A Two-Stage Approach for Estimating a Statewide Truck Trip Table

MPC 14-269 Srwt Jsuw, Seugkyu Ryu, Athoy Che, d Kevi Heslip MAY 2014 A Two-Stge Approch for Estimtig Sttewide Truck Trip Tble A Uiveity Trsporttio Ceter sposored by the U.S. Deprtmet of Trsporttio servig the Mouti-Plis Regio. Cosortium membe: Colordo Stte Uiveity North Dkot Stte Uiveity South Dkot Stte Uiveity Uiveity of Colordo Dever Uiveity of Dever Uiveity of Uth Uth Stte Uiveity Uiveity of Wyomig

A Two-Stge Approch for Estimtig Sttewide Truck Trip Tble Srwut Jsuw Seugkyu Ryu Athoy Che Kevi Heslip Uth Trsporttio Ceter Uth Stte Uiveity Log UT My 2014

Disclimer This documet is dissemited i the iterest of iformtio exchge. The cotets of this report reflect the views of the utho, who re resposible for the fcts d ccurcy of the dt preseted herei. The cotets do ot ecessrily reflect the officil views or policies of Uth Trsporttio Ceter (UTC) t Uth Stte Uiveity (USU) d Mouti-Plis Cosortium (MPC). North Dkot Stte Uiveity does ot discrimite o the bsis of ge, color, disbility, geder expressio/idetity, geetic iformtio, mritl sttus, tiol origi, public ssistce sttus, sex, sexul oriettio, sttus s U.S. veter, rce or religio. Direct iquiries to the Vice Presidet for Equity, Diveity d Globl Outrech, 205 Old Mi, (701) 231-7708.

TABLE OF CONTENTS 1. INTRODUCTION... 1 1.1 Bckgroud... 1 1.2 Reserch Need... 2 1.3 Objective of the Study... 3 1.4 Orgiztio of the Report... 4 2. LITERATURE REVIEW... 5 2.1 Literture Review o Truck O-D Estimtio... 5 2.1.1 Trip-bsed Modelig Approch... 5 2.1.2 Commodity-bsed Modelig Approch... 7 2.2 Literture Review o Truck O-D Estimtio... 9 2.2.1 Lik-bsed Fctorig Method... 9 2.2.2 O-D Fctorig Method... 9 2.2.3 Three-step Truck Model... 9 2.2.4 Four-step Commodity Flow Model... 9 2.2.5 Ecoomic Activity Model... 11 2.2.6 Hybrid Model... 11 2.2.7 Logistics/Supply Chi Model... 11 2.2.8 Tour-bsed Model... 11 3. STATEWIDE TRUCK DEMAND OVERVIEW... 13 3.1 Freight Treds... 13 3.1.1 Ntiol Freight Trsporttio Treds... 13 3.1.2 Uth Freight Trsporttio Treds... 14 3.1.3 Top 10 Commodity Flows i Uth... 17 3.2 Uth Sttewide Trvel Model (USTM): Freight Compoet... 18 3.2.1 USTM Overview... 18 3.2.2 USTM Freight Model... 20 4. A TWO-STAGE APPROACH FOR ESTIMATING TRUCK TRIP TABLE... 22 4.1 Stge 1: Develop Commodity-Bsed Truck O-D Trip Tble... 22 4.2 Commercil d Empty Truck Demd Estimtio... 26 4.2.1 Commercil Truck Demd Estimtio... 26 4.2.2 Empty Truck Demd Estimtio... 27 4.3 Stge 2: PFE Formultio, Optimlity Coditios, d Solutio Algorithm... 28 4.3.1 Bckgroud d Formultio... 28 4.3.2 Optimlity Coditios... 31 4.3.3 Uiqueess Coditios... 36 4.3.4 Solutio Procedure... 37 5. NUMERICAL RESULTS... 42 5.1 Uth Network... 42 5.2 Numericl Results... 43 5.2.1 Commodity-bsed Truck O-D Trip Tble... 43 5.2.2 Effect of sptil costrits... 50 5.2.3 Truck Corridor Alysis... 52

6. CONCLUSIONS... 54 REFERENCES... 56 APPENDIX A. Commodity Codes Bsed o the SCTG... 60 APPENDIX B. Disggregted Productio-Attrctio of Uth... 62 APPENDIX C. Derivtios of the Adjustmet Equtios... 64

LIST OF TABLES Tble 2.1 Freight demd modelig pproches, methods, d dt sources... 8 Tble 3.1 Modl shre of freight shipmet i Uth by volume i 2007 (uit: MTo)... 15 Tble 3.2 Top 10 commodities by volume i Uth for 2007 d 2040... 17 Tble 3.3 Top 10 commodities by vlue i Uth for 2007 d 2040... 18 Tble 3.4 Iterl truck trip rtes (QFRM)... 21 Tble 3.5 Iterl truck trip rte (Urb)... 21 Tble 3.6 Iterl truck trip rte (Rurl)... 21 Tble 4.1 Destitio choice probbility fuctios for empty truck trips... 28 Tble 4.2 Nottio for the PFE model... 29 Tble 5.1 Commercil truck trips by couty (trucks/dy)... 45 Tble 5.2 Empty truck trips by couty (trucks/dy)... 45

LIST OF FIGURES Figure 1.1 Mjor highwy iterchge bottleecks for trucks... 2 Figure 2.1 Trip-bsed d commodity-bsed pproches... 6 Figure 2.2 Four-step commodity flow modelig process... 10 Figure 2.3 Truck freight demd modelig metrics... 12 Figure 3.1 Ntiol freight trsporttio treds... 14 Figure 3.2 Uth freight trsporttio treds... 16 Figure 3.3 Uth freight trsporttio treds (Cot.)... 16 Figure 3.4 USTM frmework... 19 Figure 3.5 Uth mjor freight corrido... 20 Figure 4.1 Coceptul frmework of the two-stge pproch... 22 Figure 4.2 A simplified procedure for estimtig the truck O-D trip tble from commodity flows... 23 Figure 4.3 FAF etwork, freight lysis zoes, d four types of truck flows i Uth... 25 Figure 4.4 PFE solutio procedure... 37 Figure 5.1 Uth sttewide freight trsporttio etwork... 43 Figure 5.2 Commodity-bsed truck O-D trip tble... 44 Figure 5.3 Estimted sttewide commodity-bsed truck flows... 47 Figure 5.4 Compriso betwee oe-stge d two-stge pproches... 48 Figure 5.5 Sttewide truck trffic d volume/cpcity lysis... 49 Figure 5.6 Comprisos of observed d estimted sttewide truck flows... 50 Figure 5.7 Comprisos of estimted productio flows... 51 Figure 5.8 Estimted truck flows d truck vehicle miles trveled o I-15 corridor, Uth... 53

1. INTRODUCTION 1.1 Bckgroud Sttewide models, icludig psseger d freight movemets, re frequetly used for supportig umerous sttewide plig ctivities. My sttes use them for trffic impct studies, ir qulity coformity lysis, freight plig, ecoomic developmet studies, project prioritiztio, d my other plig eeds (Horowitz 2006). Accordig to the dtbses from FHWA (2009) d Cesus Bureu (2010, 2012), the Uited Sttes (U.S.) trsporttio system trsported totl of 17.6 billio tos per yer i 2011 to serve lmost 117 millio households d 7.4 millio busiess estblishmets. The importce of truck demd hs bee icresed i the sttewide plig process becuse of its strog ifluece o the ecoomy of the sttes d the tio overll. Truck is the domit mode of freight trsporttio, with the idustry hulig 11.9 billio tos i 2011, equtig to pproximtely two-thirds (i.e., 67%) of ll freight trsported i the U.S. (FHWA 2009). Accordig to the Freight Alysis Frmework 3 (FAF) dtbse, truck shres pproximtely 75% of the domestic freight shipmets, d this tred is expected to cotiue util 2040. However, freight trsporttio cpcity, especilly rodwy trsporttio, is expdig too slowly to keep up with demd (Cmbridge Systemtics 2005). This growth imblce could sigifictly cotribute to cogestio t highwy segmets, iterchges, d highwy bottleecks (i.e., loctios tht re physiclly rrow d/or cogested) d hece re very susceptible to icidets d disruptios. Cogestio is lso cused by restrictios o freight movemet, such s the lck of spce for trucks i dese urb res (FHWA 2008) s posted o the rodwys due to height, legth, width, weight limits, icidet, or costructio. Figure 1.1 shows the loctios of highwy iterchge bottleecks (i.e., solid dots) for trucks o the tiol highwy etwork (Cmbridge Systemtics 2005). The bottleecks i Uth iclude Slt Lke City d Wstch Frot peripherl res. Truck origi-destitio (O-D) trip tble is importt compoet tht c be used to help strtegic trsporttio ple, provide, d govermet gecies to idetify the potetil bottleecks i their res. The subsequet results of truck trip tble obtied from the proposed frmework will be beeficil for ssistig stte deprtmets of trsporttio (DOTs) d metropolit plig orgiztios (MPOs) o evlutig opertiol strtegies to ddress the cosequet impcts due to truck trffic, icludig cogestio, ifrstructure deteriortio, sfety, d eviromet. 1

Slt Lke City d Wstch Frot Peripherl Ares i Uth Source: Cmbridge Systemtics, Ic. (2005) Figure 1.1 Mjor highwy iterchge bottleecks for trucks 1.2 Reserch Need The curret prctice i estimtig sttewide truck O-D trip tble is through the use of truck trip rtes estimted i the Quick Respose Freight Mul (QRFM) developed by Cmbridge Systemtics (2007), or usig commercil freight dtbse (e.g., TRANSEARCH, developed by IHS Globl Isight, Ic.). However, becuse of the ture of the shred dtbses, the stte DOT hs to exert tremedous efforts to improve the ccurcy of the estimtios to mtch the locl observtios (e.g., truck couts, vehicle-miles of trvel (VMT), etc.). The clibrtio process is usully legthy d requires specilized techicl stffs to operte. I dditio, commercil freight dtbses (e.g., TRANSEARCH by Globl Isight, Ic.) re typiclly proprietry, ot vilble for public ccess. My smll sttes usully do ot hve sufficiet resources to coduct freight surveys or house techicl stffs to develop the freight demd model. My existig models overlook this compoet or simply ssume tht freight trips follow some behviorl mechism similr to psseger trips, i.e., truck trffic is estimted s fuctio of psseger-cr trffic (Ogde 1992). This could be potetil wekess of truck demd modelig i the sttewide model, where truck flow chrcteristics hve bee determied by other cotributig fcto such s loctio fcto (i.e., plces of productio d mrket), physicl fcto (i.e., wys tht goods c be trsported: i bulk, tk, flt bed, or refrigerted cotier), geogrphicl fcto (the loctio d desity of popultio my ifluece the distributio of ed products), d so o (Ortuzr d Willumse 2002). 2

Holguí d Thoo (2000) summrized differet wys tht could be used for modelig freight trsporttio demd d divided them ito two mjor modelig pproches: trip-bsed d commodity-bsed. For trip-bsed modelig pproch, the model hs three mjor compoets: trip geertio, trip distributio, d trffic ssigmet. The trip-bsed model does ot eed modl split step s it ssumes mode choice hs lredy bee selected. List et l. (2002), for istce, the trip-bsed modelig method is used to estimte truck O-D trip tble from prtil d frgmetry truck observtios i the New York regio. The mi dvtge of the trip-bsed modelig method is tht it typiclly requires less dt (i.e., oly truck trffic couts) to reproduce O-D mtrix. However, the trip-bsed modelig method teds to overlook the behviorl chrcteristics of commodity flows. Commodity-bsed modelig method, o the other hd, uses the commodity flows to estimte truck flows produced d ttrcted by ech zoe i the study re. Sorrtii d Smith (2000), for exmple, developed sttewide truck trip model usig commodity flow dt obtied from the commodity flow survey (CFS) d improve the estimtio usig the iput-output (I-O) ecoomic dt. Although the commodity-bsed models hve more dvtges th trip-bsed models, s they c cpture more ccurtely the fudmetl ecoomic mechisms of freight movemets, truck O-D trip tble estimted from this method ofte overlooks the o-freight truck trips (e.g., light commercil truck or empty truck trips). To fill this modelig gp, this reserch proposes two-stge pproch to estimte sttewide truck O-D trip tble. The proposed pproch is supported by two sequetil stges: stge oe estimtes the commodity-bsed truck O-D trip tble primrily derived from the commodity flow dtbse, d stge two dopts the cocept of pth flow estimtor (PFE) to refie the commodity-bsed truck O-D trip tble usig the observed truck couts. The proposed pproch uses the secodry dt sources vilble for public d reserch ccess such s the Freight Alysis Frmework (FAF) dtbse, sttewide trffic couts, d socioecoomic d ld use dt to estimte sttewide etwork truck trffic. A cse study usig the Uth sttewide freight trsporttio etwork is coducted to demostrte the pplictio of the proposed method. 1.3 Objective of the Study The gol of this reserch is to develop two-stge pproch for estimtig truck O-D trip tble usig both commodity flows d truck couts. The specific objectives of this reserch iclude the followig: Ivestigte d updte the sttewide truck dt from the followig dt sources: o Freight Alysis Frmework veio 3 (FAF3), ewly relesed tiol commodity O-D dtbse o The up-to-dte sttewide truck cout progrms o The Uth Sttewide Trvel Model (USTM) 3

