Relating Safety and Capacity on Urban Freeways

Transcription

1 Avalable ole at Proceda Socal ad Behavoral Sceces 16 (2011) th Iteratoal Symposum o Hghway Capacty ad Qualty of Servce Stockholm, Swede Jue 28 July 1, 2011 Relatg Safety ad Capacty o Urba Freeways Jace R. Dael a * ad Eugee Maa a a New Jerseys Isttute of Techology, Dept. of Cvl ad Ev. Egeerg, Newark NJ Abstract Ths research sought to vestgate the relatoshp betwee capacty ad safety o freeway roadways New Jersey. Usg the State s roadway database, capacty was estmated for State roadways usg the procedures the Hghway Capacty Maual. Crash predcto models were developed relatg crashes ad crash rates to the geometrc varables used to estmate capacty as well as to capacty ad v/c rato. The research showed that as capacty creases the umber of crashes ad crash rate also creases. As v/c rato creased the umber of crashes ad crash rate decreased dcatg that cogesto may result reduced speeds ad as a result a lower umber of crashes ad crash rates. The research pots to the eed to clude operatoal parameters performg road safety evaluatos Publshed by Elsever Ltd. Ope access uder CC BY-NC-ND lcese. Keywords: Safety, Capacty, Crash Modelg, Freeway; 1. Itroducto The ewly released Hghway Safety maual (HSM) s a valuable resource to assst plaers ad desgers o roadway safety fudametals. Aalytcal tools for predctg road safety are cluded to allow egeers the ablty to estmate the expected effectveess of roadway treatmets. The predctve methodologes rely o the use of safety performace models ad crash modfcato factors for roadway segmets, tersectos ad terchages o two-lae, multlae ad arteral roadways. The Hghway Safety Maual s smlar to the Hghway Capacty Maual (HCM), whch wll also be updated 2010, that they both allow for the performace of roadway facltes to be evaluated. The Hghway Safety Maual reports the expected average crash frequecy assocated for the tme perod, volume ad geometrc codtos of a roadway. The Hghway Capacty maual provdes the Level of Servce for the operato of the roadway. To desg ad operate safe roadways, there s a eed to better uderstad the relatoshp betwee the safety ad operatoal mpacts of roadway treatmets. Both the HSM ad HCM fall short provdg a clear relatoshp betwee the safety ad operatoal performace of roadways. 2. Problem statemet Several studes have bee performed showg the mpact of geometrc features o the safety of freeway roadways. Although may of these geometrc features are used the estmato of capacty of a freeway, lttle research has bee performed to demostrate the relatoshp betwee safety ad capacty. I fact, the relatoshp betwee capacty ad safety s ot etrely clear. Kooov et. al (2008) cocluded that addg laes o urba freeways tally results safety mprovemet that dmshes as cogesto creases. Huag et. al (2002) foud * Correspodg author. Tel.: (973) ; fax: (973) E-mal address: dael@jt.edu Publshed by Elsever Ltd. do: /j.sbspro Ope access uder CC BY-NC-ND lcese.

