Prediction of Design Hourly Volume on Rural Roads

Abstract

Design hourly volume (DHV) represents one of the most significant parameters in the procedures of developing and evaluating road designs. DHV values can be accurately and precisely calculated only on the road sections with the implemented automatic traffic counters (ATCs) which constantly monitor the traffic volume. Unfortunately, many road sections do not contain ATCs primarily because of the implementation costs. Consequently, for many years, the DHV values have been defined on the basis of occasional counting and the factors related to traffic flow variability over time. However, it has been determined that this approach has significant limitations and that the predicted values considerably deviate from the actual values. Therefore, the main objective of this paper is to develop a model which will enable DHV prediction on rural roads in cases of insufficient data. The suggested model is based on the correlation between DHVs and the parameters defining the characteristics of traffic flows, that is, the relationship between the traffic volumes on design working days and non-working days, and annual average daily traffic. The results of the conducted research indicate that the application of the proposed model enables the prediction of DHV values with a significant level of data accuracy and reliability. The coefficient of determination (R²) shows that more than 98% of the variance of the calculated DHVs was explained by the observed DHV values, while the mean error ranged from 4.86% to 7.84% depending on the number of hours for which DHV was predicted.

In the process of evaluating, designing, and defining the arguments required for making investment decisions for the proposed road or network designs, the phases of the project design evaluation have a significant role ( 1 ). Evaluation represents defining the criteria for making decisions in relation to whether or not, when, and which of the planned designs will be realized. In analytical procedures, the efficient calculation of total benefits significantly depends on the basic parameters of the traffic flow, primarily the annual average daily traffic (AADT) and design hourly volume (DHV).

DHVs are the values of traffic demands which best represent the average conditions in the traffic flow on the observed section ( 2 , 3 ). AADT is not a suitable parameter since it “masks” changes or the traffic volume variations during a day. This is the main reason for using a short-term period, most commonly 1 h, in the processes of creating and evaluating project designs. Certainly, such a “design hour” cannot be defined as an average annual value because the values are significantly higher in the peak hours of the year. Therefore, the design hour has to be defined so that its traffic flow is higher than the average AADT and lower than the maximum hourly volume during the year. The aim is to find the appropriate state of the traffic flow which will enable rational and sustainable creation and evaluation of project designs. The approach for defining DHV values which is predominantly used today is based on chronologically arranged volumes during the year and the characteristic position of the curve knee. This approach was first proposed by Peabody and Nonnan ( 4 ).

The ultimate objective of all plans and designs should be adapting the road to the planned traffic demands, with the required and acceptable level of service. The first DHV findings which can satisfy these criteria date back to 1921 when Johnson first declared that average daily traffic (ADT) was not a suitable parameter for dimensioning road facilities, that is, that ADT did not provide the number of vehicles which had to be ensured in a specific period because of seasonal and hourly traffic volume variations ( 5 ). This hypothesis is still supported. For example, the American Association of State Transportation Officials (AASHTO) recommends using traffic demands for the period shorter than a day, that is, using the period of 1 h in almost all design procedures ( 6 ). Similarly, the Highway Capacity Manual (HCM 2010) recommends that the selection of the appropriate hour for planning, designing, and evaluating road designs should ensure a compromise between the provided (adequate) level of service for users (during most hours in a year) and economic efficency, that is, more rational realization of designs ( 7 ).

DHV values can be accurately and precisely calculated only on the road sections with the implemented automatic traffic counters (ATC) which monitor and measure the traffic volume during all 8,760 h of the year. Unfortunately, many sections do not contain ATCs primarily because of the implementation costs. Consequently, for many years the design values were defined on the basis of occasional counting and the factors related to traffic demand variations over time. However, the results of numerous authors indicated significant limitations of this approach ( 8 – 10 ). There were significant deviations of the calculated values from the actually realized values, particularly on the sections with considerable traffic flow variations during the year.

Therefore, the main objective of this paper is to develop a model which will enable the DHV prediction on rural roads in cases of insufficient data. The model proposed in this paper is based on the correlation between DHVs and the parameters defining traffic flow characteristics, that is, the relationship between the flows on design working days and non-working days, and AADT.

The paper consists of five sections. Following the Introduction, the second section provides the review of the references and relevant literature from the field of DHV prediction. The third section is related to the manner in which the research was conducted and presents the defined methodology. The next section contains the results accompanied by the discussion, while the final section defines the main conclusions and directions for further research.