Develop commodity-bsed truck trip tble from FAF3 for the stte of Uth Refie the commodity-bsed truck trip tble usig truck couts obtied from the sttewide truck cout progrm d the USTM. 1.4 Orgiztio of the Report The orgiztio of this report is summrized s follows: Sectio 2 reviews the reserch studies for estimtig the truck O-D trip tble d the sttewide freight demd modelig pproches. The review provides the bckgroud, fetures of the models, d potetil cpbilities for developig two-stge pproch for estimtig the truck O-D trip tble. Sectio 3 provides overview of the sttewide truck demd, icludig the freight trsporttio treds d the truck freight compoet i the Uth Sttewide Trvel Model (USTM). Sectio 4 describes the two-stge modelig pproch for estimtig truck O-D trip tble: (1) usig the commodity-bsed modelig techique d (2) usig the PFE techique to updte the results from the fit stge with the observed truck trffic couts. The solutio lgorithm for solvig the PFE is lso provided i this sectio. Sectio 5 demostrtes the cpbility of the two-stge pproch usig cse study i Uth. Numericl results s well s the pplictios to the Uth sttewide freight trsporttio etwork re summrized i this sectio. Sectio 6 cocludes this reserch project d provides some suggestios for future reserch. 4

2. LITERATURE REVIEW 2.1 Literture Review o Truck O-D Estimtio Holguí d Thoo (2000) summrized differet wys tht could be used for modelig freight demd d divided them ito two mjor modelig pltforms: (1) trip-bsed modelig d (2) commodity-bsed modelig. Figure 2.1 depicts the modelig of these two pproches. This sectio provides literture review bsed o these two modelig pproches. 2.1.1 Trip-bsed Modelig Approch For trip-bsed modelig pproch, the model hs three mjor compoets: trip geertio, trip distributio, d trffic ssigmet. The trip-bsed model begis with trip geertio. I this step, regressio models for trip productio d trip ttrctio re estimted i cojuctio with ld use d socio-ecoomic chrcteristics for ech trffic lysis zoes (TAZ). The ext step is trip distributio, which is ccomplished through sptil iterctio model (i.e., grvity model or growth fctor method). The lst step is to ssig the trip tble from the trip distributio step to the etwork. This trip-bsed modelig pproch is lso kow s three-step model s the mode choice hs bee lredy mde i the truck freight model. The curret prctice i estimtig truck trip tble is through the use of the truck trip rtes estimted i the Quick Respose Freight Mul (QRFM) II developed by Cmbridge Systemtics (2007). The QRFM provides truck trip geertio rtes bsed o the survey dt collected from Phoeix, Arizo. Usig trip rtes to reflect the trip-mkig propesity bsed o ld use cofigurtios is commo prctice, d provides ecoomicl d resoble estimte whe plig resources re limited. My reserche hve lso demostrted tht the estimtio of truck O-D trip tble could be chieved usig secodry dt sources bsed o the trip-bsed modelig pproch. 5

Trip-bsed Modelig Commodity-bsed Modelig Trip Geertio Commodity Geertio Trip Distributio Commodity Distributio Commodity Mode Split Vehicle Trip Estimtio Trffic Assigmet Trffic Assigmet Figure 2.1 Trip-bsed d commodity-bsed pproches (modified from Holguí-Vers d Thoo 2001) Tmi d Willumse (1989) itroduced three-step model to estimte freight demd from observed trffic cout dt. They used two types of grvity models i the trip distributio step: the grvity model d the grvity-opportuity model. They proposed the olier lest squre d mximum likelihood estimtio methods to esure tht the models estimte lik flows s close s possible to the observed dt. List d Turquist (1994) developed lier progrmmig (LP) method to sythesize the truck flow ptter from the observed truck couts o some liks d cordo lies. This LP method miimizes the weighted sum of the residul betwee the estimted d observed vlues usig fixed lik-use coefficiets for ech O-D pir from probbilistic pth ssigmet procedure. Lter, List et l. (2002) used similr techique to estimte lrge-scle truck O-D trip tble i the New York regio. The model ws implemeted i two-step process: the fit step estimtes the trip productio d trip ttrctio t ech TAZ; the secod step uses the lik-use coefficiets bsed o multi-pth trffic ssigmet procedure to estimte the truck O-D trip tble. Criic et l. (2001) used bi-level optimiztio progrm to djust the trget freight demd mtrix such tht the differeces betwee the observed d ssiged truck flows i the upper level re miimized. The lower level for this bi-level progrm is system optimum (SO) trffic ssigmet procedure. They implemeted the bi-level progrmmig method i the Strtegic Plig of Freight trsporttio (STAN) softwre, iterctive-grphic trsporttio plig pckge for multimodl multiproduct freight trsporttio. The mi dvtge of the trip-bsed modelig pproch is tht it typiclly requires less dt (i.e., oly truck trffic couts) with some existig plig dt (e.g., trip productio, trip ttrctio, prtil or full size of trget trip tble) to estimte O-D mtrix. However, the mi disdvtge of the trip-bsed 6

modelig pproch is tht it teds to overlook the behviorl chrcteristics of commodity flows i the urb d regiol models. Holguí-Vers et l. (2001) oted tht trip-bsed models hve limited rge of pplicbility to ccout for mjor chges of the study res such s chges i ld use d tht it could be difficult to model multimodl systems usig this modelig pproch. 2.1.2 Commodity-bsed Modelig Approch The commodity-bsed modelig pproch, o the other hd, uses the commodity flows to estimte truck flows produced d ttrcted by ech TAZ. I the Uited Sttes, the FAF estimtes commodity flows over the tiol highwy etworks, wterwys, d ril systems mog the sttes d regios. The curret veio of the FAF commodity O-D dtbse (FAF veio 3) provides estimtes of commodity flows by origi, destitio, d by mode for the bse yer 2007 d the forecst ye from 2010 to 2040 with five-yer itervl. Note tht the FAF commodity O-D dtbse ws developed usig the 2007 Commodity Flow Survey (CFS) d other public dt sources. To estimte truck demd from the CFS dt, the commodity flows i toge hve to be disggregted from the stte to the fier zol level such s TAZ by couty d the covert them to truck trips usig the truck pylod equivlet fctor (TPEF). Becuse the CFS dtbse is bsed o survey dt estblished through shipper-bsed survey, the commodity-bsed models c better cpture the fudmetl behviorl chrcteristics of commodity flows. Sorrtii d Smith (2000), for exmple, developed sttewide truck trip model usig the commodity flow dt obtied from the CFS dtbse d improved the estimtio usig the I-O ecoomic dt. A similr techique ws lso dopted by Fischer et l. (2005) for estimtig the hevy-duty truck O-D trip tble for the Souther Clifori Associtio of Govermet (SCAG) regio. The commodity-bsed modelig pproch is ofte used i sttewide d regiol prctices. Zhg et l. (2003), for istce, estimted the itermodl freight flow ptters of highwy, rilwy, d wterwy etworks for the stte of Mississippi usig the CFS dtbse d public domi dt. They further developed simultio model to ssess the freight opertios d the modl shift effect (i.e., from truck to itermodl brge/truck). Al-Bttieh d Kysi (2005) used geetic lgorithm (GA) procedure to fid the best O-D mtrix tht gives the miimum devitio betwee observed d estimted dt whe the O-D mtrix is ssiged to the etwork. Trip productio d trip ttrctio derived from the trip geertio step were lso used to preserve the sptil distributio of the commodity flow ptter. However, it is kow tht GA cot gurtee fidig the globl optimum. Stef et l. (2005) oted tht it my be difficult to obti the I-O dt for certi regiol d urb res. While the commodity-bsed models hve more dvtges th the trip-bsed models, s they c cpture more ccurtely the fudmetl ecoomic mechisms of freight movemets, truck O-D trip tble estimted from the commodity-bsed method ofte overlooks the ofreight truck trips (e.g., commercil truck or empty truck trips). Hybrid models hve bee developed to bridge the modelig gp of trip-bsed d commodity-bsed models. Holguí- Vers d Ptil (2008) developed multi-commodity O-D estimtio model tht combied two submodels: (1) commodity-bsed model d (2) complemetry model of empty truck trips. The fidigs of this study highlights the sigifict beefits of cosiderig empty truck trip model i the estimtio process s it c improve the bility to replicte the observed trffic couts. 7

The hybrid pproch ws lso dopted i the SCAG s truck demd model. Hybrid models forecst the iterl-iterl truck trips through the use of trip-bsed model d forecst the exterl truck trips through the use of commodity flow survey. Some of the truck freight demd modelig pproches, icludig trip-bsed, commodity-bsed, d hybrid models, re summrized i Tble 2.1. Tble 2.1 Freight demd modelig pproches, methods, d dt sources Autho List d Turquist (1994) Modelig pproches Trip-bsed Methods Lier progrmmig model Dt sources Observed truck couts for some liks d cordo lies Sorrtii d Smith (2000) I-O model CFS, TRANSEARCH List et l. (2002) Lier progrmmig model Observed truck couts for some liks d cordo lies Zhg et l. (2003) Plig d simultio models CFS, TRANSEARCH, itermodl dtbses Al-Bttieh d Kysi (2005) I-O model, Geetic Algorithm Commodity flows, observed truck couts Liedtke (2006), Wisetjidwt et l. (2006) Commoditybsed Microsimultio Fischer et l. (2005) Hybrid model Commodity flow surveys Shipper d receiver surveys (for iterl trips), commodity flow surveys (for exterl trips) Houlgui-Vers d Ptil (2008) Hybrid model, lest squre method Multi-commodity flows, estimted empty truck trips, observed truck couts Note: represets hybrid model 8

2.2 Literture Review o Truck O-D Estimtio Stte-of-the-prctice i truck freight modelig pproches c be clssified brodly ito the followig eight ctegories bsed o the objective, methodology, d dt requiremets: (1) likbsed fctorig method, (2) O-D fctorig method, (3) three-step truck model, (4) four-step commodity flow model, (5) ecoomic ctivity model, (6) hybrid model, (7) logistics/supply chi model, d (8) tour-bsed model (see detils d discussios i Fischer et l. 2005). 2.2.1 Lik-bsed Fctorig Method The lik-bsed fctorig method uses the growth fcto bsed o the historicl freight tred lysis or ecoomic growth forecsts for sclig the bse-yer lik volumes to obti the future-yer lik volumes. For istce, this method ws pplied i the Quick Respose Freight Mul II (Cmbridge Systemtics 2007). Though this method is simple d requires less dt to coduct the lysis, the drwbck of this method is the lck of behviorl bsis for modelig freight trffic. I some cses, it ssumes freight trips follow behviorl mechism similr to the psseger trips; tht is, truck trffic is estimted s fuctio of psseger-cr trffic (Ogde 1992). 2.2.2 O-D Fctorig Method The O-D fctorig method lso pplies the growth fcto to scle the bse-yer trip tble d ssigs the updted demd to the rod etwork. The bse-yer truck O-D trip tble is usully lyzed from some freight surveys such s the commodity flow dt (e.g., Commodity Flow Survey (CFS) by BTS, or privte freight dtbse such s the TRANSEARCH dtbse by IHS Globl Isight, Ic.). These dtbses typiclly chrcterize the commodity flows or log-hul truck trffic, but lck the detils of freight flows such s locl, service, d empty truck trips. 2.2.3 Three-step Truck Model The three-step truck model follows the trditiol trvel demd forecstig process, icludig trip geertio, trip distributio, d trffic ssigmet, without the modl split step. Mode choice is ssumed to hve lredy bee mde i the three-step truck model. The trip geertio step c be ccomplished usig trip geertio rtes or equtios bsed o the chrcteristics of the locl sites, icludig existig d forecst zol employmet d popultio dt, to geerte truck productios d ttrctios. The trip distributio step is the pplied to geerte truck O- D trip tble, d the trffic ssigmet step ssigs the truck O-D trip tble to the rod etwork. This method hs ofte bee criticized s it does ot cpture other possible modes d/or multimodl freight demd. 2.2.4 Four-step Commodity Flow Model The four-step commodity flow model follows similr structure s the trditiol four-step model for pssege. The commodity-bsed trip geertio model estimtes the toge commodity flows betwee origis d destitios bsed o the tiol or commercil freight dtbse (i.e., Freight Alysis Frmework (FAF) or TRANSEARCH by IHS Globl Isight, Ic.). The commodity flows re the disggregted to TAZ bsed o the couty s popultio d 9

employmet dt. The trip distributio step estimtes trip tble usig the grvity model. The modl split step ssumes tht the bse yer truck shre or truck proportio remis the sme i the future yer. The verge pylod fcto re further used to covert the dily commodity flows (i toge) to the dily truck trips. A ll-or-othig (AON) trffic ssigmet procedure is typiclly used to prelod the freight truck trffic by lloctig ll the truck trips from ech O-D pir to the shortest free-flow time pth, d user equilibrium (UE) trffic ssigmet procedure is the used to ssig the psseger trips. A multiclss trffic ssigmet procedure c lso be used to simulteously ssig both psseger d truck trips i the sttewide trvel demd model (e.g., the Florid Itermodl Sttewide Highwy Freight Model (FISHFM) d the Souther Clifori Associtios of Govermet (SCAG) model). Figure 2.2 provides grphicl illustrtio of the four-step commodity flow modelig process. Commodity Flow Dt, FAF, QFRM II Four-step freight forecstig process Figure 2.2 Four-step commodity flow modelig process Network Trffic Coditio Adpted from QFRM II (2008) 10

