ISSN 1822-427X/eISSN 1822-4288 2018 Volume 13 Issue 3: 238 260 https://doi.org/10.7250/bjrbe.2018-13.414 ANALYSIS AND ASSESSMENT OF LITHUANIAN ROAD ACCIDENTS BY AHP METHOD MARIUS JAKIMAVIČIUS * Dept of Roads, Vilius Gedimias Techical Uiversity, Vilius, Lithuaia Received 08 Jue 2018; accepted 23 August 2018 Abstract. Lithuaia road accidets were evaluated based o the geographic iformatio systems ad multi-criteria method of Aalytical Hierarchy Process This paper presets the methodology for selectig ad rakig high accidet cocetratio sectios o the roads of atioal sigificace. Methodology ivolves the followig process phases: 1) preparatio of spatial data of the road accidets; 2) estimatio of road sectios with a high accidet rate; 3) calculatio of spatial statistics for estimatio of accidet poits ad hot spots; 4) selectig idicators for multi-criteria assessmet; 5) calculatio by Aalytical Hierarchy Process method ad rakig the selected high accidet cocetratio sectios. Assessmet of spatial clusterig of accidets ad hot spots was carried out * followig geo-iformatio techologies ad usig Getis-Ord G i statistics ad poit desity fuctios. This geospatial criterio was itegrated ito multicriteria assessmet for rakig the high accidet cocetratio sectios by usig the Aalytical Hierarchy Process method. Preseted method is useful for various agecies i order to improve their plaig ad maagemet strategies for better traffic coditios as well as to reduce the umber of accidets. The result of the research presets selectio methodology of dagerous accidet sectio ad rakig of the teth the most dagerous sectios ivolvig geographic iformatio systems ad Aalytical Hierarchy Process method. Keywords: accidet coefficiet, Aalytical Hierarchy Process (AHP), Getis-Ord G i*, GIS, multi-criteria aalysis, road accidet. * Correspodig author. E-mail: marius.jakimavicius@vgtu.lt 238 Copyright 2018 The Author(s). Published by RTU Press This is a Ope Access article distributed uder the terms of the Creative Commos Attributio Licese (http://creativecommos.org/liceses/by/4.0/), which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial author ad source are credited.
Itroductio Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method Road accidets (hereafter accidet) have bee ad are cotiuig to be the major cotributor of huma ad ecoomic costs to requirig cocerted multi-discipliary efforts for effective ad sustaiable prevetio. Furthermore, accidets are oe of the top te causes of the global burde of disease ad ijury. Traffic accidets probably will be i third place by 2020, whe measured i disability (World Health Orgaizatio, 2013). With oly 25 percet of all motorized vehicles, developig coutries accout for 86 percet of all road traffic deaths (Lagarde, 2011). Over 20 years, almost 100 000 accidets occurred o the roads ad streets of Lithuaia where more tha 10 000 people were killed, ad 120 399 were ijured. I 2017, 3192 fatal ad ijury, accidets took place o the roads ad streets of Lithuaia where 192 people were killed, ad 3752 were ijured. I compariso to 2015, the umber of accidets ad people ijured icreased by 8.1 percet ad 7.8 percet, respectively. However, the umber of people killed decreased by 22.3 percet (Lithuaia Road Admiistratio, 2017). The most of these accidets result from huma error, maily carelessess of the drivers or pedestrias. Hece, it is ofte possible to reduce the probability of accidet occurrece, ad its severity. The mai meas are aalysis of the accidet circumstaces ad implemetig the appropriate solutios ivolvig the applicatio of proper traffic cotrol devices. Also suitable roadway desig practices, ad useful traffic police activities. However, the task of devisig effective solutios warrats aalysis of spatial ad temporal patters i the locatig accidets o road segmets. Applicatio of geospatial techology allows to perform aalysis ad to idetify accidets desity i road sectios (Cheg & Washigto, 2008; Li, Zhu, & Sui, 2007). The o-radom distributio of accidets, both i time ad space, ofte raises questios about the locatio ad the reasos for accidet locatio (Mohaymay, Shahri, & Mirbagheri, 2013; Shafabakhsh, Famili, & Bahadori, 2017). Importatly, spatial thikig helps to defie the patters of accidets, to aalyse spatial autocorrelatio based o the feature locatios. This aalysis idetifies ad suggests the reasos for the patter characteristics (dispersed or clustered distributio). Geographic iformatio system (GIS) techology has bee a effective tool for visualizatio of the accidet data ad aalysis of hot spots. Therefore, it is used by may traffic agecies (Dereli, & Erdoga, 2017; Erdoga, Yilmaz, Baybura, & Gullu, 2008; Schuurma, Ciamo, Crooks, & Hameed, 2009 Kumar, & Toshiwal, 2017). 239
