10562 FACTA UNIVERSITATIS Series:Mechanical Engineering Vol. 20, No 1, 2022, pp. 177 - 197 https://doi.org/10.22190/FUME220215012D © 2022 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper IMPACT OF THE NUMBER OF VEHICLES ON TRAFFIC SAFETY: MULTIPHASE MODELING Milanko Damjanović1, Željko Stević2, Dragan Stanimirović3, Ilija Tanackov4, Dragan Marinković5 1University of Montenegro, Faculty of Mechanical Engineering, Podgorica, Montenegro 2University of East Sarajevo, Faculty of Transport and Traffic Engineering, Doboj, Bosnia and Herzegovina 3Ministry of Transport and Communications of Republic of Srpska, Banja Luka, Bosnia and Herzegovina 4University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia 5Faculty of Mechanical Engineering and Traffic Systems, TU Berlin, Germany Abstract. Traffic safety is one of the key issues nowadays, given the fact that a large number of people lose their lives in traffic accidents every day. There are various influential factors in the occurrence of traffic accidents, the number of vehicles being one of them. This paper assesses the traffic safety in Montenegro in the period 1998-2020 by applying the multiphase modeling with a purpose to obtain comparative results which enable implementation of adequate strategies. A total of six scenarios were formed with two inputs and two outputs in a DEA (Data Envelopment Analysis) model, with the number of registered vehicles per year being an input in all scenarios. In addition, as inputs, the scenarios included AADT (Annual Average Daily Traffic), passengers in road transport, passenger-km by road transport, goods transported by road, tone-km by road, and passengers in local transport. The number of traffic accidents with casualties, the number of traffic accidents with material damage, the number of fatal cases and the number of injured persons, depending on a scenario, were observed as outputs. After the DEA model, IMF SWARA (Improved Fuzzy Stepwise Weight Assessment Ratio Analysis) was applied to determine the weights of inputs and outputs, while the final state of traffic safety by years was determined using the MARCOS (Measurement of alternatives and ranking according to COmpromise solution) method. Key Words: Vehicle, Traffic Safety, IMF SWARA, MARCOS, Traffic Accident Received February 15, 2022 / Accepted March 16, 2022 Corresponding author: Željko Stević University of East Sarajevo, Faculty of Transport and Traffic Engineering, Vojvode Mišića 52, 74000 Doboj, Bosnia and Herzegovina Email-address zeljko.stevic@sf.ues.rs.ba, zeljkostevic88@yahoo.com 178 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ 1. INTRODUCTION Globalization, as one of important factors nowadays in every field, affects the course of traffic and transport processes as well as the risks of possible occurrence of undesirable situations. Certainly, for years, traffic safety has been a burning issue that is a subject of daily professional and scientific analysis. Its significance does not need to be emphasized and described too much since every participant in traffic strives to make it as safe as possible. It is necessary to find adequate measures and balance between frequently conflict situations. Modern motor vehicles with exceptional performance, excellent mechanical characteristics, equipped in a way to provide greater comfort and safety represent, on the one hand, a significant contribution to this area. However, on the other hand, if it is added a shorter time needed to reach high speeds, which also frequently leads to unsafe overtaking, we have an increased risk of accidents. It reflects the interaction between vehicles and people as important factors that can influence the emergence of risky traffic situations. This paper analyzes traffic safety in Montenegro for a period of 23 years through creating multiphase modeling. It involves creating different scenarios with different impact parameters and integrating multiple approaches into a single model. According to Podvezko and Sivilevičius [1], a system of road transport involves vehicles, roads, traffic participants and freight that are interconnected. Transportation infrastructure and logistics are core elements supporting trade facilitation efforts at the local level [2] and, consequently, mobility and an increasing number of vehicles involved in traffic. Therefore, this paper analyzes the impact of various factors: the number of registered motor vehicles, AADT, passengers in road transport, passenger-km by road transport, goods transported by road, tonne-km by road, and passengers in local transport. The number of traffic