2 318 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) that road dets, whch volve covertg a four-lae udvded roadway to three laes (two through laes plus a ceter tur lae), resulted 6% reducto crashes, o sgfcat chage crash rates ad o mpact o crash severty. 3. Research objectves Ths research sought to vestgate the relatoshp betwee capacty ad safety o freeways New Jersey. Usg the State s roadway database, capacty was estmated for State roadways usg the procedures the Hghway Capacty Maual. Total crashes ad crash rates were the related to the capactes of homogeeous sectos of these roadways. The results beg to detfy the relatoshps betwee safety ad freeway operatos. 4. Backgroud Accordg to the Hghway Capacty Maual (2010), the capacty of a roadway faclty s defed as The maxmum hourly rate at whch persos or vehcles reasoably ca be expected to traverse a pot or a uform secto of a lae or roadway durg a gve tme perod uder prevalg roadway, traffc, ad cotrol codtos. For basc freeway segmets, capacty s determed as the servce flow rate for level of servce E codtos. The servce flow rate s calculated as follows: SF MSF N f HV f p (1) where: SF = servce flow rate at level of servce (vph) MSF = maxmum servce flow rate at level of servce (pcphpl); N = umber of laes; f HV = heavy vehcle adjustmet factor f p = drver populato factor. The maxmum servce flow rate (MSF) used calculatg the servce flow rate s a fucto of the free-flow speed o the roadway. The free-flow speed s estmated as follows: FFS f LW f LC 3.22TRD (2) where: FFS = free-flow speed of the freeway, m/h f LW = adjustmet for lae wdth, m/h f LC = adjustmet for rght-sde lateral clearace, m/h TRD = total ramp desty, ramps/m Equatos (1) ad (2) detfy the varables used determg the capacty for a freeway. The relatoshp betwee safety ad capacty should the volve establshg the relatoshp betwee safety ad the varables used to estmate capacty. The varables used estmatg capacty clude: umber of laes, percet heavy vehcles, grade, drver type, lae wdth, shoulder wdth ad total ramp desty. 5. Lterature revew No lterature could be foud relatg crashes to capacty of the roadway, however, several research studes have bee performed relatg crash couts ad crash rates to the geometrc varables used estmatg capacty. Kooov et. al (2008) vestgated the relatoshp betwee safety ad the umber of laes o freeways Colorado, Calfora ad Texas. Safety Performace Fuctos (SPFs) relatg the aual average daly traffc to the umber of crashes per mles were developed for dfferg umber of laes. The slopes of the SPF curves, whch dcate the