Meawhile, some researchers have performed the aalysis of accidets ad suggested the accidet predictio models. Predictio models are based o the classificatio of the roads ito homogeeous roads groups accordig to its sigificace, differet carriageway width, the permissible speed limit ad Average Aual Daily Traffic (AADT i vpd) (Jasiūieė & Čygas, 2013). Selectig ad prioritizig road sectios (hereafter sectio) which have higher tha the average accidet savig potetial i each road category was required for rakig the potetially dagerous road spots (Jasiūieė, Čygas, Ratkevičiūtė, & Peltola, 2012). Ait-Mlouk, Gharati, & Agouti (2017) used multi-criteria methods to select the most importat criteria from the sets of idicators, related with traffic safety. For example, the characteristics of a accidet, traffic coditios, evirometal coditios, road coditios, huma coditios ad geographic coditios. Saaty (1995) applied the Aalytical Hierarchy Process (AHP) method to the trasportatio plaig ad accidet rakig. Meawhile, other researches preseted a classificatio model of high accidet cocetratio sectios i the road etworks usig a decisio support system based o the cluster aalysis techiques (Dell Acqua, De Luca, & Mauro, 2011). Moreover, some scietists proposed MOORA method for group decisio-makig (Staujkic, 2016). Multi-criteria methods, especially AHP, are widely used for evaluatio of differet idicators to calculate safety coditios ad estimate the sigificace of trasport system elemets with sigificat ifluece o traffic safety (Aghdaie, Hashemkhai Zolfai, & Zavadskas, 2012; Hajeeh, 2012; Podvezko & Sivilevičius 2013; Facello, Carta, & Fadda, 2015. Fially, Che et. al. (2016), Mostafa & El-Gohary (2014), ad Sivilevičius & Maskeliūaitė (2010) used the AHP method to evaluate strategic ad ecoomic factors. This paper itroduces the methodology for assessmet of the sectios of roads of atioal sigificace with high accidet coefficiet i Lithuaia. First, the sectios with high accidet cocetratio were estimated. The, the accidet coefficiet ad the Getis-Ord G i * statistics z-score value was calculated for each sectio by usig GIS techologies. Scietific ovelty of this research is the fact of supplemetig the criteria of traffic safety ad pavemet coditios with criteria from GIS aalysis for multi-criteria AHP method assessmet ad rakig. Alteratives to te sectios with the highest accidet coefficiet have bee raked accordig to the AHP method. Z-score values have bee icluded i the rakig process. Z-score criterio shows the depedece of the spatial distributio of accidet poits ad idetifies the areas with high accidet cocetratio. 240
1. Overview of Lithuaia accidets statistics Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method This research was developed by usig the accidet data for all roads of atioal sigificace from 2014 to 2017. This period was selected due to two reasos. Firstly, the use of 3 5 years data for predictio purposes is recommeded i the scietific literature, ad the larger amout of observatio data allows to assess the data dyamics ad to make a more reliable predictio. Secodly, the methodology for determiig high accidet cocetratio sectios ad black spots, approved by the Miistry of Trasport ad Commuicatios of the Republic of Lithuaia, declares to use accidet observatios of four years. Road etwork, AADT, ad accidet poits were take for aalysis ad assessmet of sectios with high accidet cocetratio. Data from the Lithuaia Road Iformatio System (LAKIS) database was used for this research. I 2014, the umber of vehicles decreased by oe third upo chaged vehicle registratio procedure i July 2014. Vehicles, which fail to meet the requiremets of compulsory civil liability isurace ad techical ispectio, are removed from the register (Iteratioal Trasport Forum, 2017; Lithuaia Road Admiistratio, 2017). However, i 2017, i compariso to 2015, the vehicle stock of Lithuaia icreased by 4 percet from 1 549 