accidents with casualties, the number of traffic accidents with material damage, the number of dead persons and the number of injured persons, depending on a scenario, were observed as outputs. Motivation for writing this paper can be explained through the necessity of existing original and quality quantitative model which can be base for bringing adequate strategies which should increase traffic safety field. The goal of creating an integrated model implies the overall quantification of the safety for a specified period and the possibility of identifying a benchmark year according to which further strategies will be created. The main contribution of the study is the developed integrated DEA-IMF SWARA-MARCOS model presented for the first time in literature which can be used for solving various transport, traffic, and others problems. Another contribution is the fact that it is through the applied model that the possibility for preventive engineering in traffic safety can be created. The rest of the paper is described through the following five sections. Section 2 provides a brief review of the application of different methodologies in the field of traffic safety. Section 3 presents materials and methods, giving a detailed overview of all the data used in this paper. Additionally, scenarios with a description of influential input-output factors are formed, and the methods that make up the developed integrated model are presented in detail. In Section 4, the results obtained for all scenarios are presented and discussed. Section 5 is the analysis of the impact of the number of motor vehicles on the occurrence of traffic accidents using regression analysis. The final, Section 6, summarizes the conclusions along with guidelines for continuing the research. Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 179 2. LITERATURE REVIEW The DEA model has often been applied in the field of traffic safety, sometimes individually, and very often in integration with other approaches to ensure the most accurate decision-making. This section of the paper presents the studies that used DEA in a whole model or a phase of a model for determining traffic safety. 2.1. The application of DEA model in traffic safety Mozaffaria et al. [3] applied the DEA model to assess traffic safety culture in order to achieve desired safety performance. They observed a three-year period and analyzed a total of 31 provinces in Iran. Based on the results obtained, they concluded that road safety culture increased on average. The double-frontier DEA was applied in [4, 5] to assess the efficiency of Iranian safety programs in order to reduce the number of traffic accidents with fatalities. A serial two-stage additive DEA model [6] was applied to analyze traffic safety performance in 31 provinces in China. The results showed certain differences between the regions in the level of traffic safety, and suggested certain procedures for adequate traffic safety management. The authors of the paper [7] have evaluated 197 municipalities in terms of traffic safety, applying a DEA model, which consists of several phases. In the same paper, different scenarios with two inputs and 14, eight and six outputs, respectively, were modeled. Fancello et al. [8] compared CCR and BCC models in order to support traffic management in terms of urban road safety. The goal was to identify the critical roads that have the greatest need for intervention and increase in traffic safety. The fuzzy form of DEA method can be successfully applied in the traffic safety field. For example, fuzzy DEA has been applied in [9] to evaluating road safety index in Iran. 2.2. The application of integrated models in traffic safety Infrastructure improvement is one of significant instruments for increasing traffic safety, as stated in the paper [10] in which DEA and GIS (geographical information system) were combined to assess the risk level of problematic road segments with a length of 100 km. In that way, traffic safety is improved through locating and visualizing problematic points on the observed road segment. In [11], a combination of PCA-DEA model was used considering undesirable input and output indices. The authors state that the advantage of the applied approach is the benchmarking of the safest roads in order to best allocate budget funds in the field of traffic safety. Stanković et al. [12] extended the MARCOS method with fuzzy numbers to determine traffic safety in Bosnia and Herzegovina on defined road sections. A total of 38 short sections of 200 m each were evaluated based on six influential factors. The original