Literature Review

Revewing the relevant literature, it was determined that numerous models had been developed to define DHV values. Traditional approaches were mostly based on establishing a correlation between the DHV and AADT, while more recent models have also considered other influential factors.

In his study, Byrne used a model for DHV prediction in Vermont based on the linear regression of DHV and AADT ( 11 ). The main reason for developing and applying this model was the need for DHV prediction for the future period and the need for determining DHV values based on historical data in case of ATC breakdown. The data for the 10-year period were used for developing the model. The complete model was based on predicting DHV as a function of AADT. On the basis of traffic demand variations over time and functional importance of each road in the network, six road groups were defined: rural interregional roads; rural state roads class I and II; urban roads; summer—recreational roads; summer and winter—rural recreational roads; and summer and winter—urban recreational roads. The results of this research showed a significant compatibility between the predicted and observed volumes, which was confirmed by the coefficients of determination (R²) ranging from 0.81 to 1.00 for different road groups.

In research in the territory of Florida, Ghanim et al. also established the correlation between DHV and AADT ( 12 ). For the basis of their model, these researchers used historical data about traffic volume from ATCs for the period from 1992 to 2007. The conclusions of their analyses showed that there was a strong correlative dependence between the analyzed parameters only at lower AADT values, while the increase in AADT resulted in significant weakening of the correlation. According to the authors, these results indicated that the use of the linear model for DHV prediction could lead to prediction errors on the road sections with a higher traffic demand. In these cases, the increase in AADT led to slightly higher values of predicted DHVs in comparison with the actually realized values. Therefore, the authors suggested the application of non-linear models for the prediction of design volumes, and stated that one of the most suitable models was the artificial neural network model. They later developed the model, based on artificial neural networks, which established a correlation between DHV and other variables such as AADT, functional classification, and number of traffic lanes. The objective of their paper was to solve the following problems: predicting DHV for different road categories without the need for continuous traffic counting; modelling the nonlinear relationship between AADT and DHV; and modelling quantitative and qualitative variables, while previously knowing the AADT values and functional road classification. The analysis was conducted using the sample of 363 ATCs, and the sample was randomly divided into three groups. The first group of data was used for developing the model, the second for calibration, and the third for testing the model. Following the development and verification, the model was applied to predicting the data for the following year (2008) and a comparative analysis was conducted with the actually obtained values. The results of the analysis showed that the artificial neural network model could predict DHV values with significant accuracy (R² = 0.98).

Khan et al. examined the possibility of predicting DHV and AADT values on the basis of the data from 163 ATCs in South Carolina, U.S., ( 13 ). To this purpose, they analyzed models based on recurrent neural networks. The research was conducted for a 10-year period (2008–2017). Overall, the long short-term memory model was proven to be the best model for DHV prediction with an average root mean square error of 824 and mean absolute percentage error (MAPE) of 2.10%. It was also found that this model could include long-term variations in a dataset while maintaining the high percentage of prediction precision.

In her paper, Spławińska presented the results of various DHV prediction models in Poland, including the traditional approach of using the factors of traffic volume variability over time and regression models, as well as artificial neural network models ( 14 ). The input data were AADT, share of commercial vehicles, road cross-section, characteristics of the volume on the sections, and nature of the surroundings. Comparing the obtained results using different models, it was determined that the multiple regression models showed the best matching between the predicted and actual volume values.

During certain periods of the year, particularly holidays, roads experience a significantly higher traffic demand. This prompted Liu and Sharma to develop a DHV prediction model by paying particular attention to the periods with the highest traffic volume, since the smallest imprecision in calculations could lead to large deviations in cost estimation ( 9 ). The research was conducted on the basis of the 20-year volume data on the rural road network in Alberta, Canada. A genetic algorithm was used for developing the DHV prediction model. The results showed that the application of the models developed in this manner ensured better matching between the predicted and actual values in comparison with traditional models.

To solve problems related to defining DHVs, Sharma et al. included another parameter referring to the distribution of volumes per direction ( 8 ). According to that study, directional traffic distribution can cause significant inaccuracies when estimating DHV values, primarily because of traffic demand variability over time and space. Namely, the authors suggested establishing the relationship between AADT and DHV for each direction, and conducting the analysis in the months with the highest traffic volume. According to that study, the main advantage of the model was that it was not necessary to classify roads according to the traffic flow characteristics and to consider the relationship between directional volumes when predicting DHV values. In this manner, they managed to avoid the greatest source of error. On the other hand, the authors stated that the limitation of the proposed model was that, to estimate the volume, the data had to be recorded continuously during the minimum period of 1 month. The comparative analysis of the results showed that the results of the applied model did not have significant deviations from the traditional model results, and that they were the most precise when using the volume data for the month of August.