158 to 1 614 040 vehicles. Accordigly, the umber of vehicles per 1000 ihabitats icreased from 544 to 571. I compariso to 2015, the umber of accidets ad people ijured icreased by 8.0 percet ad 7.5 percet, respectively, however, the Table 1. ad their victims i 2013 2017 (Lithuaia Road Admiistratio, 2017) Killed Ijured Years Total Per 1 millio ihabitats Per 1000 vehicles Total Per 1 millio ihabitats Per 1000 vehicles Total Per 1 millio ihabitats Per 1000 vehicles 2013 3391 1152 1.49 256 87 0.11 4007 1361 1.76 2014 3255 1138 2.20 267 91 0.17 3785 1331 2.61 2015 3033 1050 1.90 242 84 0.16 3594 1244 2.32 2016 3201 1124 1.20 192 67 0.11 3750 1317 2.32 2017 3192 1136 2.10 192 68 0.13 3752 1335 2.44 Total 12959 953 15261 241
umber of people killed decreased by 21 percet (Lithuaia Road Admiistratio 2017). Table 1 presets the umber of accidets ad their victims from 2013 to 2017. Recetly, the traffic safety idicators have show good treds i Lithuaia. I 2017, the vehicle fleet of Lithuaia icreased by 4.0 percet i compariso to 2015, ad the umber of automobiles for 1000 ihabitats icreased from 544 i 2015 to 571 i 2017; however, the umber of fatalities per 1 millio ihabitats has bee decreasig sice 2014. I compariso to 2014, the umber of fatalities per 1 millio ihabitats has decreased by 27.0 percet. Dyamics of vehicles ad fatalities is preseted i Figure 1. This research aalyses the accidets data for the roads of atioal sigificace for the period of four years from 2014 to 2017 i the etire territory of Lithuaia. From aalyse were excluded accidets i the cities of Lithuaia. Accordig to the level of sigificace, the roads i Lithuaia are classified o the roads of atioal sigificace ad the roads of local sigificace. Accordig to the purpose, the roads of atioal sigificace are further classified to the mai, atioal, ad regioal roads. Types of roads differ from each other by their fuctio, the level of traffic quality, geometric parameters. The total legth of the roads of atioal sigificace is 21 244 km, where the mai roads make up 1751 km, atioal 4925 km, ad regioal 14 568 km (Lithuaia Road Admiistratio, 2017). Table 2 presets the distributio of accidets o the roads of atioal sigificace. 87 773 91 84 510 544 67 68 566 571 2013 2014 2015 2016 2017 Years Fatalies per 1 millio ihabitats Number of vehicles per 1000 ihabitats Figure 1. Number of vehicles ad fatalities i 2013 2017 (Lithuaia Road Admiistratio, 2017) 242
Table 2. ad their victims o atioal sigificace roads i 2013 2016 (Lithuaia Road Admiistratio, 2017) Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method 2013 2014 2015 2016 Road sigificace Fatalities Ijured Fatalities Ijured Fatalities Ijured Fatalities Ijured Mai 249 49 328 260 49 317 227 51 295 264 43 352 Natioal 434 79 572 419 60 539 449 74 592 420 43 564 Regioal 350 45 431 349 62 433 342 49 437 325 34 395 Total 1033 173 1331 1028 171 1289 1018 174 1324 1009 120 1331 I 2016, 31 percet of the total umber of accidets occurred o the roads of atioal sigificace. The highest umber of accidets ad victims i 2016 was recorded o the mai road A1 Vilius Kauas Klaipėda. I additio, there are settlemets, bus statios, pedestrias, ad bicyclists, causig a high risk of accidets i the road eviromet, sice high speeds prevail o the mai roads (Lithuaia Road Admiistratio, 2017). 2. Methodology The methodology ivolves geospatial techologies. GIS techologies were used to prepare the accidet data for aalysis by idetifyig the accidet sectios ad calculatig the accidet coefficiet i these sectios. The geo-processig model, which creates 500 meters sectios from each accidet alog the road ad performs accidets aalysis for each sectio, was developed. Furthermore, GIS was applied for calculatio of spatial statistics for the accidet poits. Methodology for 1. GIS data preparatio 2. sectios estimatio o atioal sigificace roads ad calculatio of accidet coefficiet 3. Evaluatio of road accidets decity ad hot spots based o GIS spatial statistics 4. Selectig idicators for multicriteria assessmet ad rakig 5. High accidet sectio rakig by AHP Figure 2. Steps of accidets aalysis ad assessmet 243