2.2.5 Ecoomic Activity Model The ecoomic ctivity model is lrgely drive by the ecoomic ctivity dt or existig ecoomic d ld-use models such s the sptil I-O model. The model uses the I-O structure to estimte the ecoomic reltioship betwee idustries d betwee idustries d households. Network flows re the derived d ggregted from these prticulr structures (see the Orego sttewide model s exmple). 2.2.6 Hybrid Model The hybrid model ttempts to bridge the gps betwee the commodity flow modelig techiques d freight truck modelig techiques. The commodity-bsed model hs some dvtges over the trip-bsed model s it c better cpture the fudmetl ecoomic mechisms of freight movemets; however, truck O-D trip tble estimted from this method ofte overlooks the ofreight truck trips (e.g., light commercil truck d/or empty truck trips) i urb res. The hybrid model typiclly dopts trip geertio model to compeste these udercouted truck trips bsed o the socio-ecoomic dt of ech TAZ, d uses trip distributio model (e.g., grvity model) to estimte the truck O-D trip tble. The model hs the flexibility to icorporte specil trip geerto (e.g., wrehouses, distributio cete, termils, etc.) d exterl trips obtied from dditiol freight surveys. 2.2.7 Logistics/Supply Chi Model The logistics/supply chi model combies the ecoomic I-O model with logistics model to form itegrted model. The ecoomic I-O model clcultes the supply-demd iterctios from differet ecoomic secto, while the logistics/supply chi model ssigs the goods to determie the sptil commodity flow ptter. Exmples of the logistics/supply chi model iclude the Strtegic Model for Itegrted Logistics Evlutio (SMILE) of the Dutch Miistry of Trsport d the GoodTrip model (Boerkmps 1999). 2.2.8 Tour-bsed Model The tour-bsed model follows the cocept of the ctivity-bsed model for psseger trvel demd modelig. It focuses o the tour chrcteristics of truck trips, especilly i the urb freight movemets. The tour-bsed model typiclly uses micro-simultio model to simulte the commodity flow movemets d ssess differet scerios of urb freight distributio (e.g., see Liedtke [2006]; Wisetjidwt et l. [2006]; de Jog d Be-Akiv [2007]; Ru et l. [2011]). This tour-bsed truck model combied with logistics/supply chi model hs bee developed for modelig the regiol freight etwork trffic i the Chicgo regio to ddress the preset wekesses idetified i the curret freight trvel demd forecstig models (i.e., lck of detiled iformtio bout freight delivery systems, log- d short-hul demds, d trip chi). Although this modelig pproch provides much fier resolutio of truck flows over time periods, this techique is dt demdig d computtiolly expesive. It is more suitble for ssessig truck opertios of urb freight trffic th strtegic plig of regiol freight trffic. 11

Tcticl & Opertio Strtegic Plig Figure 2.3 provides summry of the truck freight modelig pproches bsed o two metrics: modelig pltforms (i.e., trip-bsed or commodity-bsed methods) d pplictio horizos (i.e., strtegic plig, tcticl, d opertiol). As c be see, the ecoomic ctivity, logistics/supply chi, d tour-bsed models re more suitble for tcticl d opertiol pplictios, while the three-step, four-step, d hybrid models re ofte used for log-term strtegic plig pplictios. Note tht these tcticl d opertiol models typiclly require much more iput dt to cpture the detils of truck opertios i urb res. As result, these models require much more effort i the clibrtio d vlidtio processes. Trip-bsed Lik-bsed fctor Commodity-bsed O-D-bsed fctor Dt requiremet for modelig Low Three-step model Four-step model Hybrid model Ecoomic Activity model Logistics d Supply Chi model Tour-bsed Simultio model Figure 2.3 Truck freight demd modelig metrics High 12

3. STATEWIDE TRUCK DEMAND OVERVIEW 3.1 Freight Treds Demd of psseger d freight upo the tio s trsporttio etworks is expected to icrese sigifictly. Estimted d forecst totl freight volumes i FAF3 hve idicted stedy growth from yer 2007 to 2040. Freight volumes will icrese pproximtely 40% from 2007 to 2040 d the mjority of them will be trsported by trucks. This sectio provides overview of the freight trsporttio treds i the tio d i Uth. It should be oted tht FAF3 provides comprehesive tiol d stte-level estimtes d forecsts of freight flows coverig 131 freight lysis zoes, icludig 123 domestic regios d eight itertiol regios for import d exports (FHWA 2009). This prticulr dtbse is crucil compoet i our study s it will be used to develop commodity-bsed truck trip tble for the stte of Uth. 3.1.1 Ntiol Freight Trsporttio Treds This sectio provides iformtio bout the freight trsporttio treds from 2007 to 2040 i the Uited Sttes. Figure 3.1() shows the modl shre of freight shipmet by volume for the bse yer 2007. As c be see, the mjority of the freight shipmet mesured i volume (i toge) is crried out by trucks, followed by ril, pipelie, wter, d multiple mode, respectively. Trucks loe ccout for 74.69% i volume for domestic freight trsporttio, idictig the importce of truckig service for the tio s freight trsporttio d ecoomic developmet. Figure 3.1(b) depicts the domestic (DOM) freight trsporttio treds by percetges of mode shre i volume (millios of tos) d vlue (billios of doll) from 2007 to 2040. () Modl shre of freight shipmet by volume i 2007 (Ntiol) 13

Percetge Totl Toge (Millio of Tos) 100.00 90.00 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 74.69% 75.08% 74.63% 75.49% 76.04% 76.63% 77.34% 2010 2015 2020 2025 2030 2035 2040 Truck Ril Wter Air & Truck Multiple Modes & Mil Pipelie Other d Ukow Totl Toge 25,000 20,000 15,000 10,000 5,000 0 (b) Projectio of freight growth d mode shre by volume from 2007 to 2040 (Ntiol) Figure 3.1 Ntiol freight trsporttio treds As c be see, the projectio of freight growth is icresig stedily, d the tio s freight volumes re expected to icrese erly 37% from 2007 to 2040. This will pose chllege i cpcity plig to dequtely ddress freight demd, especilly the growig truck trffic o the tio s ifrstructure. 3.1.2 Uth Freight Trsporttio Treds I Uth, the demd for freight trsporttio, especilly truck, hs bee risig stedily d the forecst shows cotiuous growth t lest over the ext two decdes. Usig the FAF3 Domestic Dtbse, this sectio provides brief summry of the freight movemet treds for the stte of Uth. Tble 3.1 summrizes the modl shre of freight shipmets i Uth by volume d vlue for the bse yer 2007. 14

Tble 3.1 Modl shre of freight shipmet i Uth by volume i 2007 (uit: MTo) UT Other Sttes UT Withi UT Mode Other Sttes UT Itertiol Itertiol UT MTo % MTo % MTo % MTo % MTo % Truck 93.30 86.17 15.51 28.43 17.79 49.39 0.56 24.17 0.71 22.87 Ril 8.21 7.59 24.16 44.29 7.34 20.37 0.67 28.97 0.67 21.79 Air 0.00 0.00 0.02 0.03 0.03 0.09 0.00 0.10 0.00 0.03 Multiple modes 0.06 0.05 3.40 6.23 3.20 8.89 0.96 41.66 0.40 12.79 Pipelie 6.25 5.77 9.98 18.29 7.44 20.65 0.00 0.00 1.31 42.25 Other & ukow 0.46 0.42 1.49 2.73 0.22 0.61 0.12 5.11 0.01 0.29 Totl 108.28 100.00 54.56 100.00 36.01 100.00 2.31 100.00 3.10 100.00 The results idicte tht erly 200 millio tos of freight were moved from, to, d withi Uth i 2007. Specificlly, 108 millio tos were moved withi Uth, 55 millio tos were moved out of Uth, 36 millio tos were moved ito Uth, d 5.4 millio tos were itertiol freight. The vlue of these freight shipmets ws pproximtely $195 billio. Freight volume mesured i toge crried by truck ccouts for 64% of the modl shre by volume d 67% by vlue. The freight vlue trsported by truck ws bout $125 billio i 2007 d is expected to icrese to $291 billio by 2040. Figure 3.2 shows the modl shre of freight shipmets by volume for the bse yer 2007 i Uth. Similr to tiol level treds, the mjority of freight shipmets mesured i volume is crried out by trucks. The projectio of freight growth i Uth, show i Figure 3.3, ppe to icrese t fster rte th the tiol verge (i.e., erly 60% from 2007 to 2040). 15

Percetge Totl Toge (Millio of tos) Modl shre of freight shipmets by volume i 2007 (Uth) Figure 3.2 Uth freight trsporttio treds 100.00 90.00 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 63.67% 64.25% 64.93% 66.11% 67.37% 68.47% 69.57% 70.73% 2007 2010 2015 2020 2025 2030 2035 2040 350 300 250 200 150 100 50 0 Truck Ril Air (iclude truck-ir) Multiple modes & mil Pipelie Other d ukow Totl Toge Projectio of freight growth d mode shre by volume from 2007 to 2040 (Uth) Figure 3.3 Uth freight trsporttio treds (cot.) 16

3.1.3 Top 10 Commodity Flows i Uth I order to provide better udetdig of freight trsporttio demd i Uth, the top 10 commodity flows re described i this sectio. Tble 3.2 d Tble 3.3 provide summry of the top 10 commodities by volume d vlue i Uth for 2007 d 2040. These tbles idicte tht col d ometl mierl products re the top commodities by volume from 2007 to 2040. I 2040, precisio istrumets will become the top commodity by vlue. The top vlue commodity from Uth to other sttes is mixed freight d lso the top vlue commodity from other sttes to Uth for 2007 d 2040, respectively. For the shipmets withi Uth, the top vlue commodity is mchiery for 2007 d 2040. I dditio, the top volume commodity shipped from, to, d withi Uth remis to be ometl mierl products for 2007 d 2040. The highlighted commodities i these tbles re the commodities tht re lso the top commodities trsported by truck. Plese refer to Appedix A for the top commodities trsported by truck shipped from, to, d withi Uth. Tble 3.2 Top 10 commodities by volume i Uth for 2007 d 2040 Commodity 2007 (Millios of tos) Commodity 2040 (Millios of tos) Col 25.84 Nometl mi. prods. 35.48 Nometl mi. prods. 20.29 Col 34.23 Grvel 19.19 Grvel 26.82 Wste/scrp 15.90 Wste/scrp 21.94 Bsic chemicls 12.99 Col-.e.c. 18.59 Col-.e.c. 12.89 Mixed freight 16.06 Bse metls 10.12 Gsolie 15.24 Gsolie 10.11 Fuel oils 11.70 Crude petroleum 7.29 Bse metls 11.59 Fuel oils 7.19 Cerel gris 11.43 Note: Commodities re sorted by volume.e.c. = ot elsewhere clssified. Highlighted commodities re lso top commodities trsported by truck 17