CRITIC (The CRiteria Importance Through Intercriteria Correlation), Fuzzy FUCOM (Full Consistency Method), DEA, and Fuzzy MARCOS model were created in [13] which evaluated nine sections of the road network based on eight criteria divided into four inputs and four outputs. The methodology for assessing road sections is similar to that in this paper because a DEA method was applied first, and then the others depending on their purposefulness. The integration of BWM (Best Worst Method) with a DEA model being modified to be applicable and adaptable in the field of traffic safety has been applied in [14]. A DEA-RS (Road Safety) model has been defined and verified through a case study in Iran. An integrated DEA and Monte-Carlo simulation prioritizing approach is proposed 180 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ in [15] to determine the prioritization of traffic safety management projects. Stević et al. [16] have created an original DEA-CRITIC-MARCOS model for evaluating traffic safety on 17 important roads of South Africa city. In comparison to other studies, the authors have used DEA for calculation criteria weights instead of initial safety performance. 3. MATERIALS AND METHODS 3.1. Research description and problem setting A research flow diagram is shown in Fig. 1. It consists of forming a total of six scenarios where different inputs and outputs are modeled. A multi-phase model of traffic accident analysis, which includes a DEA-IMF SWARA-MARCOS model has been applied. DEA CCR model has been selected because of its simplicity and previous exploration in literature. However, the power discrimination of the DEA model can be low in many cases. For that reason, we have applied IMF SWARA and MARCOS model in order to obtain final results with clear differences between the variants. Fig. 1 A research flow diagram Inputs are results of integration mostly literature review and dialogues with experts. The first scenario S1 includes AADT (Annual Average Daily Traffic) [13, 16] and the number of registered vehicles (NRV) [5,17,19] as inputs; and traffic accidents with casualties (TAC) and traffic accidents with material damage (TAMD) [20]. Overall data for the first scenario are presented in Table 1. =1 Y e s No Outputs: S1, S4 and S5: TAC, TAMD S2, S3 and S6: DP, IP Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 181 The second scenario S2 implies the number of passengers in road transport as the first input, and the number of registered vehicles (which are one of the inputs in each scenario). In this scenario, the number of dead persons (DP) [21] and the number of injured persons (IP) [14, 20] are outputs. The data for the second scenario are presented in Fig. 2. Table 1.Data for the DEA model for the first scenario S1 AADT NRV TAC TAMD 2009 7388 183,441 1718 8394 2010 7164 187,913 1520 7618 2011 7140 196,419 1451 7068 2012 5593 197,826 1217 6886 2013 4733 203,266 1266 3998 2014 6440 196,059 1334 4197 2015 7471 198,772 1554 3390 2016 7912 209,098 1698 3531 2017 7969 219,378 1831 3847 2018 8953 235,385 1855 4017 2019 4078 249,301 1924 4286 2020 3052 240,611 1490 3102 Fig. 2 Data for the DEA model for the second scenario S2 The third scenario implies only one change compared to the previous, second scenario, and it is reflected through the change of the first input. Instead of passengers in road transport, the results with passenger-km by road transport [20, 22] were modeled and the data are presented in Fig. 3. 182 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ Fig. 3 Data for the DEA model for the third scenario S3 Fig. 4 shows the data for the fourth and fifth scenarios since the only difference is in the first input. Transport according to Sénquiz-Díaz [23] remains a key development factor in any country and has an influence on the transport of goods. In the fourth scenario, the first input is goods transported by road [6] in thousands, while tkm [14] is the first input in the fifth scenario. Fig. 4 Data for the DEA model for the fourth (S4) and fifth scenario (S5) Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 183 Fig. 5 shows the data for the last, sixth scenario (S6) for the DEA model in which the inputs are passengers in local road transport and the number of registered vehicles, and the outputs are the number of dead persons and the number of injured persons in traffic accidents. Fig. 5 Data for the DEA model for the sixth scenario After that, the DEA model was applied for each scenario separately. In the first scenario, it was observed the period 2009-2020 considering the availability of data for AADT, while