3 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) chage crashes wth creasg umber of laes, were the compared. The research showed that the slope of the SPF curves, or the chage crashes, creases as the umber of laes creases. I addto, addg laes may tally result safety mprovemets that are ot sustaed as cogesto creases. The researchers state that ths fdg may be explaed wth the fact that as the umber of laes creases, the potetal for lae chagg creases ad so does the potetal for coflct. Regarasu et. al. (2009) vestgated the effects of road geometry ad cross-varables, cludg the umber of laes, o umber of crashes. Sxtee years of crash data from roadways Japa were collected through the ato s hghway database system. Data for 14 smple roadway varables were collected. The cross-secto data used cluded shoulder wdth, average lae wdth, umber of laes, ad truck lae. Crash data ad smple roadway varable data were combed to make two databases: oe wth homogeeous road segmets ad the other wth 1-m road segmets. A decso tree was used to detfy combatoal varables ad a egatve bomal regresso performed to determe the relatoshp betwee umber of crashes ad the set of depedet varables. Thrtee combatos of varables were foud to be sgfcat at a ch-square level of 5% wth umber of laes as the most sgfcat factor. Road segmets wth two or more laes per drecto, a maxmum shoulder wdth of less tha 1.1 m, ad a lae wdth of less tha 3.25 m were foud to have the hghest crash rate per klometer. Road segmets wth oe lae per drecto, at least 2.3 m of maxmum shoulder wdth, ad a lae wdth betwee 3.1 ad 3.3 m were foud to have the lowest crash rate per klometer. Gross et. al (2009) detfed whether t was safer to crease lae wdth or crease shoulder wdth for a fxed total wdth o a roadway. Usg geometrc, traffc ad crash data from Pesylvaa ad Washgto, a casecotrol approach was used to evaluate the safety effectveess of varous lae shoulder cofguratos. The casecotrol method detfes samples of cases ad cotrols for a gve outcome ad compares the prevalece of rsk factors betwee the two groups. I ths study, cases were defed as road segmets experecg at least oe crash durg a partcular year ad cotrols draw from segmets ot experecg a crash durg the same year. Models were developed for pavemet wdths betwee 26 ad 36 feet wth the 36-ft wdth pavemet, cosstg of 12-ft laes ad 6-ft shoulders, selected as the basele codto. The model developed for Pesylvaa showed a declg odds rato as total paved wdth creases. The model also dcates a geeral reducto crash odds a lae wdth creases whle holdg shoulder wdth costat, as well as a whe shoulder wdth creases whle holdg lae wdth costat. The model developed for Washgto showed a clear tred reduced crash odds as shoulder wdth creases for a fxed lae wdth of 11 feet. Zegeer et. al.(1995) revewed ad summarzed kow relatoshps betwee crash experece ad cross-sectoal roadway elemets. The elemets cosdered cluded lae wdth, shoulder wdth, shoulder type, roadsde features, brdge wdth, meda desg, ad others. The study focused o two-lae, rural roadways. Oly crash types related to cross-sectoal elemets, such as ru-off-road ad head-o crashes were cluded the umber of crashes evaluated. The study foud that lae wdeg ca reduce related crashes by up to 40. Addg a 8-foot paved shoulder ca reduce related crashes by 49 percet. Icreasg the roadsde clear zoe by 20 feet ca reduce crashes as much as 44 percet. Flatteg a 2:1 sdeslope to 7:1 or flatter ca reduce sgle vehcle crashes by up to 27 percet. Wder ad flatter medas were foud to result reduced crash rates o multlae roadways. Huag et. al (2002) vestgated the effects of road dets o the motor vehcle crashes ad jures. I ths case, road dets refer to covertg a four-lae udvded roadway to a three-lae roadway wth two through laes ad a ceter tur lae. Twelve roadways where these coversos were mplemeted were evaluated ad a before-after aalyss usg a yoked comparso was performed. Usg ths approach, crashes both for locatos experecg the treatmet ad locatos selected for comparso were obtaed for a perod before the stallato ad after stallato. The comparso locatos cluded locatos wth four-lae roadways smlar fuctoal classfcato, type of developmet, speed lmt, tersecto spacg ad access cotrol to the treatmet locatos. The study foud that gve the total umber of crashes that occurred at both the road det ad comparso stes, a hgher percetage of crashes at comparso stes (41.0 percet) occurred the after perod tha at the road det locatos (35.8 percet). Crash rates dd ot chage sgfcatly from the before to the after perod ad road det coversos dd ot affect crash severty.

4 320 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) Rogess et. al (1982) evaluated the safety mpacts of addg pave shoulders o rural two-lae hghways ad the mpacts of covertg two-lae roadways wth full-wdth paved shoulders to udvded, four-lae roadways wthout shoulders. Crash frequeces were compared by crash type ad roadway class, before ad after the treatmets were mplemeted. I addto, a pared t-test was used to determe whether the dfferece betwee the before ad after codtos was statstcally sgfcat for ether crash type or for crash severty. The study foud that the addto of full-wdth paved shoulders to a two-lae roadway reduced the total umber of crashes. The coverso of a paved shoulder to a addtoal travel lae resulted fewer total crashes f the traffc volume was greater tha 3000 vehcles per day. 6. Methodology The approach used to develop relatoshps betwee safety ad capacty volved developg crash predcto models where total crashes ad crash rates were estmated as a fucto of the geometrc codtos ad capacty of the roadway. Models predctg umber of crashes ad crash rates were developed: (1) usg all of the varables used to estmate capacty; (2) usg capacty as a explct varable; ad (3) usg v/c rato, rather tha capacty. Crash predcto models were developed usg both the Posso ad egatve bomal models to estmate the umber of crashes. Posso regresso models provde relatoshps betwee observed cout data that follow a Posso dstrbuto ad a set of explaatory varables. Ths relatoshp betwee the expected umber of crashes ad the explaatory varables s expressed as (Bauer, 1996): log( ) X (3) o j1 j j The umber of crashes, Y, follows a Posso dstrbuto wth the probablty that y crashes are observed, expressed as: P( Y y e y ) y! (4) where s the mea or expected umber of crashes. The model coeffcets, j, are estmated usg the maxmum lkelhood method. Usg ths method, the maxmum lkelhood estmates (MLE) of the regresso coeffcets are obtaed by maxmzg the log lkelhood fucto whch s stated as: y log( ) log(y! ) log( L) (5) 1 The model parameters are estmated by maxmzg the log lkelhood fucto or by mmzg the egatve of the log lkelhood wth the maxmum value occurrg f the model fts the data exactly. A lmtato of the Posso regresso model s that the varace should be equal to the mea. If ths codto s ot met, the data s overdspersed ad the Posso model s ot approprate. I that case, the egatve bomal model may provde a better modelg approach. For the egatve bomal, the umber of crashes, Y, follows a egatve bomal dstrbuto wth the mea ad varace of the dstrbuto as follows: E(Y ) Var(Y ) 2 (6)