Tble 3.3 Top 10 commodities by vlue i Uth for 2007 d 2040 Commodity 2007 (Billios of doll) Commodity 2040 (Billios of doll) Bse metls 20.64 Precisio istrumets 123.04 Mchiery 16.25 Phrmceuticls 46.01 Mixed freight 14.46 Mixed freight 40.15 Misc. mfg. prods. 10.67 Misc. mufcture prods. 34.69 Phrmceuticls 9.65 Bse metls 34.24 Electroics 8.53 Mchiery 33.35 Motorized vehicles 8.13 Electroics 27.08 Articles-bsed metl 7.51 Textiles/lether 18.75 Other foodstuffs 7.40 Motorized vehicles 18.04 Textiles/lether 7.00 Other foodstuffs 16.79 Note: Commodities re sorted by vlue Highlighted commodities re lso top commodities trsported by truck 3.2 Uth Sttewide Trvel Model (USTM): Freight Compoet 3.2.1 USTM Overview The USTM ws coducted i 2008 by the Uth Deprtmet of Trsporttio (UDOT) s cosultt tem (i.e., Wilbur Smith Assocites (WSA) i coopertio with Resource Systems Group (RSG), Ic.). The mi objective of the USTM is to forecst future trffic o Uth s stte d itette fcilities bsed o rodwy cpcity d socio-ecoomic projectio to support strtegic plig d ivestmet mgemet t the stte level. The USTM frmework is depicted i Figure 3.4. The cosultt tem hve solicited iputs from locl trsporttio plig models (i.e., metropolit plig orgiztio (MPO) models) d tiol models icludig log distce psseger d commodity-bsed truck freight demd models. The study re cosists of 29 couties d four MPOs. 18

Figure 3.4 USTM frmework The MPOs i Uth cosist of Cche, Dixie, Mouti Associtio of Govermet (MAG), d Wstch Frot Regiol Coucil (WFRC). The iterl TAZs outside the four MPOs d rurl plig orgiztios (RPOs) were creted by ggregtig the cesus blocks bsed o rod etwork detils, cesus plce boudries tht outlie popultio cete, couty boudries, d mjor ttrctio res (Wilbur Smith Assocites i coopertio with Resource Systems Group, Ic. 2009). The USTM trsporttio etwork cosists of 23,532 odes d 31,630 liks, excludig 8,098 cetroid coecto d 3,464 iterl d 27 exterl TAZs. The etwork lik free-flow speeds d cpcities re clculted bsed o the WFRC/MAG models s fuctio of the umber of les, fcility type, d re type. Lik cpcities re expressed i level of service (LOS) E i vehicle/hour/le. The trip geertio models for ll iterl trips i Uth re estimted icludig trip eds withi WFRC/MAG d Cche MPOs. The trip productio flows re estimted usig two-wy cross clssifictio model, d the trip ttrctio flows re estimted usig regressio models. The exterl psseger movemets dopted tiol trip tble from the Ntiowide Peol Trsporttio Survey (NPTS). The exterl truck flows re estimted usig the FAF dtbse, while the iterl truck flows re estimted from the clibrted regressio models, similr to the QFRM trip rtes. The detils of freight models i USTM re explied i the ext subsectio. The trip distributio model uses grvity model pproch d the frictio fcto re clibrted for ech trip purpose. The frictio fcto for truck purpose re clibrted bsed o trvel distce. Trffic ssigmet i USTM is simulteous multi-clss user equilibrium model. Differet truck clsses (i.e., commercil, sigle, multiple uits) re coverted to psseger c usig psseger cr equivlet (PCE) fcto. It should be oted tht the high-occupt vehicle 19

(HOV) d sigle-occupt vehicle (SOV) trip tbles re distiguished i the WFRC/MAG trip tbles. 3.2.2 USTM Freight Model The developmet of the USTM freight model mkes use of the TRANSEARCH dtbse to lyze the curret d projected future freight movemets i Uth s rod ifrstructure. The primry freight corrido or truck routes re depicted i Figure 3.5, d iclude I-15, I-70, I-80, U.S. 6, U.S. 89, U.S. 191, d U.S. 40. As c be see, I-15 is the mjor orth/south itette d is lso prt of the North Americ Free Trde Act (NAFTA) CANAMEX corridor likig betwee Cd d Mexico through the Uited Sttes. I-80 d I-70 re two of the primry itettes for est/west trvel, both of which hve hevy truck trffic volumes. The results from the USTM freight report idicted tht Los Ageles is the origi of most freight trips pssig through Uth. Other mjor origis d destitios re cities i Clifori, New York, d the Midwest. Figure 3.5 Uth mjor freight corrido Source: USTM Uth Freight Plig Report (2010) 20

The iterl trip geertio models dopted trip rte prmete from QFRM to ddress three types of vehicles, icludig 1) Commercil (COMM), 2) Sigle Uit (SU), d 3) Multiple Uit (MU). The trip geertio prmete were further clibrted i the feedbck loop util the estimted sttewide vehicle-mile of trvel (VMT) d the observed VMT were withi cceptble tolerce. Tble 3.4 summrizes the trip geertio prmete from QFRM. Tble 3.5 d Tble 3.6 show the clibrted trip rtes for urb d rurl res obtied from the fil itertio i the USTM. The socio-ecoomic dt, icludig umber of households, retil, bsic, service, d griculturl employmet, of ech freight lysis zoe re the mjor iput dt for clcultig iterl truck trips. The prmete i Tble 3.5 d Tble 3.6 re lower th the oes i Tble 3.4. This idictes tht the borrowed trip rtes from QFRM could overestimte the iterl truck trips i Uth, d suggests the eed to clibrte these trip rtes for their ow sttes. Tble 3.4 Iterl truck trip rtes (QFRM) Trip Geertio Prmete - QRFM Truck type Households Retil Bsic Service Agriculture Commercil 0.251 0.888 0.938 0.437 1.11 Sigle-uit 0.099 0.253 0.242 0.068 0.289 Multi-uit 0.038 0.065 0.104 0.009 0.174 Tble 3.5 Iterl truck trip rte (Urb) Trip Geertio Prmete - Urb Truck type Households Retil Bsic Service Agriculture Commercil 0.03765 0.1332 0.1407 0.06555 0.1665 Sigle-uit 0.0495 0.1265 0.121 0.034 0.1445 Multi-uit 0.0152 0.026 0.0416 0.0036 0.0696 Tble 3.6 Iterl truck trip rte (Rurl) Trip Geertio Prmete - Rurl Truck type Households Retil Bsic Service Agriculture Commercil 0.0502 0.1776 0.1876 0.0874 0.222 Sigle-uit 0.05445 0.13915 0.1331 0.0374 0.15895 Multi-uit 0.0152 0.026 0.0416 0.0036 0.0696 21

4. A TWO-STAGE APPROACH FOR ESTIMATING TRUCK TRIP TABLE This sectio describes the two-stge pproch for estimtig sttewide truck trip tble. Figure 4.1 depicts coceptul frmework of the two-stge pproch. The fit stge uses tiol commodity flow dt from the Freight Alysis Frmework Veio 3 (FAF 3 ) dtbse to develop commodity-bsed truck trip tble. The secod stge uses the pth flow estimtor (PFE) cocept to refie the truck trip tble obtied from the fit stge usig the truck couts from the sttewide truck cout progrm. Detils of these two stges re described i the followig sectios. Stge 1: Estimte Commodity-Bsed Truck O-D Trip Tble Stge 2: Updte Truck O-D Trip Tble Usig Pth Flow Estimtor Required Iput Dt FAF Dtbse Extrct Truck Flows by weight from FAF Dtbse Distribute Truck Flows to Iterl d Exterl Zoes Sttewide Truck Coutig Progrm Specil Geerto for Commercil d Empty Trucks Estimte Locl & Commercil Trucks s specil geerto Freight Trsporttio Network Observed Truck Trffic Couts Disggregte Truck Flows to Couty-Level Estimte Empty Trucks Pth Flow Estimtor Covert Truck Flows to Truck Trips Commodity-Bsed Truck O-D Trip Tble Figure 4.1 Coceptul frmework of the two-stge pproch Refied Truck O-D Trip Tble 4.1 Stge 1: Develop Commodity-Bsed Truck O-D Trip Tble Stge 1 is to develop simplified procedure, depicted i Figure 4.2, for estimtig truck O-D trip tble from the FAF commodity flow dtbse. It mily cosists of four steps: 1) extrct truck flows by weight from FAF dtbse, 2) distribute truck flows to iterl d exterl zoes, 3) disggregte truck flows to the couty level, d 4) covert truck flows to truck trips. The steps re briefly explied s follows: 22

FAF 3 Dt Itertiol Dt (SEA) Domestic Dt (DOM) Border Dt (BRD) Domestic Ntiol Truck Commodity Flow Dt (KTo) Subre Alysis Techique Seprtig Study Are from Ntiol Network Subre Alysis Disggregte Model Disggregtio Techique Proportioig CoutybsedTruck Flows Bsed o Socioecoomic Fcto Couty d Exterl Truck Commodity Flow Dt (KTo) Truck Movemets (Dily Truck Trips) Itrstte (I-I), Productio (I-E), Attrctio (E-I), Through (E-E) Coveio to Dily Truck Trips To to Truck Coveio Covertig Aul to Dily Truck Flows Usig Dt from VIUS d HCM Dt Figure 4.2 A simplified procedure for estimtig the truck O-D trip tble from commodity flows (1) Extrct Truck Flows by Weight from FAF Dtbse The fit step is to extrct truck flows from the FAF commodity flow dtbse. It should be oted tht the FAF3 commodity dtbse c be publicly ccessed from the Freight Mgemet d Opertios Dtbse website 1. It cosists of three mjor dtbses: 1) DOM dtbse: the commodity flows betwee domestic origis d domestic destitios, 2) BRD dtbse: the commodity flows by ld from Cd d Mexico to domestic destitios vi ports of etry o the U.S. border d vice ve, d 3) SEA dtbse: the commodity flows by wter from ovees origis vi ports of etry to domestic destitios d vice ve. The commodity flows re clssified bsed o the Stdrd Clssifictio of Trsported Goods (SCTG). Detils of the SCTG re foud i Appedix A. The mesuremet uits of the commodity flow dtbse re i uits of thousds of tos (KT) d millios of doll (MDOL). The DOM truck flows were 1 Avilble t: http://ops.fhw.dot.gov/freight/freight_lysis/ff/idex.htm 23

extrcted from the FAF dtbse d the outputs of this step re truck flows by weight i uits of thousd tos (kto). (2) Distribute Truck Flows to Iterl d Exterl Zoes This step requires qutifyig four types of truck flows, which re: 1) truck flows withi Uth (Iterl-Iterl [I-I]) 2) truck flows from Uth to other sttes (Iterl-Exterl [I-E]) or productio flows 3) truck flows from other sttes to Uth (Exterl-Iterl [E-I]) or ttrctio flows 4) through truck flows ([E-E]) The results of I-I, I-E, d E-I truck flows re provided i Appedix B. Figure 4.3() depicts the FAF3 etwork tht ws origilly obtied from the Ntiol Highwy Plig Network (NHPN). As prt of the NHPN, the Uth etwork for freight lysis cosists of 2,430 liks, 34 exterl sttios i two FAF zoes. It should be oted tht the FAF dtbse does ot provide eough iformtio to estimte the through truck flows (E-E). I order to estimte the through truck flows for the stte of Uth from the DOM dtbse, pre-processig techique clled Subre Alysis ws implemeted i CUBE, trsporttio plig softwre by Citilbs. This step distributes the commodity flows mog 131 FAF zoes. () FAF etwork d 131 freight lysis zoes (UT is highlighted) 24

E-E I-84 ID WY I-80 Exterl Sttios I-80 Slt Lke City NV I-I CO I-70 E-I I-E I-15 AZ (b) Four types of truck flows d exterl sttios NM Figure 4.3 FAF etwork, freight lysis zoes, d four types of truck flows i Uth (3) Disggregte Truck Flows to the Couty Level The ext step is to disggregte the truck flows from the stte level to the couty level usig popultio d employmet iformtio of ech couty. Note tht employmet d popultio re the most commo disggregtio fcto, d this iformtio c be obtied from stte govermet orgiztios, e.g., Uth Goveror s Office of Plig d Budget (GOPB) for popultio d Uth Deprtmet of Work Force Services for employmet i this study (U.S. Bureu of Ecoomic Alysis, Uth Deprtmet of Work Force Services 2000). The disggregte fctor of employmet is used for truck trip productio, while the disggregte fctor of popultio is used for truck trip ttrctio. These fcto re clculted s follows: O c C c1 Emp c Emp c, (4.1) 25