the period from 1998 to 2020 was observed in other scenarios. Data on traffic accidents sorted by categories are available for the whole period, while data on the number of registered motor vehicles, passengers in road transport, passenger-km, goods transported by road, tonne-kilometers by road and passengers in local transport are available for limited periods, maximum for 15 years. In order to obtain the most relevant analysis for each of these elements, the annual increase or decrease was calculated, and based on that, the average annual trend was calculated. Finally, data for the previous historical period that was missing were obtained by applying a linear model based on the calculated annual trend. It is important to note that 2020 is not taken into account in these calculations due to the conditions of COVID-19 and the limitations caused by the pandemic. Also, the goods transported by road were not taken for 2012 as an input since there was a drastic decline compared to the previous two years. Clear advantages of the applied methods are presented in [24] and [25], respectively. 3.2. DEA method Here, a DEA (Data Envelopment Analysis) CCR input model [26-28] is formed for traffic safety evaluation. An input oriented model is: 184 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ 1 1 1 1 max : 0, 1,..., 1 0, 1,..., m input i i input i m m s i ij i ij i i m m s i i output i m i DEA w x st w x w y j n w y w i m s − = + = = + + − = + = −  = =  = +     (1) In this model, a Decision-Making Unit (DMU) consists of m inputs for each xij, while s represents outputs for each yij. 3.3. IMF SWARA method The IMF SWARA method is a recently developed method presented byVrtagić et al. [24]. It consists of the following steps [29, 30]. Step 1: The criteria were arranged in descending order based on their expected significance. Step 2: Starting from the previously determined rank, the significance of the criterion (Cj) was determined in relation to the previous one (Cj−1) according to the scale represented in Table 2, and this was repeated for each subsequent criterion. This relation is marked with j . Table 2 Linguistics and the TFN scale for comparing criteria in the IMF SWARA method Linguistic Variable Abbreviation TFN Scale Absolutely less significant ALS (1, 1, 1) Dominantly less significant DLS (1/2, 2/3, 1) Much less significant MLS (2/5, 1/2, 2/3) Really less significant RLS (1/3, 2/5, 1/2) Less significant LS (2/7, 1/3, 2/5) Moderately less significant MDLS (1/4, 2/7, 1/3) Weakly less significant WLS (2/9, 1/4, 2/7) Equally significant ES (0, 0, 0) Step 3: The fuzzy coefficient was determined j : (1,1,1) 1 1 j j j j   = =   (2) Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 185 Step 4: The calculated weights were determined j : 1 (1,1,1) 1 1 jj j j j   − =  =    (3) Step 5: The fuzzy weight coefficients were calculated using the following Eq. (4): 1 j j m j j w   = =  (4) where wj represents the fuzzy relative weight of criteria j, and m represents the total number of criteria. 3.4. MARCOS method The Measurement Alternatives and Ranking according to COmpromise Solution (MARCOS) method [25] is based on defining the relationship between alternatives and reference values (ideal and anti-ideal alternatives). The MARCOS method is performed through the following steps [31, 32]. Step 1: Formation of an initial decision-making matrix. Step 2: Formation of an extended initial matrix with the ideal (AI) and anti-ideal (AAI) solution. 1 2 1 2 11 11 12 2 21 22 2 1 22 21 ... ... ... ... ... ... ... ... ... ... ... n aanaa aa n n m m mn aiai ain C C C xx xAAI xA x x A x x x X A x xx AI xx x         =            (5) min maxij ij i i AAI x if j B and x if j C=   (6) max minij ij ii AI x if j B and x if j C=   (7) Step 3: Normalization of extended initial matrix (X). ai ij ij x n if j C x =  (8) 186 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ ij ij ai x n if j B x =  (9) where elements xij and xai represent the elements of matrix X. Step 4: Determination of weighted matrix [ ]ij m nV v = . ij ij jv n w=  (10) Step 5: Calculation of the utility degree of alternatives Ki. ii aai S K S − = (11) ii ai S K S + = (12) where Si (i=1,2,..,m) represents the sum of the elements of weighted matrix V, Eq. (13). 