rakig ad assessmet of idetified accidet sectios that have a high umber of accidets icludes AHP multi-criteria method. The steps of aalysis ad assessmet are described i Figure 2. The first step of accidet aalysis is to select the accidet data from LAKIS database ad filter them for the relevat aalysis period. Next, spatial aalysis was performed with ArcGIS software to estimate the accidet sectios ad to calculate their accidet coefficiet. Data preparatio was followed by aalysis of the accidet hot spots ad estimatio of z- score. This criterio was used i AHP aalysis i combiatio with the other five criteria, idicatig safety ad pavemet coditios. 2.1. data preparatio ad accidet sectios estimatio The data o the poits of accidets, which took place o the roads of the atioal sigificace of Lithuaia, were take from LAKIS geodatabase seekig to perform the aalysis. The, the accidet poit data were filtered for the period from 2014 to 2017. This dataset cosists of 16 202 poits objects. The geo-processig model was developed to idetify the accidet sectios o the road. This model creates 500 meters sectios from each road accidet alog the road directio. poits itersect with these sectios cout the umber of accidets i each sectio. Sectios satisfyig coditio Eq. (1), are used i further research (Road ad Trasport, 2011): A actual > A mi, (1) where A actual the umber of accidets i the road sectio over four years, umber; A mi miimum defied accidets umber over four years for icludig the sectio i further aalysis, umber. Accordig to methodology, A mi = 3. Sectios satisfyig this coditio, are used i further aalysis. Geo-processig model updates overlapped with accidet sectios ad merged them ito oe sectio. Updated sectios start ad ed with the accidet. Seve hudred fifty-ie (759) accidet sectios were idetified durig aalysis. Locatios of accidet sectios are preseted i Figure 3. Next geo-processig task is to calculate the accidet coefficiet for each sectio. Accidet sectios were itersected with the polylie layer. This layer represets AADT o the roads of atioal sigificace, to calculate accidet coefficiet. It tured out 759 accidet sectios have the ecessary attribute values to perform the calculatio of accidet coefficiet accordig to Eq. (2): 244
Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method Figure 3. Accidet sectios AC j 365 6 Aj 10, (2) AADT L m j j where: AC j the value of a accidet coefficiet i the accidet sectio j; A j the umber of accidets i the sectio j, i umbers; AADT j average aual daily traffic i accidet sectio j, i vpd; L j the legth of the accidet sectio, i meters; m year, i umbers. The calculated accidet coefficiet varies from 0.1 to 22.6 i 759 accidet sectios o the roads of atioal sigificace. 2.2. Calculatio of accidet hot spots The Hot Spot Aalysis calculates the Getis-Ord G i * statistics for each accidet feature i the dataset. Formulas are give i Eqs (3) (5). The resultat z-scores ad p-values tell where features with either high or low values cluster spatially. GIS calculatio works by lookig at each feature withi the cotext of eighbourig features (Satria & Castro, 2016). A feature with a high value is cosiderig beig a statistically sigificat hot spot. Statistically sigificat hot spot have a high value ad is surrouded by other features with high values. The local sum for a feature ad its eighbours is compared proportioally to the sum of all features. If the local sum is very differet from the expected local sum, whe differece is too large to be the result of a radom chace, statistically sigificat z-score results. The Getis-Ord G i * statistics are give by Eqs (3) (5): (Ebdo, 1991; Esri, 2017): 245
G * i S j1 wx X w ij j ij j1, (3) wij 2 wij j 2 j 1 1 1 X x j j1, (4) x 2 j 2 j1 S X, (5) where x j the attribute value of the feature j, a umber of people ivolved i the accidet, i umbers; w ij is the spatial weight betwee the accidet feature i ad j, distace i meters, equal to the total umber of accidet features, i umbers. The G i * statistic, retured for each feature i the dataset, is a z-score. Z-scores are measures of S stadard deviatio. Whe ArcGIS spatial statistics tool returs a z-score of +2.5, it is iterpreted that +2.5 stadard deviatios away from the mea is Esri (2017). Z-score Figure 4. Gi* statistic distributio model 246
Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method Figure 5. Accidet hot spots values are associated with a stadard ormal distributio. This distributio relates stadard deviatios with probabilities ad allows sigificace ad cofidece to be attached to z-scores. The critical z-score values whe usig a 95 percet cofidece level are 1.96 ad +1.96 stadard deviatios. Whe the z-score is betwee 1.96 ad +1.96, the ull hypothesis caot be rejected. The G i * statistic distributio model is preseted i Figure 4. Figure 6. Accidet hot spots for Dataset 1 247
For statistically sigificat positive z-scores, the large the z-score shows itese is the clusterig of high values (hot spot). For statistically sigificat egative z-scores, the small the z-score shows itese the clusterig of low values (cold spot). This aalysis was performed for the accidets o roads of atioal sigificace from 2014 to 2017. The area of aalysis was limited by polygo. Polygo was costructed from the accidet sectios. Hot Spot aalysis idetified 66 accidet sectios show i Figure 5. These sectios were evaluated like hot spots for the accidet data for the period of 2014 2017. Z-score i these sectios varies from 3.99 to 11.54. Upo calculatig the hot spot, accordig to Figure 4, validatio of the used hot spot detectio method followed. Validatio was doe by usig the data from differet years ad comparig the result. Eight-year data was divided i two sets: years 2011, 2013, 2015, ad 2017 (Dataset 1) ad years 2010, 2012, 2014, ad 2016 (Dataset 2). Figures 6 ad 7 presets the validatio results of hot spots aalysis by comparig dataset 1 ad dataset 2. Dataset 1 has 16 932, ad Dataset 2 has 14 694 accidet poits. Validatio results idetified hot spots i seve sectios of road accordig to data from the Dataset 1. Accordig to data from Dataset 2 there were idetified hot spots i eight sectios of road. Validatio z-scores are preseted i Table 3. Compariso of z-scores from the two datasets shows spatial locatio ad desity of accidet poit data is similar to the dataset for the period of 2014 2017. Comparig sectios of 2014 2017 accidets data with Dataset 1 ad Dataset 2 recogitio of hot spots (90 percet sigificace level) accuracy varies 10 20 percet. Figure 7. Accidet hot spots for Dataset 2 248
2.3. Criteria for multi-criteria rakig Te accidet sectios with the highest accidet coefficiet were selected for further multi-criteria rakig ad assessmet. The selected sectios with criterio values are preseted i Table 3. The followig criteria were selected for AHP multi-criteria aalysis: CR1 total umber of fatalities i the accidet sectio; CR2 total umber of ijuries i the accidet sectio; CR3 total umber of people ivolved i the accidet; CR4 total umber of damaged vehicles i the accidet sectio; CR5 percetage umber of pavemet defects i the accidet sectio; CR6 z-score of hot spots. All criteria, except for CR6, were selected based o the data, stored o LAKIS database, ad the questioaire for 32 experts. Experts were asked to rak 15 criteria, accordig to their egative impact o the accidets. Five criteria with the highest raks were used for further aalysis takig ito accout the aswers i the expert questioaire. CR6 was added for AHP aalysis to evaluate the desity ad frequecy of accidet spatial locatio. Six criteria were used i AHP aalysis. These criteria represet three groups: road safety coditios, road pavemet coditios ad geographic cocetratio of accidets (estimatio was performed by GIS Hot Spot Aalysis). Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method Table 3. Sectios ad criterios values Criterios for AHP Z-score Sectio Number of the road (sectio from to i km) CR1 CR2 CR3 CR4 CR5 CR6 Accidet coefficiet Dataset 1 Dataset 2 1 A6 (17.640 18.525) 3 3 21 20 0.06 3.41 22.63 5.33 6.08 2 218 (13.954 14.454) 0 5 9 4 0.62 3.39 18.97 0.11 0.65 3 133 (20.835 21.453) 1 3 8 7 5.92 3.40 18.81 3.52 3.70 4 2904 (21.450 22.050) 0 0 10 9 7.85 3.99 16.44 4.24 3.28 5 132 (11.450 12.500) 1 7 24 19 0.10 8.64 16.30 8.04 4.40 6 A1 (98.520 101.503) 3 17 141 134 0.21 11.54 15.27 8.58 10.00 7 A9 (48.936 50.100) 2 1 13 12 1.53 5.15 13.88 3.70 5.51 8 225 (28.570 29.070) 1 5 7 5 0.08 1.66 13.24 0.11 0.47 9 123 (65.600 66.950) 0 0 10 9 0.21 3.41 12.61 4.24 2.88 10 3415 (9.048 9.548) 1 1 7 4 9.22 1.42 12.48 0.11 4.24 249
