrad studes n Indan Insttute of technology Guwahat INDIA. Hs research nterests nclude optmzaton algorthms, modelng and AI. Hs emal d s <nune@vt.edu> PAMELA M. MURRAY-TUITE s an Assstant Professor of Cvl and Envronmental Engneerng at Vrgna Polytechnc Insttute and State Unversty (Vrgna Tech). She was prevously a senor consultant wth Booz Allen Hamlton. She receved a BS degree n Cvl Engneerng from Duke Unversty and an MS and a PhD n Cvl Engneerng from The Unversty of Texas at Austn. Her current research nterests focus on transportaton network analyss, modelng, and smulaton; securty, relablty, rsk, and reslence analyss; evacuaton modelng; dsaster recovery modelng; and congeston mtgaton. Her e-mal address s <murraytu@vt.edu>. 1167