Sharma and Oh published two interesting papers on DHV prediction, based on hourly volume research on the roads of Alberta, Canada ( 15 , 16 ). The analysis was conducted using the data from 75 ATCs for the period from 1983 to 1985. The basic aims of their studies were to examine traditional DHV prediction models, suggest alternative models, and re-examine the nature of DHV changing factors, expressed as a percentage of AADT, with respect to the flow types and characteristics. Their results were presented using a comparison between three models. The first model was based on the conventional linear correlation between DHV and AADT; the second model also included the approach related to the correlation between DHV and AADT but for different road types separately; while the third model included the volume in the months characterized by the highest traffic volume during a year (July or August). Their conclusions show that the application of the first model and definition of a unique dependence between the analyzed parameters can result in systematic errors in many cases, even when the coefficient of determination of the developed model is high. The results tend to improve significantly when the analysis is conducted for different road types (model 2). In spite of the advancement of this model, it can still contain significant errors in relation to DHV prediction. In addition, the authors believed that the limitation of the second model was the need for classifying roads according to their type and flow characteristics. Therefore, the authors suggested the application of the third model which did not require road classification. For the first time, this model considered the volume values during the design weekdays and days of the weekend ( 15 ). Generally, this approach provided better results than the two previously mentioned models.

Research Methodology

On the basis of the literature review, it can be concluded that there is a need for further studying of the problem related to DHV evaluation. The review of the previous studies showed that the most precise DHV prediction was achieved by involving hourly volume values on design working days and weekend days presented in the form of vehicles per hour (vph) ( 15 ). However, this approach does not include traffic volume variability during the year. In other words, the model is not sufficiently sensitive to the traffic flow characteristics, since explicit values of the analyzed traffic volumes do not indicate their correlation with the average values of the traffic volume during the year. Moreover, it is impossible to predict DHV of the roads with predominantly winter recreational characteristics, since in these cases DHV is not in the range of the peak summer months. Therefore, a comparison between the values of the daily traffic volumes of the design weekdays and weekend days, and AADT should be conducted. In this manner, the traffic flow character, which has a direct impact on DHV, is directly considered. This should improve the accuracy of DHV prediction on rural roads with different functions in the network, which is the main focus of this paper.

To develop the model, a system should be defined to include all relevant factors closely related to the traffic volume distribution during the year. The basic pre-condition for conducting a quality analysis and fulfilling the desired objectives is a clearly and purposefully defined methodology. Therefore, while developing the model in this study, special attention was paid to defining the algorithm presented in Figure 1.

Figure 1.

Research algorithm.

In the process of the model development, determining the design spatial and temporal framework should be firstly conducted. This represents the first step of the proposed methodology. Because of the specific characteristics of the observed problem, the data from 100 ATCs were used. The ATCs were implemented on the road sections characterized by different functional importance in the network. Namely, the analysis had to encompass all typical section groups with the different traffic flow characteristics defined by Petković et al. ( 17 ). Thus, the authors selected 24 sections of highly recreational roads, 26 sections of long-distance roads, 27 sections of interregional roads, and 23 sections of regional commuter roads.

Traffic counts by means of ATCs used for developing the model were permanently carried out on all the mentioned sections. At the moment of writing this paper, 2017 was the latest year with the available official data on traffic counts. Thus, the data from the year of 2016 were used for developing the model, with the aim of testing the model later. The model was tested for a 2-year period—for the year preceding (2015) and the year following (2017) the year used for developing the model.

The model involves traffic volume values for the design month, during design weekdays and days of the weekend. It should be mentioned that the design weekdays are Tuesday, Wednesday, or Thursday, while the design weekend day is Saturday.

On the basis of the monthly traffic volume variations, the most suitable months for analyzing the ratio of daily DHVs to AADT proved to be June, July, August, and September (Figure 2). The highest volume variations in comparison with AADT occur in July and August. Thus, to encompass the maximum volume period for developing and later testing the model, the volume data from the second half of July and the first half of August were used. Because July and August are the most appropriate months for developing a DHV prediction model was also confirmed in the papers of Sharma et al., and Sharma and Oh ( 8 , 15 , 16 ). In their studies, these months were stated to be the most suitable.

Figure 2.

Monthly volume variations depending on the flow characteristics.

Therefore, the average volume values during all design days (Tuesday, Wednesday, and Thursday for working days, and Saturday for non-working days) in the period from July 15 to August 15, 2016 were used in the process of developing the model.