5 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) As goes to zero, the egatve bomal regresso yelds the Posso regresso. 7. Goodess-of-Ft The goodess-of-ft of the Posso regresso model caot be descrbed by a R 2 value as calculated for a lear regresso model. Istead two types of R 2 values are provded: the Pearso R 2 P ad the devace R 2 D. These statstcs are calculated as: R 2 P y y ^ ^ 2 2 R 2 d 1 1 ^ y y log ( y ) ^ y y log ^ 1 (7) where: y = observed crashes; ^ _ = expected umber of crashes; = average umber of crashes. _ Both the Pearso R 2 P ad the devace R 2 D assess the mprovemet the ft that results from usg stead of to predct y. The Ch-squared ad G-squared values are also provded as a meas of assessg the goodess of ft of the models. The Pearso ch-square statstc ca be used to assess whether the model s overdspersed (Vogt, 1988). If the rato of the ch-square statstc over (-p), where s the umber of observatos ad p s the umber of parameters estmated the model, s greater tha 1, the the data has greater dsperso that s explaed by the Posso dstrbuto. The G-squared value s the sum of the devaces ad s expressed as: G 2 d 2 y l(y / ) (8) 1 1 ^ A model wth a perfect ft would show a G-squared value equal to 0.0. The mea devace, G 2 /(-p), where ad p are as prevous descrbed, should be equal to oe for the Posso regresso. Whe the mea devace s substatally greater tha oe, the data s sad to be overdspersed (Pera, 2002). 8. Data collecto To determe the relatoshp betwee capacty ad safety, crash data for the year 2008 were obtaed from the New Jerseys Departmet of Trasportato (NJDOT) crash database. The NJDOT crash database cotas crash statstcs obtaed for crash reports o the state s roadways. Ne roadways were detfed to be cluded the aalyss cludg State Routes 1, 9, 46, 55 ad 206 ad Iterstate 78, 80, 287 ad 295. The routes were selected because they represet some of the major through routes the state of New Jerseys ad are classfed as ad Urba Prcpal Arteral, Urba Freeway/Expressway or Urba Iterstate. Table 1 shows the selected roadways ad the portos of roadways used the aalyss.

6 322 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) Table 1. Study roadway characterstcs Study Roadway Mlepost Fuctoal Classfcato Average AADT (veh/day) Route Urba Freeway/ Expwy Urba Prcpal Arteral Average Secto Legth (m) Route Urba Prcpal Arteral Urba Mor Arteral Route Urba Prcpal Arteral Route Urba Freeway/ Expwy Route Urba Prcpal Arteral Iterstate Urba Iterstate Iterstate Rural Iterstate Iterstate Urba Iterstate Iterstate Urba Iterstate The data collected represeted parameters used estmatg capacty o freeway facltes. These parameters cluded each roadway s secto legth, AADT, total crashes, couty, fuctoal classfcato, truck percetage, posted speed lmt, umber of laes, legth wdth, meda wdth ad the total ramp desty. A total of 988 segmets were cluded the aalyss. Table 2 shows the roadway statstcs for the roadways used. Table 2. Roadway characterstcs Mea M. Max. Stadard Error Total Crashes Crash Rate (crashes/mvmt) Secto Legth (m) AADT (veh/day) Percet Trucks(%) Posted Speed (m/h) Number of Laes Pavemet Wdth (ft) Shoulder Wdth (ft) Total Ramp Desty (ramps/m) Aalyss 9.1. Freeway capacty estmato The capacty for each roadway segmet was estmated usg equato (2) to estmate the free-flow speed ad equato (1) to estmate the capacty or the servce flow rate at level of servce E. The maxmum servce flow rate used equato (1) was take from the Hghway Capacty Maual 2010 for level of servce E ad show Table 3.