1 n i ij i S v = = (13) Step 6: Determination of the utility function of alternatives f(Ki). ( ) ; 1 ( ) 1 ( ) 1 ( ) ( ) i i i i i i i K K f K f K f K f K f K + − + − + − + = − − + + (14) where ( )if K − represents the utility function in relation to the anti-ideal solution, while ( ) i f K + represents the utility function in relation to the ideal solution. Utility functions in relation to the ideal and anti-ideal solution are determined by applying Eqs. (15) and (16). ( ) i i i i K f K K K + − + − = + (15) ( ) i i i i K f K K K − + + − = + (16) Step 7: Ranking the alternatives is based on the final values of utility functions. It is desirable that an alternative has the highest possible value of the utility function. 4. RESULTS This section presents in detail the results obtained by applying multiphase modeling of the impact of various factors, primarily motor vehicles on traffic safety in Montenegro over a period of 23 years (1998-2020). Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 187 4.1. Results after applying the DEA model The results of the DEA model for all six scenarios are shown in Table 3. Table 3 DEA model results for all scenarios S1 S2 S3 S4 S5 S6 1998 0.415 0.391 0.719 0.948 0.555 1999 0.577 0.544 0.756 0.921 0.591 2000 0.703 0.664 0.892 1.000 0.712 2001 0.711 0.672 0.976 1.000 0.712 2002 0.777 0.734 0.952 0.987 0.786 2003 0.857 0.811 1.000 1.000 0.840 2004 0.853 0.808 0.977 0.962 0.823 2005 0.787 0.746 0.903 0.876 0.764 2006 0.693 0.657 0.799 0.765 0.678 2007 0.573 0.544 0.676 0.640 0.576 2008 0.663 0.630 0.735 0.688 0.627 2009 0.874 0.677 0.644 0.769 0.712 0.658 2010 0.958 0.818 0.778 0.887 0.815 0.761 2011 1.000 0.885 0.823 0.900 0.850 0.884 2012 1.000 1.000 1.000 1.000 1.000 1.000 2013 1.000 0.996 0.976 0.995 0.992 1.000 2014 1.000 1.000 0.930 0.910 0.939 1.000 2015 1.000 1.000 0.888 0.805 0.900 1.000 2016 1.000 0.941 0.772 0.832 0.852 1.000 2017 0.951 0.886 0.768 0.779 0.775 0.952 2018 1.000 1.000 0.990 0.788 0.786 0.955 2019 0.822 1.000 1.000 0.807 0.802 0.953 2020 1.000 1.000 1.000 1.000 1.000 1.000 The results after applying the DEA model show that in the period 1998-2010, 2003 has a satisfactory situation in terms of traffic safety only in scenarios S4 (inputs are NRV and goods) and S5 (inputs are NRV and tkm). In other years, there is no adequate level, which is in a way understandable because over time it is resorted to modern preventive engineering that gives certain results. In the first scenario when NRV and AADT were considered as inputs in the period 2009-2020, a significant number of years (eight out of 12) show a satisfactory level of safety. Taking this into account, modeling using other inputs in combination with the number of registered motor vehicles proves to be justified. The two years that can be singled out as a benchmark based on the DEA model are 2012 and 2020. However, it is necessary to make their comparative analysis. AADT in 2020 is lower (3052) compared to 2012 (5593), surely due to the limitations caused by the pandemic, so 2012 is certainly better in such conditions. The situation is similar with the scenarios S2, S3 and S5 when it comes to passengers and passenger-km, while the situation in S4 is different since in 2012, compared to all other years, the lowest amount of goods transported by road was recorded, namely only 398 thousand tons. In the sixth scenario, the values of these two observation years are approximate when it comes to the number of local passengers. 188 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ Fig. 6 shows a statistical analysis that involves the calculation of the Spearman [33] and WS [34] correlation coefficients. Fig. 6 SCC and WS after applying the DEA model Fig. 6 shows large deviations in ranks using different scenarios (S2-S6). The second, third and sixth scenarios have the highest correlation, which is very high according to the SCC, while it is lower according to the WS coefficient because these are changes in the initial ranks. Other correlations are very low. 4.2. Results of determining the weights of the criteria using the IMF SWARA method After the application of the DEA model, the final results have not been obtained since a large number of DMUs, i.e. observation years, have a value of one, depending on a scenario, so it is necessary to apply the MCDM model for their final ranking. This section presents the results of determining the significance of the criteria using the IMF SWARA method (Table 4). Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 189 Table 4 Calculation process and weights of criteria applying the IMF SWARA method S1 crisp value TAC 1.00 1.00 1.00 1.00 1.00 1.00 0.30 0.31 0.32 0.31 AADT 0.22 0.25 0.29 1.22 1.25 1.29 0.78 0.80 0.82 0.23 0.25 0.26 0.25 NRV 0.00 0.00 0.00 1.00 1.00 1.00 0.78 0.80 0.82 0.23 0.25 0.26 0.25 TAMD 0.22 0.25 0.29 1.22 1.25 1.29 0.60 0.64 0.67 0.18 0.20 0.21 0.20 3.16 3.24 3.31 S2 crisp value DP 1.00 1.00 1.00 1.00 1.00 1.00 0.32 0.33 0.34 0.33 IP 0.25 0.29 0.33 1.25 1.29 1.33 0.75 0.78 0.80 0.24 0.26 0.27 0.26 NRV 0.22 0.25 0.29 1.22 1.25 1.29 0.58 0.62 0.65 0.19 0.21 0.22 0.21 PASS. ROAD 0.00 0.00 0.00 1.00 1.00 1.00 0.58 0.62 0.65 0.19 0.21 0.22 0.21 2.92 3.02 3.11 S3 crisp value DP 1.00 1.00 1.00 1.00 1.00 1.00 0.30 0.31 0.32 0.31 IP 0.29 0.33 0.40 1.29 1.33 1.40 0.71 0.75 0.78 0.21 0.23 0.25 0.23 NRV 0.00 0.00 0.00 1.00 1.00 1.00 0.71 0.75 0.78 0.21 0.23 0.25 0.23 PASS. ROAD 0.00 0.00 0.00 1.00 1.00 1.00 0.71 0.75 0.78 0.21 0.23 0.25 0.23 3.14 3.25 3.33 S4 crisp value TAC 1.00 1.00 1.00 1.00 1.00 1.00 0.30 0.31 0.32 0.31 NRV 0.22 0.25 0.29 1.22 1.25 1.29 0.78 0.80 0.82 0.23 0.25 0.26 0.25 TAMD 0.00 0.00 0.00 1.00 1.00 1.00 0.78 0.80 0.82 0.23 0.25 0.26 0.25 Goods 0.22 0.25 0.29 1.22 1.25 1.29 0.61 0.64 0.67 0.18 0.20 0.21 0.20 3.16 3.24 3.31 S5 crisp value TAC 1.00 1.00 1.00 1.00 1.00 1.00 0.30 0.31 0.32 0.31 NRV 0.22 0.25 0.29 1.22 1.25 1.29 0.78 0.80 0.82 0.23 0.25 0.26 0.25 TAMD 0.00 0.00 0.00 1.00 1.00 1.00 0.78 0.80 0.82 0.23 0.25 0.26 0.25 tkm 0.22 0.25 0.29 1.22 1.25 1.29 0.61 0.64 0.67 0.18 0.20 0.21 0.20 3.16 3.24 3.31 S6 crisp value DP 1.00 1.00 1.00 1.00 1.00 1.00 0.33 0.34 0.35 0.34 IP 0.22 0.25 0.29 1.22 1.25 1.29 0.78 0.80 0.82 0.26 0.27 0.29 0.27 NRV 0.22 0.25 0.29 1.22 1.25 1.29 0.60 0.64 0.67 0.20 0.22 0.23 0.22 PASS. local 0.22 0.25 0.29 1.22 1.25 1.29 0.47 0.51 0.55 0.15 0.17 0.19 0.17 2.85 2.95 3.03 From the results obtained using the IMF SWARA method it can be concluded that the most important factors are TAC in the first, fourth, and fifth scenarios, while DP is the js jk jq jw js jk jq jw js jk jq jw js jk jq jw js jk jq jw js jk jq jw 190 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ most important criterion in the second, third and sixth scenarios. NRV is the second or third most important criterion in all the scenarios, while the other factors related to local passengers, goods and tkm are less important criteria, but not with significant differences. 4.3. Determining the final rank by applying the MARCOS method The years with a value of 1.000 after the application of the DEA model, shown in Table 3, represent alternatives in the further implementation of the MARCOS method. This section of the paper will provide the results for all the scenarios, and a detailed presentation of the calculation only for the first scenario in which the criteria are AADT, the number of registered motor vehicles, the number of traffic accidents with casualties and the number of traffic accidents with material damage. Out of a total of 12 observation years, eight have a value of one, which means that in those years, traffic safety in relation to the observed data set is at a relatively satisfactory level. In 2009, 2010, 2017 and 2019, there is a large number of traffic accidents of both classifications, and 2019 stands out in particular, with 1924 traffic accidents with casualties, despite the very low AADT (4078) compared to other years. In the first step of the MARCOS method, the initial matrix is formed, while in the second step, by applying Eqs. (6) and (7), the ideal and anti-ideal solutions are determined and, based on that, an extended initial decision matrix shown in Table 5 is formed. Table 5 Initial Extended Matrix AADT NRV TAC TAMD Antiideal 3052.000 196059.000 1855.000 7068.000 2011 7140 196,419 1451 7068 2012 5593 197,826 1217 6886 2013 4733 203,266 1266 3998 2014 6440 196,059 1334 4197 2015 7471 198,772 1554 3390 2016 7912 209,098 1698 3531 2018 8953 235,385 1855 4017 2020 3052 240,611 1490 3102 Ideal 8953.000 240611.000 1217.000 3102.000 It is important to note that the first and second criteria belong to the benefit criteria where a maximum value is desirable, while the third and fourth criteria belong to those for which the minimum value is desirable. In the third step, the data presented in Table 5 are normalized based on Eqs. (8) and (9) as follows. 13 1217 0.839 1451 ai ij ij x n if j C n x =   = = 11 7140 0.797 8953 ij ij ai x n if j B n x =   = = Other normalized values are obtained in an identical way depending on the orientation of the criteria and are presented in Table 6. Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 191 Table 6 Normalized matrix AADT NRV TAC TAMD Antiideal 0.341 0.815 0.656 0.439 2011 0.797 0.816 0.839 0.439 2012 0.625 0.822 1.000 0.450 2013 0.529 0.845 0.961 0.776 2014 0.719 0.815 0.912 0.739 2015 0.834 0.826 0.783 0.915 2016 0.884 0.869 0.717 0.879 2018 1.000 0.978 0.656 0.772 2020 0.341 1.000 0.817 1.000 Ideal 1.000 1.000 1.000 1.000 In the fourth step of the MARCOS method, the normalized values are weighted with the weights of the criteria that have been calculated in the previous section of the paper for all the scenarios using the IMF SWARA method. The weight coefficients of the criteria for the first scenario are: w1=w2=0.247; w3=0.309 and w4=0197. The weighted decision matrix is shown in Table 7. Table 7 Weighted decision matrix AADT NRV TAC TAMD Antiideal 0.084 0.201 0.203 0.086 2011 0.197 0.202 0.259 0.086 2012 0.154 0.203 0.309 0.089 2013 0.131 0.209 0.297 0.153 2014 0.178 0.201 0.282 0.146 2015 0.206 0.204 0.242 0.180 2016 0.218 0.215 0.221 0.173 2018 0.247 0.242 0.203 0.152 2020 0.084 0.247 0.252 0.197 Ideal 0.247 0.247 0.309 0.197 The rest of the calculation using the MARCOS method is given below, and the results for the first scenario are presented in Table 8. In the fifth step, using Eq. (13), the value of SAAI is calculated as follows: SAAI = 0.084+0.201+0.203+0.086=0.575 S1 = 0.197+0.202+0.259+0.086=0.744 etc. By applying Eq. (11), the following is calculated: 1 0.744 1.295 0.575 i i aai S K K S − − =  = = , i.e. by applying Eq. (12): 1 0.744 0.744 1.000 i i ai S K K S + + =  = = 192 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ In the sixth step, the utility function is calculated in relation to the anti-ideal solution by applying Eq. (15): 1 8 0.744 ( ) ( ) 0.365 0.744 1.295 i i i i K f K f K K K + − − −+ − =  = = ++ i.e. in relation to the ideal solution by applying Eq. (16): 1 8 1.295 ( ) ( ) 0.635 0.744 1.295 i i i i K f K f K K K − + + −+ − =  = = ++ The utility function of all the alternatives is calculated by applying Eq. (14): ( )1 0.744 1.295 ( ) 0.615 1 0.635 1 0.3651 ( ) 1 ( ) 11 0.635 0.365( ) ( ) i i i i i i i K K f K f K f K f K f K f K + − + − + − + + =  = = − −− − + ++ + Table 8 Results for the first scenario after applying the DEA-IMF SWARA-MARCOS model Ai Si AAI 0.575 Ki- Ki+ f(K-) f(K+) f(Ki) Rank 2011 0.744 1.295 0.744 0.365 0.635 0.615 8 2012 0.755 1.314 0.755 0.365 0.635 0.624 7 2013 0.789 1.373 0.789 0.365 0.635 0.652 5 2014 0.806 1.403 0.806 0.365 0.635 0.667 4 2015 0.832 1.449 0.832 0.365 0.635 0.688 2 2016 0.827 1.440 0.827 0.365 0.635 0.684 3 2018 0.843 1.468 0.843 0.365 0.635 0.697 1 2020 0.781 1.358 0.781 0.365 0.635 0.645 6 AI 1.000 Based on the results presented in Table 8, it can be concluded that the range of differences in final values among alternatives is very small (0.082). It means that, regardless of the fact that there are certain differences, traffic safety according to the first scenario in all years is approximate, i.e. there are very slight nuances. It is confirmed by the fact that there is no alternative that tends to one. The results for the remaining five scenarios are obtained in the same way, as shown in Tables 9-13. Table 9 Results for the second scenario after applying the DEA-IMF SWARA-MARCOS model Ai Si Scenario 2 – S2 AAI 0.630 Ki- Ki+ f(K-) f(K+) f(Ki) Rank 2012 0.906 1.438 0.905 0.386 0.614 0.728 1 2014 0.823 1.307 0.822 0.386 0.614 0.661 5 2015 0.854 1.357 0.854 0.386 0.614 0.687 4 2018 0.889 1.412 0.889 0.386 0.614 0.715 3 2019 0.897 1.425 0.897 0.386 0.614 0.721 2 2020 0.801 1.272 0.801 0.386 0.614 0.644 6 AI 1.000 Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 193 Table 10 Results for the third scenario after applying the DEA-IMF SWARA-MARCOS model Ai Si Scenario 3 – S3 AAI 0.683 Ki- Ki+ f(K-) f(K+) f(Ki) Rank 2012 0.947 1.387 0.946 0.406 0.594 0.741 1 2019 0.908 1.330 0.907 0.406 0.594 0.710 2 2020 0.768 1.126 0.768 0.406 0.594 0.602 3 AI 1.000 Table 11 Results for the fourth scenario after applying the DEA-IMF SWARA-MARCOS model Ai Si Scenario 4 – S4 AAI 0.561 Ki- Ki+ f(K-) f(K+) f(Ki) Rank 2003 0.865 1.540 0.864 0.359 0.641 0.719 1 2012 0.656 1.168 0.656 0.359 0.641 0.546 3 2020 0.827 1.472 0.826 0.359 0.641 0.688 2 AI 1.000 Table 12 Results for the fifth scenario after applying the DEA-IMF SWARA-MARCOS model Ai Si Scenario 5 – S5 AAI 0.548 Ki- Ki+ f(K-) f(K+) f(Ki) Rank 2000 0.808 1.474 0.808 0.354 0.646 0.677 2 2001 0.807 1.471 0.807 0.354 0.646 0.676 3 2003 0.825 1.505 0.825 0.354 0.646 0.691 1 2012 0.654 1.193 0.654 0.354 0.646 0.548 5 2020 0.788 1.437 0.787 0.354 0.646 0.659 4 AI 1.000 Table 13 Results for the sixth scenario after applying the DEA-IMF SWARA-MARCOS model Ai Si Scenario 6 – S6 AAI 0.703 Ki- Ki+ f(K-) f(K+) f(Ki) Rank 2012 0.906 1.289 0.906 0.413 0.587 0.702 1 2013 0.780 1.110 0.780 0.413 0.587 0.605 6 2014 0.813 1.157 0.813 0.413 0.587 0.631 4 2015 0.863 1.228 0.863 0.413 0.587 0.669 3 2016 0.799 1.137 0.799 0.413 0.587 0.620 5 2020 0.894 1.272 0.894 0.413 0.587 0.693 2 AI 1.000 Fig. 7 shows a comparative analysis of the ranks through the complete DEA-IMF SWARA-MARCOS model 194 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ Fig. 7 Comparative analysis of the ranks through all the scenarios In Fig. 7, it can be seen that by applying the DEA-IMF SWARA-MARCOS model, the ranks vary in relation to the set criteria, but here, 2012 can also be singled out as a benchmark. 