2.4. Problem descriptio ad rakig by AHP method The primary objective of this research is to idetify the most problematic sectios o roads of atioal sigificace i respect to traffic safety. Te accidet sectios were selected for further aalysis ad assessmet. The AHP was utilized to aalyse the problem. Figure 8 presets the hierarchy of this problem i the AHP structure. Aalytical Hierarchy Process has three uderlyig cocepts. The first is structurig the complex decisio problem how a hierarchy of goal, criteria, ad alteratives. The secod is pairwise comparisos of elemets at each level of the hierarchy cocerig each criterio o the previous level. The third is vertically sythesizig the judgmets over the differet levels hierarchy. The basic theory of AHP is: the problem uder study has idepedet alteratives (A1, A2, A3, ad A) with the weights (W1, W2, W3, ad W ) respectively (i research case = 10) (Al-Harbi, 2001; Saaty, 1990b). The decisio maker does ot kow i advace the values of the weights, but decisio maker is makig pairwise comparisos of the differet alteratives like the oes, give i Eq. (6). 1 1 1... a11 a12... a 1 2 1 a a a A 21 22... 2 2 2 2............... 1 2, (6)............ a1 a2... a... 1 2 where A pairwise compariso matrix; a12 value is supposed to approximate the relative importace of A1 to A2, i.e., a 12 ω 1 ω 2 ; ω 1, ω 2, ω 3, ad ω relative priorities (weights) for the criteria; the umber of idepedet alteratives. Accidet sectio rakig CR1 CR2 CR3 CR4 CR5 CR6 Sectio 1 Sectio 2 Sectio 3 Sectio 4 Sectio 5 Sectio 6 Sectio 7 Sectio 8 Sectio 9 Sectio 10 Figure 8. Hierarchy of the accidet sectios ad criterios 250
Compariso matrix is calculated: Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method i 1. a ij, i, j = 1, 2,,. j 2. a ij =1, i, j = 1, 2,,. All diagoal cells have the value 1. 3. a ji = 1 j, a ji, i, j =1, 2,,. a ij i i 4. a ij 1, A i is more preferred tha A j. If aij < 1, A i is less preferred j tha A j. The values assiged to aij accordig to (Saaty 1990a; Saaty & Vargas 2012). AHP scale are usually i the iterval of 1 9 or their reciprocals: 1 i equal preferred to j; 3 i moderate more preferred tha j; 5 i strogly more preferred tha j; 7 i very strogly more preferred tha j; 9 i extremely more preferred tha j. 2, 4, 6, 8 are itermediate values. Oce the matrix A is built, it is possible to derive from A the ormalized pairwise compariso matrix A orm by makig equal to 1 the sum of the etries o each colum, i.e., each etry aij of the matrix A orm is computed i Eq. (7): aij aij, (7) a i1 where a ij relative importace value i matrix A row i ad colum j; the umber of alteratives. The Eigevector w (-dimesioal colum vector), built by averagig the etries o each row of A orm, is described i Eq. (8): aij j1 wi, (8) where aij etry of ormalized pairwise compariso matrix A orm i row i ad colum j; the umber of alteratives. The it is ecessary to check cosistecy for each pairwise compariso matrix. The cosistecy ratio (CR) calculated, accordig to the followig steps: calculate the eigevector or the relative weights ad maximum eigevalue λ max for each matrix of order by Eq. (9): 1 ( Aw) i max ; (9) i1 wi compute the cosistecy idex (CI) for each matrix of order by Eq. (10): CI max 1 ; (10) ij 251
the cosistecy ratio is the calculated usig Eq. (11): CR = CI, (11) RI where RI is a kow radom CI (Saaty 1990a; Saaty & Vargas 2012). obtaied from a large umber of simulatio rus ad varies depedig o the order of the matrix, preseted i Table 4. A value of CR o more tha 10 percet is cosidered acceptable. Whe values of CR are more tha 10 percet require the decisio maker to revise his judgmets. I ext step, it is ecessary to perform model sythesis ad calculate the overall priority for each alterative. To calculate priorities, it is ecessary to take ito accout preferece of alteratives for each criterio ad the fact each criterio has a differet weight. 3. Aalysis results ad discussio AHP multi-criteria method was used to aalyse the accidet sectios ad to idetify the most dagerous oes. First, a pairwise compariso was made amog the various criteria to rak them based o their importace. Table 5 presets these results. Next step of AHP is to compare aalysed road sectios to the highest accidet coefficiet cocerig each criterio. The pairwise comparisos Table 4. Radom Idex values 2 3 4 5 6 7 8 9 10 RI 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.51 Table 5. Pairwise compariso of criterios Criterio CR1 CR2 CR3 CR4 CR5 CR6 Eigevector Priority (rak) CR1 1 2 3 4 6 5 0.378 1 CR2 1/2 1 2 3 5 4 0.247 2 CR3 1/3 1/2 1 2 4 3 0.159 3 CR4 1/4 1/3 1/2 1 3 2 0.102 4 CR5 1/6 1/5 1/4 1/3 1 1/3 0.041 6 CR6 1/5 1/4 1/3 1/2 3 1 0.072 5 λ max = 6.235, CI = 0.047, CR = 0.038 (acceptable) 252