7 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) Table 3. Freeway capacty uder deal codtos Free-Flow Speed (m/h) Maxmum Servce Flow Rate (pc/h/l) 70 2, , , ,250 The calculated free-flow speed ad capactes for the roadways are gve Table 4. The table shows that freeflow speeds for the roadways vared betwee 58 ad 75 mph ad the capacty vared betwee 5945 ad 13,991 pcph. The volume used to calculate the v/c rato s based o the AADT ad usg a assumed K ad D value of 0.1 ad 0.5. Table 4. Roadway capacty factors Average M Max Std. Error FFS (m/h) Capacty (pc/h) DDHV (veh/hr) v/c rato Fgure 1 shows the relatoshp betwee total crashes ad the free-flow speed. The fgure shows that as the freeflow speed creases, there s a geeral crease total crashes. However, the fgure also shows a crease the varablty of the total crashes as the free-flow speed creases. Ths dcates that the total crashes caot be explaed by oly the free-flow speed of the roadway. Fgure 2 shows the relatoshp betwee the capacty ad the total crashes. The fgure shows that the capacty estmates are qute smlar for segmets wth the same umber of laes. As a result, total crashes are clustered to four capacty estmates assocated wth 2-lae, 3-lae, 4-lae ad 5-lae segmets. The fgure shows that smlar to the relatoshp betwee free-flow speed ad total crashes, there s a wde rage total crashes for a capacty estmate. 10. Crash predcto models Crash predcto models were developed for the study roadways usg both Posso regresso ad egatve bomal models. The statstcal package Lmdep 7.0 was used for developg the crash predcto models. The varables cosdered modelg truck crashes cluded: Secto Legth, AADT, Percet Trucks, Posted Speed, Number of Laes, Pavemet Wdth, Shoulder Wdth ad Total Ramp Desty. Models predctg umber of crashes ad crash rates were developed: (1) usg all of the varables used to estmate capacty; (2) usg capacty as a explct varable; ad (3) usg v/c rato, rather tha capacty.

8 324 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) Total Crashes Free-flow Speed (mph) Fgure 1. Free-Flow speed versus total crashes Total Crashes Capacty (vph) Fgure 2. Capacty versus total crashes