D c C c1 Pop c Pop c, (4.2) where Oc is the disggregtio fctor for truck productio flows t couty c; Dc is the disggregtio fctor for truck ttrctio flows t couty c; Empc is the employmet rte of couty c; Popc is the popultio rte of couty c, d C is the umber of couties i Uth. (4) Covert Truck Flows to Truck Trips The lst step is to covert truck flows to truck trips usig the truck pylod equivlet fctor (TPEF). Note tht the TPEF is computed bsed o the truck weight dt obtied from the Federl Vehicle Ivetory d User Survey (VIUS) dt (Office of Freight Mgemet d Opertios, FHWA 2007), Weigh-I-Motio (WIM), d Port of Etry (POE) sttios i Uth. The result idictes tht the TPEF for Uth is 41,196 lbs/vehicle or 20.6 tos/vehicle. This umber is withi resoble rge compred with the empiricl studies i other sttes (e.g., 16.07 tos/vehicle for Ohio (Cmbridge Systemtics 2002), 24.00 tos/vehicle for Wiscosi (Wiscosi Deprtmet of Trsporttio 1995), d 25.77 tos/vehicle for Texs (Cmbridge Systemtics 2004). Note tht the TPEF computed bove is the me pylod for ll commodities d truck types. The TPEF c be further lyzed to better cpture the commodity d truck body types s suggested by the Ok Ridge Ntiol Lbortory (2011). The coveio equtio is expressed s follows: J I J K ijk Yj Xi j1 i1 j1 k1 ijk (4.3) where Yj is the umber of trucks i group j (i.e., sigle uit, truck triler, combitio semitriler, combitio double, combitio triple; J = 5); Xi is the toge of commodity i (i.e., clssified usig SCTG; I = 43); ijk is the frctio of commodity i moved by group j with body type k (i.e., dry v, flt bed, bulk, reefer, tk, loggig, livestock, utomobile, other; K = 9); d ijk is the TPEF of group j with body type k trsportig commodity i. I the fil step, the umber of workig dys per yer for truck opertios from the Highwy Cpcity Mul (HCM) (Trsporttio Reserch Bord 2000) (i.e., 300 workdys per yer) is used to covert the ul truck flows to dily truck flows 4.2 Commercil d Empty Truck Demd Estimtio 4.2.1 Commercil Truck Demd Estimtio It hs bee oted tht estimtig truck O-D trip tble from the commodity flows ofte uderestimtes the locl truck trips such s the light commercil d empty truck trips. I the USTM, the locl truck flows re domited by the itr-couty flows t the couty level. The results idicte tht locl truck movemets re cocetrted betwee Ogde d Provo, log the 26

I-15 corridor i Slt Lke City. Locl trffic o U.S. 6 d U.S. 89 is projected to icrese substtilly by 2040, while trffic o I-80 shows slight decrese. This shows the sigifict role of locl truck trffic for estimtig sttewide freight movemets. Thus, i this study, we dopt the commercil truck trip geertio model to estimte the locl d commercil trucks s follows: O y y y y y comm griculture griculture bsic bsic rtil retil office office household household r r r r r r where d office y r comm O r is the productio flows of origi r for commercil truck; griculture y r,, (4.4) bsic y r, retil y r, re the employmet rtes for griculture, bsic (e.g., mufcturig, trsporttio, wholesle, d utilities), retil, d office, respectively; d griculture household y r is the umber of households i origi r. The clibrted coefficiets (,,,, ) were borrowed from the USTM (i.e., (0.166, 0.141, 0.133, 0.065, 0.038) for urb re, d (0.050, 0.222, 0.133, 0.065, 0.038) for rurl re). Plese refer to Tble 3.5 d Tble 3.6 for detils. The ttrctio flows of destitio s ( ) for commercil truck re ssumed to be the sme s the productio flows. comm D s 4.2.2 Empty Truck Demd Estimtio bsic rtil office household The empty truck trips re estimted usig the Holguí-Vers d Thoo (HV-T) model developed by Holgui-Vers et l. (2010). The empty truck trip model ws developed usig the destitio choice probbility fuctios expressed s fuctio of trip distce d the mgitude of opposig commodity flows. The probbility fuctios for empty truck trips goig from origi r to destitio s d returig empty re summrized i Tble 4.1. I this study, we selected the logit probbility (model umber 2 i Tble 4.1) for estimtig the totl truck trips from r to s with cosidertio of both loded d empty trips s follows: Ez ( ) loded z Ez ( ) 1 l z e ze rl d drl, (4.5) where loded z re the loded truck trips betwee (r, s); is the coveio fctor or the verge pylod (tos/trip) for the loded trips obtied from Eq. (4.3); z re the commodity flows betwee (r, s); is prmeter determied empiriclly from the observed dt; d d is the returig distce betwee (r, s). 27

Tble 4.1 Destitio choice probbility fuctios for empty truck trips Probbility fuctios Vribles Ps () l z z rl HV-T 1: Commodity flows betwee origi r d destitio s: z Ps () l z e ze rl d drl HV-T 2: Commodity flows betwee origi r d destitio s: distce betwee origi r d destitio s: d z ; () Ps l z d zd rl rl HV-T 3: Commodity flows betwee origi r d destitio s: distce betwee origi r d destitio s: d z ; Ps () z ( d d ) l hr z ( d d ) rl rl hr HV-T 4 (trip chi): Commodity flows betwee origi r d destitio s: z ; distce betwee origi h d destitio r : distce betwee origi r d destitio s: d. d hr ; 4.3 Stge 2: PFE Formultio, Optimlity Coditios, d Solutio Algorithm 4.3.1 Bckgroud d Formultio This stge uses the optimiztio pproch to refie the commodity-bsed truck O-D trip tble obtied from the fit stge. The bsic ide is to use the cocept of Pth Flow Estimtor (PFE) to estimte pth flows tht c reproduce the observed lik couts d flows o other sptil levels. PFE is cpble of estimtig pth flows d pth trvel times usig oly trffic couts from subset of etwork liks. PFE ws origilly developed by Bell d Shields (1995) d further ehced by Che et l. (2005). Herefter, the followig ottio i Tble 4.2 is cosidered. 28

Tble 4.2 Nottio for the PFE model Nottio Descriptio Set of Vribles : Set of etwork liks with truck couts M U A R S : Set of etwork liks without truck couts : Set of ll etwork liks A=M U : Set of origis : Set of destitios RS : Set of O-D pi K : Set of pths coectig origi r d destitio s : Set of origis with commodity-bsed dt : Set of destitios with commodity-bsed dt RS : Set of trget (or prior) O-D pi Iput Vribles d Prmete : Observed truck volume o lik R S v C O r D s z F r s t () k f k x P r A s q, : Cpcity of lik : Commodity-bsed truck trip productio of origi r : Commodity-bsed truck trip ttrctio of destitio s : Commodity-bsed O-D flows betwee origi r d destitio s : Trget totl demd : Percetge mesuremet error llowed for truck cout o lik : Percetge mesuremet error llowed for truck trip productio of origi r : Percetge mesuremet error llowed for truck trip ttrctio of destitio s : Percetge mesuremet error llowed for the commodity-bsed O-D demds betwee origi r d destitio s : Percetge mesuremet error llowed for the trget totl demd : Dispeio prmeter i the logit model : Truck trvel time o lik : Pth-lik idictor, 1 if lik is o pth k betwee O-D pir d 0 otherwise : Flow o pth k coectig O-D pir : Estimted truck trffic volume o lik : Estimted truck trip productio of origi r : Estimted truck trip ttrctio of destitio s : Estimted truck O-D flows betwee origi r d destitio s : Prmete for BPR lik cost fuctio The core compoet of PFE is logit-bsed pth choice model i which the perceptio erro of pth trvel times re ssumed to be idepedetly d ideticlly Gumbel vrites. The logit model itercts with lik cost fuctios to produce stochstic user equilibrium (SUE) trffic ptter. It should be oted tht the SUE trffic ssigmet procedure ws lso implemeted to estimte the freight flows i the FAF veio 3 (plese refer to Chpter 5 of FAF3 report [FHWA 2009]). The im of this stge is to dpt the PFE to tke ot oly truck trffic couts but lso the 29

vilble freight plig dt (i.e., truck productio d ttrctio flows) to updte the commodity-bsed truck O-D trip tble. PFE requires trffic cout dt to estimte the sttewide truck O-D trip tble while the plig dt re optiol iputs i this process. However, the commodity-bsed truck O-D trip tble obtied from the fit stge c ehce the observbility of the O-D estimtio problem s well s preservig the sptil commodity flow ptter i the study re. Mi Z= s.t. x 1 t ( ) dw fk l fk A 0 RS kk (1 ) v x (1 ) v, M, x, U, C (1 ) z q (1 ) z, RS, (1 ) O P (1 ) O, r R, r r r r r (1 ) D A (1 ) D, s S, s s s s s (1- ) F T (1 ) F, f 0, k K, RS, k where x f, A, k k RS kk q f, RS, kk k P f, r R, r ss kk A f, s S, T s rr kk RS kk f k k k, (4.6) (4.7) (4.8) (4.9) (4.10) (4.11) (4.12) (4.13) (4.14) (4.15) (4.16) (4.17) (4.18) Objective fuctio i Eq. (4.6) hs two terms: user equilibrium term d etropy term. The etropy term seeks to spred trips oto multiple pths ccordig to the dispeio prmeter, while the user equilibrium term teds to cluster trips o the miimum cost pths. As opposed to the trditiol logit-bsed SUE model, PFE fids pth flows tht miimize the SUE objective fuctio while simulteously reproducig truck trffic couts o ll observed liks i Eq. (4.7), commodity-bsed demds of certi O-D pi i Eq. (4.9), truck productio d ttrctio of certi origi d destitio i Eqs. (4.10) d (4.11), d totl demd i Eq. (4.12) withi some predefied error bouds. These error bouds re essetilly cofidece levels of the observed dt t differet sptil levels used to costri the pth flow estimtio. More relible dt will use smller error boud (or tolerce) to costri the estimted flow withi rrower rge, while less relible dt will use lrger tolerce to llow for lrger rge of the estimted flow. For the uobserved liks, the estimted flows cot exceed their respective 30

cpcities, s idicted by Eq. (4.8). Eq. (4.13) costris the pth flows to be o-egtivity, while Eqs. (4.14)-(4.18) re defiitiol costrits tht sum up the estimted pth flows to obti the lik flows, O-D flows, zol productio flows, zol ttrctio flows, d totl demd, respectively. 4.3.2 Optimlity Coditios The Lgrgi fuctio of the bove PFE formultio d its fit prtil derivtives with respect to the pth-flow vribles c be expressed s follows. + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η, ψ, ψ ) Z u v 1 fk k M RS kk 1 k k k k M RS kk U RS kk RS u v f d C f o z 1 f k kk o z 1 fk RS kk P f P f 1 1 r r r k r r r k rr ss kk rr ss kk A f A f 1 1 s s s k s s s k ss rr kk ss rr kk T1 fk T1 fk RS kk RS kk (4.19) where u, u, d, o, o, r, r, s, s,, d (4.7), (4.8), (4.9), (4.10), (4.11), d (4.12) respectively. The vlues of re restricted to be o-positive, while the vlue of oegtive; u re the dul vribles of costrits, o, r, s u, d, o, r, d must be, s, d u d u c be viewed s the correctios i the lik cost fuctio, which brig the estimted pth flows ito greemet with the observed lik volumes; similrly, s, s,, d c be iterpreted s correctios to the O-D trvel times, zol productio ttrctiveess, zol ttrctio ttrctiveess, d totl demd ttrctiveess, respectively, tht c be used to steer the estimted pth flow ptter to withi the O-D itervl costrits specified by Eqs. (4.9), (4.10), (4.11), d (4.12). These dul vribles re zero if the estimted lik flows, O-D flows, zol productio flows, zol ttrctio flows, d totl demd re withi cceptble rge defied by the mesuremet error boud, d o-zero if they re bidig t oe of the limits. is relted to the lik queuig dely whe the estimted lik flow reches its cpcity (Bell d Iid 1997). Additiolly, the followig reltio must hold. d o, o, r, r, 31

+ - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ, ψ ) fk 0, k K, RS f u u d o o k + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ, ψ ) 0, M u + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η, ψ,ψ ) 0, M u + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ, ψ ) 0, U d + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ, ψ ) 0, RS o + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ, ψ ) 0, RS o + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ, ψ ) r 0, r R r + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ, ψ ) r 0, r R r + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η, ψ,ψ ) s 0, s S s + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) s 0, s S s + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η, ψ,ψ ) 0, + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η, ψ,ψ ) 0 fk k 1 l ( ) fk t x k uk uk dk A M M U 0, K, RS o o r r s s (4.20) (4.21) Sice lwys f 0, k K, RS, i the logit-bsed SUE model, k 1 l ( ) fk t x k uk uk dk A M M U 0 o o r r s s (4.22) 32

For u + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) 0, M u v 1 fk k 0 v 1 x, if u 0 RS kk v 1 fk k 0 v 1 x, if u 0 RS kk : (4.23) For u + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) 0, M u v 1 fk k 0 v 1 x, if u 0 RS kk v 1 fk k 0 v 1 x, if u 0 RS kk : (4.24) For d + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) 0, U : d C fk k 0 C x, if d 0 RS kk C fk k 0 C x, if d 0 RS kk (4.25) For o + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) 0, RS o z 1 fk 0 z 1 q, if o 0 kk z 1 fk 0 z 1 q, if o 0 kk : (4.26) For o + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) 0, RS : o z 1 fk 0 z 1 q, if o 0 kk z 1 fk 0 z 1 q, if o 0 kk (4.27) 33

For + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) r 0, r R r Pr 1 r fk 0 Pr 1 r Or, if r 0 ss kk Pr 1 r fk 0 Pr 1 r Or, if r 0 ss kk : (4.28) For + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) r 0, r R r Pr 1 r fk 0 Pr 1 r Or, if r 0 ss kk Pr 1 r fk 0 Pr 1 r Or, if r 0 ss kk : (4.29) + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) For s 0, s S : s Ar 1 s fk 0 As 1 s Ds, if s 0 rr kk Ar 1 s fk 0 As 1 s Ds, if s 0 rr kk (4.30) For + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) s 0, s S s Ar 1 s fk 0 As 1 s Ds, if s 0 rr kk Ar 1 s fk 0 As 1 s Ds, if s 0 rr kk : (4.31) For + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) 0 F 1 f 0 F 1 T, if 0 k RS kk F fk F T if RS kk 1 0 1, 0 : (4.32) 34

For + - + - - + - + - + L( f, u, u, d, o, o,ρ,ρ, η, η,ψ,ψ ) 0 F 1 f 0 F 1 T, if 0 k RS kk F fk F T if RS kk 1 0 1, 0 : (4.33) Let the geerlized route cost c c u u d o o k k k k r r s s M U where ( c k = A t ( x ) k ). Rerrge the Equtio (4.21) d obti:, (4.34) k f exp c, k K, RS k (4.35) Hece, the route choice probbility fuctio c be expressed s follows: kk kk exp f c k k Pk, k K, RS f exp c k k (4.36) Similr to the logit-bsed SUE model, pth flows from PFE c be derived lyticlly s fuctio of pth costs d dul vribles ssocited with costrits (4.7)-(4.12) s follows: c u u d f k o o r r s s k k k exp M U k K, RS (4.37) 35

4.3.3 Uiqueess Coditios We proceed to the secod-order coditio to show the uiqueess of pth-flow solutio. Differetitig equtio (4.21) by the pth flow vrible gives the followig: c 1 2 k od L if fk f l fk fk, k K, l K, RS, od RS od fk fl 0 otherwise (4.38) Equtio (4.35) idictes tht ll digol elemets re positive (i.e., c f k k 0, 0, d fk 0 ) d ll off-digols re zero. I other words, the Hessi mtrix with respect to O-D pir is 2 L f f k l c1 1 0 0 f1 f1 c2 1 0 0 f2 f2 0 0 ck 1 fk f k (4.39) c f k k Sice the digol elemets of the block mtrix with respect to O-D pir re equl to 1 f k, the mtrix 2 f is positive defiite for ll O-D pir. Hece, objective fuctio (4.6) is strictly covex with respect to pth flows; therefore, the pth-flow solutio is uique. 36

4.3.4 Solutio Procedure The overll solutio procedure for solvig the PFE formultio is provided i Figure 4.4. Iitiliztio Set =0 Iitil Priml Vribles: fd x 0 Iitil Dul Vribles: u,d,ο, η, d ψ 0 =+1 Updte Lik Cost usig Dul Vrible 1 t t x u u d 1 1 1 Set 0 Itertive Blcig u,d,ο,η, ψ Set Dul Vribles: d 0 Updte Priml Vribles : Updte Dul Vribles : 1 f u, d, ο, η, ψ d d x Colum Geertio (Pth Geertio) Determie the Shortest Pth: Updte Workig Pth Set: 1 K K k k Divergece =+1 Covergece Test Covergece 1 Pth Flows : Lik Flows : x fk k, A, RS kk O-D Demd : q fk, RS kk Figure 4.2 PFE solutio procedure Output f, k K, RS Productio Flows : k Attrctio Flows : Totl Demd : P f, r R r ss kk A f, s S T s rr kk RS kk k k f k (1) Itertive blcig scheme The sectio describes the detiled steps of the itertive blcig scheme. Step 1. Iitiliztio 1.1 Set = 0, 1.2 Set dul vribles: u u d r r s s d Step 2. Compute priml vribles,,,,,,, 0, 37

. Compute pth costs k k A c t x b. Compute pth flows f k k k c u u d o k K M U exp k, c. Compute lik flows k k RS kk x f, A o r r s s d. Compute zol productio d ttrctio flows P f, r R r ss kk A f, s S s rr kk e. Compute O-D flows kk k q f, RS f. Compute totl demd T fk k RS kk Step 3. Updte dul vribles k. For ech mesured lik ( M ), updte the dul vribles u Mx 0, u 1 1 (1 ) v l x u Mi 0, u 1 1 (1 ) v l x, d. RS 38

39 b. For ech umesured lik ( U ), updte the dul vribles 1 1 Mi 0, l C d d x. c. For ech trget O-D flow ( RS), updte the dul vribles 1 (1 ) 1 Mx 0, l z o o q, d 1 (1 ) 1 Mi 0, l z o o q. d. For ech zol productio flow (r R ), updte the dul vribles 1 (1 ) 1 Mx 0, l r r r r r O P, d 1 (1 ) 1 Mi 0, l r r r r r O P. e. For ech zol ttrctio flow (s S), updte the dul vribles 1 (1 ) 1 Mx 0, l s s s s s D A, d 1 (1 ) 1 Mi 0, l s s s s s D A. f. For the totl demd, updte the dul vribles 1 1 (1 ) Mx 0, l F T, d 1 1 (1 ) Mi 0, l F T.

Step 4. Covergece test u u u u d d o o 1 1 1 1,,,, 1 1 1 1 If η0 Mx o o, r r, r r, s s, η 1 1 1 s s,, where η 0 is covergece tolerce (e.g., 10-6 ) d is the upper limit of chge i dul vribles, the set ll prmete of the ext itertio equl to those of the curret itertio, set, d go to step 2. u u u u d d o o 1 1 1 1,,,, 1 1 1 1 If Mx o o, r r, r r, s s, η 1 1 1 s s,, the set ll prmete of the ext outer itertio equl to those of the curret itertio, set = + 1, d termite the ier loop (itertive blcig). I the bove procedure, we just provide the djustmet equtios for differet types of costrit (e.g., observed liks, uobserved liks, observed iteectios, trget O-D flows, etc.). The detiled derivtios of the djustmet equtios c be foud i Che et l. (2009, 2010), d covergece of the itertive blcig scheme is discussed i detils i Bell et l. (1997) d Bell d Iid (1997). (2) Colum geertio The bove itertive blcig scheme ssumes tht workig pth set is give. For lrge etworks, it is ot prcticl to eumerte workig pth set i dvce sice the umber of possible pths grows expoetilly with respect to etwork size. To circumvet pth eumertio, colum (or pth) geertio procedure c be ugmeted to the itertive blcig scheme. Bsiclly, the lgorithm itroduces outer loop (or itertio) to itertively geerte pths to the workig pth set s eeded to replicte the observed itervl costrits (e.g., lik couts, turig movemet couts, selected prior O-D flows, etc.), d to ccout for the cpcity restrits for the uobserved liks s well s the cogestio effects, while the itertive blcig scheme itertively djusts the priml vribles (e.g., pth flows, lik flows, iteectio turig movemet flows, O-D flows, etc.) d the dul vribles i the ier loop for give workig pth set from the outer loop. Note tht the workig pth set is geerted by colum geertio scheme (or shortest pth lgorithm) usig the geerlized lik costs, which re bsed o ot oly the lik costs but lso the dul vribles from the ctive side costrits. The dul vribles force the colum geertio scheme to geerte pths tht stisfy the side costrits. For dditiol discussios o the issue of usig the geerlized lik costs to geerte pths, refer to Bell et l. (1997) d Che et l. (2009, 2010). 1,, 40

(3) Output derivtio from pth flows Usig the pth flow solutio, vrious outputs c be derived s follows. Totl demd: the sum of ll pth flows from ll O-D pi gives the totl demd utilizig the etwork. Zol productio: the sum of ll pth flows emtig from give origi gives the zol productio. Zol ttrctio: the sum of ll pth flows termitig t give destitio gives the zol ttrctio. O-D flow: the sum of ll pths flows coectig tht O-D pir gives the O-D flow. Lik flow: the sum of ll pth flows pssig through give lik gives the lik flow. 41

5. NUMERICAL RESULTS 5.1 Uth Network This sectio presets umericl results to demostrte the fetures of the proposed pproch s well s the pplictios to the Uth sttewide freight trsporttio etwork. Uth s freight trsporttio etwork depicted i Figure 5.1 ws extrcted from the FAF3 etwork. The etwork cosists of 385 odes, 944 liks, d 2,256 O-D pi. The study re cosists of 29 couties d 19 exterl sttios (i.e., etry d exit poits roud the stte borde). The Wstch Frot Regiol Coucil (WFRC), the mjor truck geertio re i the stte highlighted i Figure 5.1, cosists of three mjor couties: Slt Lke, Weber d Dvis. Truck trffic couts from 222 loctios (bout 23% of etwork liks) were collected from the Uth Deprtmet of Trsporttio (UDOT) trffic mp (UDOT trffic mps 2013). The observtios re mily locted o the mjor itette freewys of Uth, such s I-15, I-70, I-80, d I-84 (see the itette freewys i Figure 5.1). These mjor itette freewys re the mjor truck routes for Uth, especilly I-15, which rus orth-south d psses through Slt Lke City d my other cities. Note tht the freight demd derived from the FAF3 dtbse ws bsed o the verge ul dily truck trffic (AADTT), so lik cpcity vlues were required to replicte the dily equivlet cpcity for give lik. To do so, we dopted the dily cpcity coveio fcto bsed o the fuctiol clss of the rodwys. The cpcity ws the expded by dividig the hourly cpcity by the coveio fctor d used for subsequet steps. 42

Dvis Weber Slt Lke WFRC (Slt Lke, Dvis d Weber Couties) Figure 5.1 Uth sttewide freight trsporttio etwork 5.2 Numericl Results 5.2.1 Commodity-bsed Truck O-D Trip Tble The estimtio procedure described i Figure 4.1 ws pplied for the bse yer (2007) FAF commodity flow dtbse. There re 29 iterl zoes or couties withi Uth d 27 exterl sttios. However, we foud tht oly 19 exterl sttios re used for truck trffic, hece the size of the trip tble is 48 48 (i.e., 29 iterl zoes or couties withi Uth d 19 exterl sttios). Figure 5.2 depicts the truck O-D trip tble for Uth (i.e., from ll origis to ll destitios). The totl dily truck trips obtied from the fit stge ws 25,508 truck trips/dy. Specificlly, this totl cosists of 45.6% withi Uth (I-I), 9.8% from Uth to other sttes (I-E), 11.0% from other sttes to Uth (E-I), d 33.6% through truck flows (E-E). We c observe the through truck flows (E-E) betwee I-80E d I-15N d betwee I-80E to I-80W re quite hevy. The highlighted br series (i drk gree) represet the productio flows from the mjor couties log the Wstch Frot re such s Slt Lke, Cche, Weber, Dvis, d Uth. 43