are show i Tables 6 11. Also, the priority for the criterio is calculated i each Table. Sectios rakig was based o actual data of criteria i each sectio. Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method Table 6. Pairwise compariso of the accidet sectios cocerig the total umber of fatalities (CR1) Sectios Sectios 1 2 3 4 5 6 7 8 9 10 Eigevector Priority (rak) 1 1 9 3 9 3 1 6 6 9 3 0.260 2 2 1/9 1 1/3 1 1/3 1/9 1/6 1/3 1 1/3 0.023 8 10 3 1/3 3 1 3 1 1/6 1/3 1 3 1 0.063 4 6 4 1/9 1 1/3 1 1/3 1/9 1/6 1/3 1 1/3 0.023 8 10 5 1/3 3 1 3 1 1/6 1/3 1 3 1 0.063 4 6 6 1 9 6 9 6 1 3 6 9 6 0.288 1 7 1/6 6 3 6 3 1/3 1 3 6 3 0.137 3 8 1/6 3 1 3 1 1/6 1/3 1 3 1 0.058 7 9 1/9 1 1/3 1 1/3 1/9 1/6 1/3 1 1/3 0.023 8 10 10 1/3 3 1 3 1 1/6 1/3 1 3 1 0.063 4 6 λ max = 10.584, CI = 0.065, CR = 0.043 (acceptable) Table 7. Pairwise compariso of the accidet sectios cocerig the total umber of ijuries (CR2) Sectios Sectios 1 2 3 4 5 6 7 8 9 10 Eigevector Priority (rak) 1 1 1/2 1 2 1/3 1/7 3 1/3 3 2 0.062 6 2 2 1 2 4 1/2 1/5 3 1 4 3 0.103 4 3 1 1/2 1 2 1/2 1/7 3 1/2 3 2 0.067 5 4 1/2 1/4 1/2 1 1/5 1/9 1/2 1/3 1 1/2 0.028 9 5 3 2 2 5 1 1/3 6 2 7 6 0.174 2 6 7 5 7 9 3 1 7 3 8 7 0.342 1 7 1/3 1/3 1/3 2 1/6 1/7 1 1/5 2 1 0.036 8 8 3 1 2 3 1/2 1/3 5 1 5 4 0.124 3 9 1/3 1/4 1/3 1 1/7 1/8 1/2 1/5 1 1/2 0.025 10 10 1/2 1/3 1/2 2 1/6 1/7 1 1/4 2 1 0.038 7 λ max = 10.455, CI = 0.051, CR = 0.034 (acceptable) 253
Table 8. Pairwise compariso of the accidet sectios cocerig the total umber of participated people i accidet sectio (CR3) Sectios Sectios 1 2 3 4 5 6 7 8 9 10 Eigevector Priority (rak) 1 1 3 5 3 1/2 1/5 2 4 3 4 0.119 3 2 1/3 1 2 1/2 1/5 1/8 1/3 2 1/2 3 0.044 7 3 1/5 1/2 1 1/2 1/5 1/9 1/3 2 1/3 2 0.033 8 4 1/3 2 2 1 1/4 1/7 1/2 2 1 2 0.052 6 5 2 5 5 4 1 1/6 4 5 4 5 0.169 2 6 5 8 9 7 6 1 7 9 8 9 0.393 1 7 1/2 3 3 2 1/4 1/7 1 3 2 3 0.080 4 8 1/4 1/2 1/2 1/2 1/5 1/9 1/3 1 1/3 1 0.026 9 10 9 1/3 2 3 1 1/4 1/8 1/2 3 1 2 0.058 5 10 1/4 1/3 1/2 1/2 1/5 1/9 1/3 1 1/2 1 0.026 9 10 λ max = 10.952, CI = 0.106, CR = 0.070 (acceptable) Table 9. Pairwise compariso of the accidet sectios cocerig the total umber of damaged vehicles (CR4) Sectios Sectios 1 2 3 4 5 6 7 8 9 10 Eigevector Priority (rak) 1 1 5 2 3 1/2 1/6 3 2 6 2 0.121 3 2 1/5 1 1/2 1/3 1/5 1/9 1/3 1 1/2 1 0.028 10 3 1/2 2 1 1/2 1/5 1/9 1/3 2 1/2 2 0.044 8 4 1/3 3 2 1 1/3 1/8 1/2 1/3 1 2 0.050 6 5 2 5 5 3 1 1/5 2 4 3 5 0.147 2 6 6 9 9 8 5 1 7 8 7 9 0.397 1 7 1/3 3 3 2 1/2 1/7 1 2 2 3 0.080 4 8 1/2 1 1/2 3 1/4 1/8 1/2 1 1/3 2 0.047 7 9 1/6 2 2 1 1/3 1/7 1/2 3 1 2 0.058 5 10 1/2 1 1/2 1/2 1/5 1/9 1/3 1/2 1/2 1 0.029 9 λ max = 11.119, CI = 0.124, CR = 0.082 (acceptable) 254
Table 10. Pairwise compariso of the accidet sectios cocerig the percetage umber of pavemet defects (CR5) Sectios Sectios 1 2 3 4 5 6 7 8 9 10 Eigevector Priority (rak) 1 1 1/2 1/7 1/8 1/2 1/2 1/3 1 1/2 1/9 0.023 9 2 2 1 1/6 1/7 3 2 1/2 3 2 1/6 0.055 5 3 7 6 1 1/4 5 3 2 6 4 1/6 0.133 3 4 8 7 4 1 7 6 4 9 5 1 0.254 2 5 2 1/3 1/5 1/7 1 1/3 1/5 2 1/3 1/9 0.028 8 6 2 1/2 1/3 1/6 3 1 1/4 3 1 1/6 0.044 6 7 3 2 1/2 1/4 5 4 1 4 3 1/6 0.090 4 8 1 1/3 1/6 1/9 1/2 1/3 1/4 1 1/2 1/9 0.021 10 9 2 1/2 1/4 1/5 3 1 1/3 2 1 1/9 0.042 7 10 9 6 6 1 9 6 6 9 9 1 0.310 1 λ max = 11.149, CI = 0.128, CR = 0.085 (acceptable) Table 11. Pairwise compariso of the accidet sectios cocerig spatial statistics value z-score (CR6) Sectios Sectios 1 2 3 4 5 6 7 8 9 10 Eigevector Priority (rak) 1 1 3 3 4 4 4 5 5 6 6 0.287 1 2 1/3 1 1 2 2 3 4 4 5 5 0.156 2 3 3 1/3 1 1 2 2 3 4 4 5 5 0.156 2 3 4 1/4 1/2 1/2 1 1 2 3 3 4 4 0.102 4 5 1/4 1/2 1/2 1 1 1 2 2 3 3 0.081 5 6 1/4 1/3 1/3 1/2 1 1 2 2 3 3 0.072 6 7 1/5 1/4 1/4 1/3 1/2 1/2 1 1 2 2 0.044 7 8 8 1/5 1/4 1/4 1/3 1/2 1/2 1 1 2 2 0.044 7 8 9 1/6 1/5 1/5 1/4 1/3 1/3 1/2 1/2 1 1 0.028 9 10 10 1/6 1/5 1/5 1/4 1/3 1/3 1/2 1/2 1 1 0.028 9 10 λ max = 10.363, CI = 0.040, CR = 0.027 (acceptable) 255