9 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) Safety ad roadway geometrcs Table 5 show the Posso ad egatve bomal model results ad Table 6 shows the Goodess-of-Ft parameters whe all the varables used for calculatg capacty were used. Table 6 provdes a estmate of alpha, the overdsperso parameter for the egatve bomal model. If the alpha coeffcet s zero the the model s better estmated usg a ordary Posso regresso model. For both the models estmatg the total crashes ad crash rate, the alpha coeffcet s sgfcat, dcatg that a egatve bomal model s a more sutable model tha the Posso regresso model. For the egatve bomal model predctg crash couts, all varables are sgfcat at a 0.05 sgfcace level, except for the percetage of truck ad the lae wdth. The percetage of truck has a sgfcace level of lae wdth has a sgfcace level of the egatve bomal model. The posted speed ad shoulder wdth have egatve coeffcets dcatg that as these varables crease, the umber of crashes decreases. The result s tutve as a crease these varables represets better desg ad safer roadways. For the egatve bomal model developed to estmate crash rate, the secto legth, AADT ad posted speed were foud to be sgfcat. All three sgfcat varables have egatve coeffcets dcatg that as these varables crease, the crash rate decreases. The segmet legth ad AADT are both used the deomator whe calculatg the crash rate ad so are versely related to the crash rate. The posted speed lmt s reflectve of the roadway desg. As the posted speed creases, so does the ablty of vehcles to travel safely o the roadway. Therefore, as the posted speed creases, t would be expected that the crash rate of the roadway decreases Safety ad capacty To evaluate the relatoshp betwee safety ad capacty, crash predcto models were developed usg capacty as a explct depedet varable. I ths modelg approach, the varables used to calculate capacty were ot used as depedet varables. The varables used to develop the predcto model clude: secto legth, AADT, posted speed ad capacty. Table 7 show the Posso ad Negatve Bomal model results ad Table 8 shows the Goodess-of-Ft parameters. Smlar to the prevous models, overdsperso parameter s sgfcat dcatg that the egatve bomal model provdes a better ft. All of the varables were foud to be sgfcat at a 0.05 sgfcace level. For the model estmatg umber of crashes, posted speed has a egatve coeffcet. For the models estmatg crash rate, the coeffcets for secto legth, AADT ad posted speed are egatve. The coeffcet for the capacty varable s postve dcatg that as capacty creases, the crash rate also creases. Ths fdg supports Kooov s (2008) study whch cocluded that crash rates creased as the umber of laes creases. The explaato gve that study was the crease umber of laes also creases the potetal for lae chagg ad the potetal for coflct. Smlarly, hgher capactes may also result hgher speeds ad a greater propesty for crashes. 11. Coclusos The objectve of ths research was to vestgate the relatoshp betwee capacty ad safety. Crash predcto models were developed relatg crashes ad crash rates to the geometrc varables used to estmate capacty as well as to capacty ad v/c rato. The research foud that the posted speed, shoulder wdth ad total ramp desty does mpact the crashes o urba freeways. As the posted speed ad shoulder wdth creased, the umber of crashes was foud to decrease. The reasog s based o the hgher speeds assocated wth roadways wth hgher posted

10 326 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) Table 5. Model results for all varables Parameter Posso Modelg Crash Couts Std. Error p-value Negatve Bomal Std. Error p- value Itercept Secto Legth, SL Average Aual Daly Traffc, AADT Truck Percetage, P T Posted Speed, SPD Number of Laes, N Lae Wdth, L W Shoulder Wdth, S W Total Ramp Desty Alpha (Over Dsperso Parameter) Modelg Crash Rates Parameter Posso Std. Error p-value Negatve Bomal Std. Error p- value Itercept Secto Legth, SL Average Aual Daly Traffc, AADT Truck Percetage, P T Posted Speed, SPD Number of Laes, N Lae Wdth, L W Shoulder Wdth, S W Total Ramp Desty Alpha (Over Dsperso Parameter)

11 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) Table 6. Goodess-of-Ft for models usg all varables Modelg Crash Couts Posso Negatve Bomal Modelg Crash Rates Posso Negatve Bomal Number of observatos Log lkelhood fucto Restrcted log lkelhood Ch-squared Sgfcace level R 2 p R 2 D Table 7. Model results relatg safety, capacty ad V/C rato Modelg Crash Couts Modelg Crash Rates Model Relatg Safety ad Capacty Std. Error p-value Std. Error p-value Itercept Secto Legth, SL Average Aual Daly Traffc, AADT Posted Speed, SPD Capacty Model Relatg Safety ad V/C Rato Std. Error p-value Std. Error p-value Itercept Secto Legth, SL Average Aual Daly Traffc, AADT Posted Speed, SPD V/C Rato speed lmts ad wder shoulders. Capacty was foud to have a postve coeffcet dcatg that as capacty creases, the umber of crashes ad crash rate also creases. The fdg dcates that hgher capactes may result hgher potetal for speedg ad a greater propesty for crashes. The research showed that as v/c rato creased the umber of crashes ad crash rate decreased dcatg that cogesto may result reduced speeds ad as a result a lower umber of crashes ad crash rates. The research pots to the eed to clude operatoal parameters performg road safety evaluatos. I addto to the v/c rato, operatg speed ad desty should be cosdered to better estmate the safety performace of a roadway. Future research may volve determg crash modfcato factors for operatoal parameters.