E-E from I-80E to I-15N ExE 33.6% IxI 45.6% E-E from I-80E to I-80W I-E Uth Dvis Weber ExI 11.0% IxE 9.8% E-E Cche I-I Slt Lke Cche Weber Dvis Uth E-I Figure 5.2 Commodity-bsed truck O-D trip tble Additiolly, Tble 5.1 summrizes the umber of commercil truck trips estimted usig the USTM commercil trips derived from Eq. 4.4, d Tble 5.2 summrizes the umber of empty truck trips estimted from Eq. 4.5. As c be see, the dily empty truck trips ccout for pproximtely 40% of the commodity flows. If this compoet is ot cosidered i the estimtio, the totl truck trffic d cogestio i the study re could be sigifictly uderestimted. 44

Tble 5.1 Commercil truck trips by couty (trucks/dy) Commercil truck trips by sector (Trucks/dy) Couty Household Agriculture Bsic Retil Office Couty totl (Trucks/dy) Bever 85 91 58 41 17 291 Box Elder 604 61 294 94 40 1,093 Cche 1,306 40 391 485 409 2,631 Crbo 300 216 216 1 44 777 Dggett 16 6 24 1 0 47 Dvis 3,517 42 607 1,290 326 5,782 Duchese 226 3 157 8 8 402 Emery 140 113 123 2 29 407 Grfield 73 5 41 18 2 139 Grd 146 24 111 5 13 300 Iro 565 38 386 7 65 1,061 Jub 116 6 102 3 40 267 Ke 109 27 51 3 71 261 Millrd 158 79 204 13 4 459 Morg 106 22 74 7 3 212 Piute 22 1 7 6 0 36 Rich 30 3 34 3 2 72 Slt Lke 12,883 52 6,803 492 1,048 21,278 S Ju 169 3 76 1 11 259 Spete 299 40 195 9 37 581 Sevier 267 11 217 13 26 534 Summit 488 8 598 7 38 1,140 Tooele 676 12 657 52 143 1,541 Uith 397 11 836 6 63 1,313 Uth 5,287 157 2,466 1,454 160 9,523 Wstch 274 3 313 3 38 631 Wshigto 1,742 8 906 11 551 3,219 Wye 40 5 41 6 2 93 Weber 2,961 48 797 117 254 4,176 Totl 33,001 1,136 16,787 4,158 3,444 58,525 Note: bsic secto iclude mufcturig, trsporttio, wholesle, d utilities 45

Tble 5.2 Empty truck trips by couty (trucks/dy) Empty Couty productio plows Empty ttrctio flows Empty totl (Trucks/dy) Bever 82 114 195 Box Elder 306 426 732 Cche 737 1,026 1,763 Crbo 218 303 521 Dggett 13 18 31 Dvis 1,619 2,255 3,874 Duchese 113 157 269 Emery 114 159 273 Grfield 39 54 93 Grd 84 117 201 Iro 297 414 711 Jub 75 104 179 Ke 73 102 175 Millrd 128 179 307 Morg 59 83 142 Piute 10 14 24 Rich 20 28 48 Slt Lke 5,958 8,298 14,256 S Ju 73 101 174 Spete 163 226 389 Sevier 149 208 358 Summit 319 444 764 Tooele 431 601 1,032 Uith 368 512 880 Uth 2,666 3,714 6,380 Wstch 177 246 423 Wshigto 901 1,255 2,157 Wye 26 36 62 Weber 1,169 1,629 2,798 Totl 16,387 22,825 39,212 46

Further, we used the desire lies to highlight selected O-D pi with high truck flows (i.e., greter th 500 trucks/dy) i Figure 5.3(). The circles i the figure show the eterig d exitig truck flows t mjor exterl sttios log the itette freewys. We c observe high eterig d exitig freight flows t the exterl sttios: betwee I-15 South d I-70, I-80 Est d I-15 North, I-80 West d I-80 Est vi I-15 er Slt Lke City, d so o. These re the importt itette truck routes i Uth d re used for coectig the through trips from/to other sttes. The O-D flows were the ggregted to show the truck trip productio d ttrctio flows t the couty level s well s the exterl sttios show i Figure 5.3(b). As c be see, truck trip productio d ttrctio flows derived from the fit stge re reltively cocetrted roud the WFRC re compred with other couties. Figure 5.3(b) revels most commercil d empty truck trips re cocetrted i the WFRC re d Uth Couty (shded res). This is to be expected becuse the mjor freight ctivities i Uth re mily geerted from these couties where wrehousig d distributio cete re locted. Overll, the truck flows withi d through Uth re two mjor demd compoets s they ccout for lmost 80% of totl commodity flows trsported i Uth. High Cocetrtio of Freight Activities i WFRC () Commodity truck flows (desire lies) Figure 5.3 Estimted sttewide commodity-bsed truck flows (b) Totl productio/ttrctio flows 47

The secod stge used the pth flow estimtor (PFE) to refie the truck trip tble obtied from the fit stge usig the truck couts from the sttewide truck cout progrm. Three differet types of iformtio, icludig truck couts, prtil set of O-D flows, productio d ttrctio flows (commodity d empty truck flows), were used to updte the truck O-D trip tble. Figure 5.4 depicts the sctter plots of observed d estimted lik flows obtied from the two-stge pproch d compres them with the oe-stge pproch (i.e., the commodity-bsed truck O-D trip tble from stge oe). Note tht the oe-stge pproch ssigs the commodity-bsed truck trips usig ll-or-othig (AON) trffic ssigmet procedure, which is typicl method used to prelod trucks to the sttewide etwork. Truck flows obtied from this method re usully ssiged bsed o the shortest distce or trvel time, d there is o cosidertio of cogestio. As c be see, the results obtied from this method re uderestimted, especilly i the WFRC re d the high freight ctivity loctios i the study re (i.e., res roud Slt Lke City Itertiol Airport d perimete of the Slt Lke Couty). Cosequetly, such issues ofte hider sttewide plig s it is icpble of cpturig the freight movemets uder cogestio d expliig the truck trffic vritios i the urb res metioed bove. O the other hd, the two-stge pproch usig PFE to refie the commodity-bsed truck O-D trip tble with truck couts c provide more resoble mtch betwee the observed d estimted vlues. The mjority of the observtios re withi cceptble tolerce with few poits outside of the error boud. Figure 5.4 Compriso betwee oe-stge d two-stge pproches Figure 5.5() shows the complete truck flow ptter o the sttewide etwork bsed o the twostge pproch. The figure revels high cocetrtio of truck trffic o I-15 roud Slt Lke Couty d I-80W i Summit Couty d Slt Lke Couty. To highlight the cogested liks, Figure 5.5(b) shows the volume-to-cpcity (V/C) rtios. As c be see, my itette d stte routes (e.g., I-15, iterchge to I-215, SR 130, SR 12, d SR 6) re quite cogested. 48

() Sttewide Truck Trffic (AADTT) (b) Volume/Cpcity Figure 5.5 Sttewide truck trffic d volume/cpcity lysis 49

5.2.2 Effect of sptil costrits I this sectio, two cses re cosidered for ssessig the effect of icludig sptil costrits i the PFE: Cse 1: PFE with truck couts oly Cse 2: PFE with truck couts with zol productio d ttrctio flow costrits derived from the fit stge Accurcy of the estimtes c be mesured by the root me squre error (RMSE) s follows: 1 N 1 2 est obs RMSE x x (4.39) where N is the umber of observtios, x est d x obs re the estimted d observed truck flows, respectively. Figure 5.6() d Figure 5.6(b) depict the sctter plots of observed d estimted lik flows d estimted trip productio for these two cses. RMSE=655.14 trips RMSE=978.56 trips () Truck cout oly (cse 1) (b) Truck cout oly + commodity bse dt (cse 2) Figure 5.6 Comprisos of observed d estimted sttewide truck flows The results show the truck trip tble estimted by PFE produces firly good mtch for both cses (i.e., cse 1: RMSE=655.14 trucks/dy, cse 2: RMSE=978.56 trucks/dy). It should be oted tht the RMSE idictes the ggregted qulity of O-D estimtes. A smller vlue idictes higher qulity of the estimtio process. Betwee the two cses, icludig sptil costrits ito the estimtio slightly deteriortes the mtchig of truck couts s idicted by the higher RMSE. This is compested by the better estimtes of zol productio d ttrctio flows. The estimted totl demd of cse 1 is pproximtely 38% less th the totl demd estimted from the fit stge. This highlights the importce of icludig the sptil costrits ito the PFE model, which c better cpture the totl demd i cse 2 (i.e., slightly over 6%). However, we still observe 50

tht cse 2 uderestimtes some lik flows, especilly those liks with high truck flows o I-15 er Slt Lke City. This is becuse those liks re locted closed to res with higher level of freight ctivities er the Slt Lke City Itertiol Airport. This is the cocetrted re with high truck trffic ccessig to/from the shippig compies d itermodl fcilities such s ril-truck d ir-truck modes. Resolvig this issue requires ddig specil geerto of truck trips from surveys of high freight desity res such s wrehouses d freight distributio cete. From the modelig poit of view, these specil geerto c be implemeted i the PFE frmework s they re hdled by the zol productio d ttrctio costrits (i Eqs. 4.8, d 4.9) similr to the commercil d empty truck trips. Figure 5.7() d Figure 5.7(b) depict the truck productio flows for cse 1 d cse 2, respectively. From these two figures, we c observe the trip productios i cse 2 re more distributed whe the sptil costrits re cosidered i the estimtio process. By ddig zol productio d ttrctio flows s costrits i cse 2, it c improve the observbility of the trip geertio ptter. Thus, this emphsizes the importce of usig two-stge pproch to cpture both the commodity flows d truck couts i the field, so tht the sttewide truck flow ptter c better reflect the relity. Without sptil costrits With sptil costrits Estimted productio flows dispee to ll couties Estimted productio flows reflectig freight ctivities i WFRC () Estimted trip productio (cse 1) (b) Estimted trip productio (cse 2) Figure 5.7 Comprisos of estimted productio flows 51

5.2.3 Truck Corridor Alysis This sectio provides the truck corridor lysis. I Uth, I-15 is primry corridor for both psseger d freight movemets. The truck corridor serves s bckboe route for truck movemets of griculturl eergy (i.e., oil, gs, d col) products i souther Uth d owrd to mjor cities i the stte such s Provo, Slt Lke City, d Ogde. Additioly, the I-15 corridor lso helps to coect the through truck trffic s prt of the CANAMEX corridor. Figure 5.() depicts the dily truck trffic flows o the I-15 corridor. Figure 5.8(b) d Figure 5.8(c) show dditiol detils of the truck flow profile strtig from the orther border (from Idho) to the southe border (to Arizo) d the correspodig dily truck V/C rtios. As expected, the hevily used truck liks re i the WFRC re, especilly the liks er Slt Lke City d its pheripherl urbized res such s Weber Couty, Dvis Couty, d Uth Couty. The most cogested lik crries dily truck trffic of 16,058 trucks/dy with AADT of 34,634 psseger c/dy, or bout 30% of this segmet beig truck trffic. Additiolly, i this re the dily truck flow to cpcity rtios rge betwee 0.3 d 0.5. The most cogested lik is bout 0.52, which idictes tht truck trffic highly cotributes to the cogestio o this prticulr lik i the urb res. Figure 5.8(d) depicts the dily truck vehicle mile trveled (TVMT) for this corridor. The dily TVMT is clculted bsed o the truck trvel distce d the dily truck flows estimted from the two-stge pproch. As c be see, the TVMT i Slt Lke couty is lower th those of Dvis d Uth couties. The mjor reso is tht higher truck flows c trvel loger distce i those couties, while similr mout of truck flows c trvel shorter distce withi Slt Lke couty. This suggests tht these liks could hve higher cogestio, which could led to stop-d-go trffic coditios roud this re. 52

() (b) Ogde Slt Lke City Provo (c) (d) Figure 5.8 Estimted truck flows d truck vehicle miles trveled o I-15 corridor, Uth 53