5. IMPACT OF THE NUMBER OF REGISTERED VEHICLES ON TRAFFIC ACCIDENTS In this section of the paper, a short regression analysis is performed of the impact of the number of registered vehicles as an independent variable on the number of dead persons in traffic accidents (Fig. 8), traffic accidents with casualties (Fig. 9) and traffic accidents with material damage (Fig. 10). Fig. 8 The impact of vehicles on the number of dead persons in traffic accidents Impact of the Number of Vehicles on Traffic Safety: Multiphase Modeling 195 In Fig. 8, it can be seen that 57% of the relation between the number of registered vehicles and the number of dead persons can be described by a linear model. The regression is negative, which means that with the increase in the number of motor vehicles, the number of dead persons in traffic accidents decreases. The reason for this regression can be found in the fact that competent institutions have taken certain measures every year due to preventive engineering when it comes to the number of dead persons in traffic accidents in Montenegro. Fig. 9 Influence of vehicles on the number of traffic accidents with casualties In Fig. 9, it can be seen that 25% of the relation between the number of registered vehicles and the number of traffic accidents with casualties can be described by a linear model. The regression is positive, which means that with the increase in the number of motor vehicles, the number of this type of traffic accidents also increases. Compared to the previous regression, this shows us that the number of motor vehicles affects the increase in the number of traffic accidents with casualties, but that these are primarily injured persons. Fig. 10 Influence of vehicles on the number of traffic accidents with material damage Fig. 10 shows a negative regression described by a polynomial model. The number of motor vehicles does not affect the increase in traffic accidents with material damage. 196 M. DAMJANOVIĆ, Ž. STEVIĆ, D. STANIMIROVIĆ, I. TANACKOV, D. MARINKOVIĆ 6. CONCLUSIONS In this paper, it was developed an integrated DEA – IMF SWARA – MARCOS model for assessing traffic safety in Montenegro over a period of 23 years. Different scenarios have been formed using different input and output factors, with the number of vehicles being an irreplaceable input parameter. The contribution of this paper is reflected in the development of an integrated multiphase model for the analysis of traffic safety in Montenegro. The first phase involves the application of a DEA model for all the scenarios, after which DMUs with a value of 1.00 are further implemented in the MCDM model. The IMF SWAFA method was applied to determine the significance of input and output parameters in each scenario, and the final ranking of alternatives was performed using the MARCOS method. The results obtained show that in terms of traffic safety in Montenegro, compared to the end of the previous and the beginning of this century, the situation has improved with certain oscillations over the years. A regression analysis of the impact of the number of motor vehicles on traffic accidents and of its consequences was also performed. With the increase in the number of motor vehicles, the number of traffic accidents with casualties also increases. The benchmark years that should serve as an example of implementing measures and creating a traffic safety strategy are 2012 and 2020, but it should be taken into account that mobility was reduced during the pandemic. Therefore, it may be better to take 2012 as a parameter year. Limitations of this study can be manifested through the following. Some of the uncertainties appear in the year 2020 which has been part of observed years due to COVID-19. We have tried to eliminate this uncertainty by creating a linear model in considering data that has been explained in the paper and giving the advantage of the 2012 year in comparison to 2020. Future research related to this paper refers to the expansion of influential factors, the application of uncertainty theories in the whole model. Additionally, the implementation of adequate preventive engineering measures after this analysis is one of the future steps. REFERENCES 1. 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