12 328 Jace R. Dael ad Eugee Maa / Proceda Socal ad Behavoral Sceces 16 (2011) Table 8. Goodess-of-Ft for Models Usg Capacty ad V/C Rato Model Relatg Safety ad Capacty Modelg Crash Couts Modelg Crash Rates Model Relatg Safety ad V/C Rato Modelg Crash Couts Modelg Crash Rates Negatve Bomal Negatve Bomal Negatve Bomal Negatve Bomal Number of observatos Log lkelhood fucto Restrcted log lkelhood Ch-squared Sgfcace level REFERENCES Hghway Capacty Maual(2010), Trasportato Research Board, Washgto, D.C. (I-Press). Bauer, K. M. ad D. W. Harwood (1996), Statstcal Models of At-Grade Itersecto Accdets, Report FHWA-RD , Federal Hghway Admstrato, U.S. Departmet of Trasportato. Gross, Frak, Paul P. Jovas, ad Kmberly Eccles (2009), Safety Effectveess of Lae ad Shoulder Wdth Combatos o Rural, Two-Lae, Udvded Roads, Joural of the Trasportato Research Board, No. 2103, Trasportato Research Board, Washgto, D.C., 2009, pp Huag, H.F., J.R. Stewart ad C.V. Zegeer (2002), Evaluato of Lae Reducto Road Det Measures o Crashes, Joural of the Trasportato Research Board 1784, Trasportato Research Board, Natoal Research Coucl, Washgto, D.C., pp Kooov, Jake, Barbara Baley ad Brya K. Allery (2008), Relatoshps Betwee Safety ad Both Cogesto ad Number of Laes o Urba Freeways, Joural of the Trasportato Research Board 2083, Trasportato Research Board, Natoal Research Coucl, Washgto, D.C., 2008, pp Pera, Jua C, Ja Joh Lu, Xagl Xe, Mchael Weg ad Deborah Syder (2002), Developmet of Models to Quatfy the Impacts of Sgalzato of Itersecto Crashes, Preseted at the 81 st Aual Meetg of the Trasportato Research Board, Washgto, D.C., Jauary Regarasu, Terrace M., Toru Hagwara, ad Masayuk Hrasawa (2009), Effects of Road Geometry ad Cross-Secto Varables o Traffc Accdets Study Usg Homogeeous Road Segmets, Joural of the Trasportato Research Board No. 2102, Trasportato Research Board, Natoal Research Coucl, Washgto, D.C., 2009, pp Rogess, R.O, D.B. Fambro ad D.S. Turer (1982), Before-After Accdet Aalyss for Two Shoulder Upgradg Alteratves, Joural of the Trasportato Research Board 855, Trasportato Research Board, Natoal Research Coucl, Washgto, D.C., pp Vogt, Adrew ad Joe Bared, Accdet Models For Two-Lae Rural Segmets ad Itersectos (1998), Joural of the Trasportato Research Record 1635, Trasportato Research Board, Natoal Research Coucl, Washgto, D.C., 1998, pp Zegeer, Charles V. ad Forrest Coucl (1995), Safety Relatoshps Assocated wth Cross-Sectoal Roadway Elemets, Joural of the Trasportato Research Record 1512, Trasportato Research Board, Natoal Research Coucl, Washgto, D.C., pp