The model sythesis was performed, ad the overall composite weight of the differet accidet sectios was calculated accordig to Eq. (12). Iput data was take from Table 5 11. The results are give i Table 12. ( wcr, j wsec, ij ) j1 ocwsec, i, (12) where ocw sec, i the overall composite weight for the sectio i; w cr,j the eigevalue of j criterio; w sec,ij the eigevalue of the accidet sectio i cocerig j criterio. The ext process is to perform a sesitivity aalysis. Sesitivity aalysis allows uderstadig how soud origial decisio is. It is ecessary to make chages to the weights of the criterio ad see how they chage the overall priorities of the alteratives to perform a sesitivity aalysis. To exemplify sesitivity, the sceario, where all criteria have the same weight, was selected. Sesitivity aalysis idetified the stability of the AHP calculatio model. The rakig of top three road sectios showed the same results: the worst from the poit of safety is Sectio 6 road A1 from 98.520 km to 101.503 km. I the secod place, there is Sectio 1 road A6 from 17.640 km to 18.525 km, ad i the third place there is Sectio 5 road 132 from 11.450 km to Table 12. The overall priority of the differet accidet sectios Sectio CR1 CR2 CR3 CR4 CR5 CR6 Criterio weights >> 0.378 0.247 0.159 0.102 0.041 0.072 Criterio weights for sesitivity aalysis 0.167 0.167 0.167 0.167 0.167 0.167 Overall composite weight Overall composite weight* Rak 1 0.260 0.062 0.119 0.121 0.023 0.287 0.166 0.146 2 2 2 0.023 0.103 0.044 0.028 0.055 0.156 0.057 0.068 7 8 3 0.063 0.067 0.033 0.044 0.133 0.156 0.067 0.083 5 5 4 0.024 0.028 0.052 0.050 0.254 0.102 0.047 0.085 9 4 5 0.063 0.174 0.169 0.147 0.028 0.081 0.116 0.111 3 3 6 0.280 0.342 0.393 0.397 0.044 0.072 0.300 0.255 1 1 7 0.145 0.036 0.080 0.080 0.090 0.044 0.091 0.079 4 7 8 0.058 0.124 0.026 0.047 0.021 0.044 0.066 0.053 6 9 9 0.023 0.025 0.058 0.058 0.042 0.028 0.034 0.039 10 10 10 0.063 0.038 0.026 0.029 0.310 0.028 0.055 0.082 8 6 Rak* Note: * whe criterio weights are the same. 256
12.500 km. Aalysis idetified whe CR1 (total umber of fatalities) weighs i the rage of 0.378 0.167 accidet sectios 6, 1, ad 5 are equally preferred. Rakig of accidet sectios based o the level of importace obtaied for the differet criteria takig ito cosideratio comparative judgmets. The AHP methodology allows determiig the most cosistet alterative with selected criterio ad judges give the level of importace. There were take criterios represetig traffic safety, pavemet coditios for multi-criteria aalysis. Furthermore, this AHP research icluded spatial statistics CR6 (z-score). Estimated spatial statistics represets spatial relatios of the accidet poits accordig to their locatios i the aalysed sectios. CR6 criterio iflueces multi-criteria rakig subject to cocetratios of the road accidets i differet accidet sectios. Traffic safety experts (Road ad Trasport, 2016) estimated five of the selected te dagerous accidet sectios like accidet black spots. Dagerous accidet sectios, cosidered black spots, are 1, 2, 5, 6, ad 7. Fially, the used multi-criteria AHP method for rakig the alteratives idetified top three dagerous accidet sectios. These road sectios also were estimated like black spots by the Road ad Trasport Research Istitute i 2016 (Road ad Trasport, 2016). Marius Jakimavičius Aalysis ad Assessmet of Lithuaia Road by AHP Method Coclusios 1. The developed geo-processig models for estimatio of the road accidet sectios are sigificat i other applicatios for idetifyig the accidet sectios o the roads. These models were created, followig the Lithuaia methodology for idetifyig high-accidet locatios o the roads of atioal sigificace. 2. GIS cocepts ad techology eable statistical evaluatios of spatial patters of the road accidet data. The use of the criterio, represetig the spatial depedecies of accidets, i the multicriteria aalysis, allows assessig the accidet sectios based o the cocetratio of accidet poits. The spatial criterio (z-score) used allows for more precise rakig of accidet sectios. 3. This research preseted the methodology for rakig the dagerous road accidet sectios. The methodology above combies GIS techologies ad multi-criteria aalysis AHP method. It was applied to a case study. Differet sectios of the roads of atioal sigificace were aalysed to idetify sectios with the worst safety coditios. Accordig to the assessmet, the sectios with the worst safety coditios are 6, 1, ad 5. A sesitivity aalysis was performed by varyig the weights of the criteria, to verify the robustess of the results. The sesitivity aalysis cofirmed the results. 257
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