6. CONCLUSIONS This study hs developed two-stge pproch for estimtig truck O-D trip tble usig both commodity flows d truck couts dt. The model is supported by two sequetil stges: Stge oe estimtes the commodity-bsed truck O-D trip tbles primrily derived from the commodity flow dtbse, while stge two uses the pth flow estimtor (PFE) to refie the truck trip tble to better mtch the observed truck couts. I the fit stge, we hve developed simplified procedure to estimte commodity-bsed truck trip tble usig the commodity flows from the ewly relesed FAF 3. The FAF 3 provides commodity flow estimtes bsed o toge d vlue by commodity type, mode, origi, d destitio for 2007, d forecsts through 2040. It is publicly ccessible from the Freight Mgemet d Opertios Dtbse from the FHWA website. This stge coside itrstte, itette, d through truck flows. Four tsks re eeded to ccomplish this: 1) extrct sttespecific commodity flows by from FAF 3, 2) coduct subre lysis to estimte through truck flows, 3) disggregte the stte-specific to couty-specific commodity flows, d 4) covert the commodity flows ito truck trips. The secod stge dopts the PFE to refie the truck trip tble obtied from the fit stge usig the up-to-dte truck couts. The bsic ide is to fid set of pth flows tht c reproduce the observed truck couts from the sttewide truck cout progrm collected from permet cout sttio loctios withi the stte d stte borde, while preservig the sptil distributio of the O-D commodity flow ptter obtied from the fit stge. To ehce the observbility of the truck O-D trip tble, dditiol plig dt, such s productio d ttrctio flows, re icluded i the PFE estimtio. Vlidtio of the results of the PFE is ssessed by the ccurcy of the ssigmet estimtes mesured by the root me squre error (RMSE) betwee the estimted d observed truck couts. The flexibility of ggregtig pth flows t differet sptil levels i the PFE llows us to mkes use of vrious existig dt (e.g., truck couts, productio d ttrctio commodity flows, truck VMT t the stte level, etc.) d commodity-bsed dt with commercil d empty truck trips for estimtig the sttewide truck trip tble. The proposed pproch c be lso used to coduct the truck corridor lysis to determie the cogested liks d potetil bottleecks. Although the results usig Uth s cse study re stisfctory, ccurte d cosistet truck couts re required i the PFE to produce relible results. Extedig the PFE to hdle icosistet trffic couts t the sttewide level should be explored (see Che et l. 2009, 2010). Costrits such s trip legth frequecy distributio is eeded to model differet types of sttewide truck trffic (i.e., short hul, log hul, d empty truck trips) i the PFE. Hece, further work should cosider multiclss d multimode (e.g., commercil, sigle- d multiple-uit trucks, d psseger c) (see, for exmple, Yg d Hug 2004; Mrcotte d Wyter 2004; Wog et l. 2005), so tht it c better reflect the ctul cogestio of the sttewide etwork. I dditio, truck surveys t freight compies d distributio cete for ech couty d stte border (e.g., Weigh-i-motio, Port of Etry sttios) should be coducted to udetd the freight movemets i the sttewide 54

etwork. The curret truck O-D trip tble is estimted from the commodity flow dt from FAF d truck couts collected by the Uth Deprtmet of Trsporttio. It should be updted usig the ewly developed Uth Sttewide Trvel Model to improve the ccurcy d qulity of the truck O-D trip tble. 55

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Uth Deprtmet of Trsporttio (UDOT) Trffic mps for 2008. www.udot.uth.gov. Accessed J. 15, 2013. Wilbur Smith Assocites i coopertio with Resource Systems Group, Ic., 2009. Uth sttewide trvel model, fil model vlidtio report. Report prepred for Uth Deprtmet of Trsporttio. Wiscosi Deprtmet of Trsporttio, 1995. Trsliks 21 Techicl Report Series: Multimodl Freight Forecsts for Wiscosi, Drft No. 2. Wisetjidwt, W., So, K., d Mtsumoto, S. Commodity distributio model icorportig sptil iterctios for urb freight movemet. Proceedig of the 85th Aul Meetig of the Trsporttio Reserch Bord. CD-ROM Trsporttio Reserch Bord, 2006. Wog, S.C., Tog, C., Wog, K., Lm, W., Lo, H. Yg, H., Lo, H., 2005. Estimtio of multiclss origi-destitio mtrices from trffic couts. Jourl of Urb Plig d Developmet 131(1), 19-29. Wog, S.C., Yg, H., 1997. Reserve cpcity of sigl-cotrolled rod etwork. Trsporttio Reserch Prt B 31(5), 397-402. Wu, J.H., Flori, M., He. S., 2006. A lgorithm for multi-clss etwork equilibrium problem i PCE of trucks: Applictio to the SCAG trvel demd model. Trsportmetric, 2(1), 1-9. Yg, H., Hug, H., 2004. The multi-clss, multi-criteri trffic etwork equilibrium d systems optimum problem. Trsporttio Reserch Prt B 38(1), 1-15. Zhg, Y., Bowde, R.O., Alle, A.J., 2003. Itermodl freight trsporttio plig usig commodity flow dt. Report prepred for the Ntiol Ceter of Itermodl Trsporttio (NCIT), the Mississippi Deprtmet of Trsporttio (MDOT). 59

APPENDIX A. COMMODITY CODES BASED ON THE STANDARD CLASSIFICATION OF TRANSPORTED GOODS (SCTG) Tble A.1 Commodity codes bsed o the SCTG SCTG BTS/Cesus Full Commodity Nme 1 Live Aimls d Fish 2 Cerel Gris (icludig seed) 3 Other Agriculturl Products, except for Aiml Feed 4 Aiml Feed d Products of Aiml Origi,.e.c. 2 5 Met, Fish, d Sefood, d Their Preprtios 6 Milled Gri Products d Preprtios, d Bkery Products 7 Other Prepred Foodstuffs, d Fts d Oils 8 Alcoholic Beverges 9 Tobcco Products 10 Moumetl or Buildig Stoe 11 Nturl Sds 12 Grvel d Crushed Stoe 13 No-Metllic Mierls,.e.c. 14 Metllic Ores d Cocetrtes 15 Col 16 Crude Petroleum Oil 17 Gsolie d Avitio Turbie Fuel 18 Fuel Oils 19 Col d Petroleum Products,.e.c. 20 Bsic Chemicls 21 Phrmceuticl Products 22 Fertilize 23 Chemicl Products d Preprtios,.e.c. 24 Plstics d Rubber 25 Logs d Other Wood i the Rough 26 Wood Products 27 Pulp, Newsprit, Pper, d Pperbord 28 Pper or Pperbord Articles 29 Prited Products 2.e.c. = ot elsewhere clssified 60

Tble A.1 Commodity codes bsed o the SCTG (Cotiued) SCTG BTS/Cesus Full Commodity Nme 30 Textiles, Lether, d Articles of Textiles or Lether 31 No-Metllic Mierl Products 32 Bse Metl i Primry or Semi-Fiished Forms d i Fiished Bsic Shpes 33 Articles of Bse Metl 34 Mchiery 35 Electroic d Other Electricl Equipmet d Compoets, d Office Equipmet 36 Motorized d Other Vehicles (icludig prts) 37 Trsporttio Equipmet,.e.c. 38 Precisio Istrumets d Apprtus 39 Furiture, Mttresses d Mttress Supports, Lmps, Lightig Fittigs, d Illumited Sigs 40 Miscelleous Mufctured Products 41 Wste d Scrp 42 Mixed Freight 43 Commodity ukow 61

APPENDIX B. DISAGGREGATED PRODUCTION-ATTRACTION OF UTAH Tble B.1 Disggregted Productio-Attrctio withi Uth (I-I) (1x1) Uth (KT) From 2007 2040 Uth 93,302.06 158,537.40 Tble B.2 Disggregted Productio-Attrctio from Uth to Other Sttes (I-E) (1x48) Destitio Yer AL AK AZ AR CA CO CT DE Uth 2007 14 4 750 44 2,575 1,314 15 1 2040 30 4 1,646 68 3,444 2,042 41 2 Uth Uth Uth Uth Uth Destitio Yer DC FL GA ID IL IN IA KS 2007 0 27 86 2,372 160 149 61 68 2040 0 50 141 3,690 351 238 243 165 Destitio Yer KY LA ME MD MA MI MN MS 2007 46 15 1 7 27 62 111 21 2040 82 27 2 18 77 45 278 54 Destitio Yer MO MT NE NV NH NJ NM NY 2007 101 920 58 2,231 1 49 145 58 2040 249 1,628 149 3,858 2 149 186 110 Destitio Yer NC ND OH OK OR PA RI SC 2007 84 36 115 61 290 103 2 42 2040 161 76 226 151 491 217 3 94 Destitio Yer SD TN TX VT VE WA WV WI WY 2007 67 44 340 16 28 729 2 210 1,849 2040 198 74 707 37 64 1,309 3 348 3,595 62

Tble B.3 Disggregted Productio-Attrctio from Other Sttes to Uth (E-I) (48x1) Origi Yer AL AK AZ AR CA CO CT DE Uth 2007 68 2 1,101 134 3,514 1,168 28 2 2040 138 2 1,574 241 12,375 2,238 54 6 Uth Uth Uth Uth Uth Origi Yer DC FL GA ID IL IN IA KS 2007 0 83 206 1,568 324 242 185 98 2040 0 166 290 3,927 561 669 195 103 Origi Yer KY LA ME MD MA MI MN MS 2007 61 93 9 15 40 130 116 60 2040 144 144 9 16 70 445 140 97 Origi Yer MO MT NE NV NH NJ NM NY 2007 384 562 148 1,928 6 93 78 122 2040 533 720 238 3,272 12 133 219 176 Origi Yer NC ND OH OK OR PA RI SC 2007 112 11 259 654 573 224 4 73 2040 200 21 473 674 1321 212 5 187 Origi Yer SD TN TX VT VE WA WV WI WY 2007 68 145 573 8 117 585 5 187 1,618 2040 156 372 1,283 9 179 1,014 8 234 2,597 63

APPENDIX C. DERIVATIONS OF THE ADJUSTMENT EQUATIONS This ppedix provides the full derivtios of the djustmet equtios for the lik-cpcity costrits, the lower limit d upper limit of lik-flow costrits, O-D demd, zol productio flow costrits, zol ttrctio flow costrits d totl demd costrit for the PFE model. Hdlig lik-cpcity costrit Cosider the lik-cpcity costrit (4.8). If flow o lik exceeds its lik-cpcity (i.e., x C ), dul vrible d is djusted to reduce the flow o lik bck to its lik-cpcity. The djustmet vlue ( ) is the root of the followig equtio, which is obtied by replcig the lyticl expressios. c u u d k k k exp M U f k k k C RS k K RS k K o o r r s s which is equivlet to: RS kk f exp C x exp C k k k k (C1) (C2) I Eq. (C2), it should be oted tht oly the pths pssig through lik re ivolved i the computtio of lik-flow (e.g., k =1). The expoetil term is commo to ll the relevt pths d therefore c be moved outside the summtio. After re-rrgig Eq. (C2), the djustmet fctor for the dul vrible of the lik-cpcity costrit (4.8) c be writte s follows: 1 C l x Hdlig observed lik flow costrit Likewise, the djust fctor ivolvig observed lik flow costrit (4.7) c be derived s follows. c u u d (C4) o o r r s s k k k (1 ) exp M U v k RS kk (1 ) v which is equivlet to: fk k exp k k RS kk (1 ) v (1 ) v (1 ) v (1 ) v x exp (C5) (C3) 1 (1 ) Hece, l v for u x d 1 (1 ) l v for u x (C6) 64

Hdlig prior O-D demd, zol productio d ttrctio flow d totl demd costrits Likewise, the djust fctor ivolvig prior O-D demd, zol productio d ttrctios flows, totl demd costrits (4.9), (4.10), (4.11) d (4.12), respectively, c be derived s follows. Prior O-D demd ck u u k dk (1 ) exp M U z o o (1 ) z kk r r s s which is equivlet to: (1 ) z (1 ) z q exp fk exp kk (1 ) z (1 ) z (C7) (C8) Hece, 1 (1 ) l z q for o d 1 (1 ) l z q for o (C9) Zol productio flow ck u u k dk (1 ) exp M U r Or o (1 ) O o r r s s ss kk r r which is equivlet to: (1 ) O (1 ) O r r r fk exp Pr exp ss kk (1 r ) Or (1 r ) O (C10) (C11) Hece, 1 (1 ) l r O r Pr for r d 1 (1 ) l r O r Pr for r (C12) Zol ttrctio flow ck u u k dk (1 ) exp M U s Ds (C13) r R k K o (1 s) Ds o r r s s which is equivlet to: (1 ) D (1 ) D s s s s fk exp As exp (C14) (1 ) D (1 ) D rr kk s s s s 1 (1 ) Hece, l s D s for As s d 1 (1 ) l s D s for As s (C15) 65

Totl Demd RS kk ck u u k dk (1 ) F exp M U (1 ) F o o r r s s which is equivlet to: RS kk Hece, f k exp (1 ) F (1 ) F (1 ) F (1 ) F T exp 1 (1 ) F l T for d 1 (1 ) F l T for (C16) (C17) (C18) 66