These values were used for defining the input variables in the model, defined as Alpha and Beta in the paper. They represent the ratio of the traffic volume during the design working days to AADT (α), and the ratio of the traffic volume during the design non-working days to AADT (β).

The traffic volume values during the design weekdays and days of the weekend were included in the model primarily to detect the flow characteristics on the observed section. Namely, a ratio of the design non-working days to AADT (β) higher than the ratio of the design working days to AADT (α) indirectly indicates that the observed section is characterized by mostly recreational travel. On the other hand, if α value is higher than β value, this indirectly shows that the observed section is mainly characterized by commuter use. In this manner, traffic variations during the design working and non-working days in relation to AADT exclude the need for additional road classification according to the flow characteristics. This approach was confirmed by Sharma and Oh ( 15 , 16 ).

The proposed model is based on linear regression, with α and β as the independent variables, and the DHV value as the dependent variable. Therefore, there is a possibility of adapting the model for calculating DHVs for different hours. The adaptation of the model is based on the adjustment of coefficient values of the independent variables and the random variable, while α and β variables remain unchanged.

To simply present and easily implement the model worldwide, the paper provides the models for the calculation of DHVs for the typical and most frequently applied hours (30th, 50th, 100th, and 200th). The application of DHVs for the 30th, 50th, and 100th hour is common globally, while less-developed countries also use the DHVs for the 200th hour. Namely, the use of the 200th hour as the design hour is considered justified in the Republic of Serbia and the other countries in the region. This is primarily the consequence of cost rationalization and relatively low deviations of the volume expressed in percentage of AADT between the 30th and 200th hour ( 17 ). This is mainly the result of low mobility, that is, the decreased presence of typical recreational and long-distance travel. This is the reason why the DHV for the 200th hour was used in the paper.

The formulations of the proposed model are presented in the following Equations 1–4.

D H V_{30 t h} = \frac{A A D T}{100} \cdot (2.934 + 2.983 \cdot α + 2.760 \cdot β) [veh/h]

(1)

D H V_{50 t h} = \frac{A A D T}{100} \cdot (3.203 + 2.832 \cdot α + 2.407 \cdot β) [veh/h]

(2)

D H V_{100 t h} = \frac{A A D T}{100} \cdot (3.689 + 2.601 \cdot α + 1.840 \cdot β) [veh/h]

(3)

D H V_{200 t h} = \frac{A A D T}{100} \cdot (4.320 + 2.355 \cdot α + 1.155 \cdot β) [veh/h]

(4)

where

${DHV}_{n - th}$ = design hourly traffic volume for the nth (30th, 50th, 100th, and 200th) hour criterion expressed as [vph],

$AADT$ = annual average daily traffic expressed as [vph],

α = ratio of the daily volume during the design weekday to AADT [–],

β = ratio of the daily volume on Saturday to AADT [–].

In the second methodology step following the definition of the model, the obtained values were used to conduct the logic data check and calibration the model. Namely, it is necessary to exclude the ATC data which are illogical because of particular reasons (ATC breakdown, road works in the ATC zone, etc.).

The final step of the defined methodology refers to testing the model. In this paper, testing was carried out for the year preceding (2015) and the year following (2017) the year used for developing the model. The traffic volume data from ATCs provided the volume values for the design days which were used for DHV calculation. Then, the results of the predicted volumes were compared with the actually realized DHV values.

To apply this model for the DHV prediction in real conditions, it is necessary to obtain data from 2-day traffic counts and AADT values on the observed section. The traffic counts have to be conducted manually and occasionally automatically on a 24-h basis on the design days. In relation to the AADT on the observed section, it is necessary to know at least the estimated AADT values obtained by means of interpolation. The road management company is required to possess and publish these data. The obtained values should be compared, that is, included in the model as input parameters.

Research Results and Discussion

Following the model formation and conducted analysis, the DHV calculation was performed using a sample of data from 157 ATCs (59 ATCs from 2015 and 98 ATCs from 2017) which were not used in the development of the model. On the basis of the ATC data, the values of AADT and traffic volume for design days were collected and they represented the input data in the model.

To examine the dependence between the DHV values calculated in the model and the actually realized DHVs, Pearson’s correlation coefficient (r) [–1.1] was used, as well as the coefficient of determination (R²) [0.1] which represents the total variation of the dependent variable (DHVs calculated in the model) explained or assigned to the variation of the independent variable (DHVs from the ATCs).

The obtained results, which are graphically represented in Figure 3, clearly show a strong positive correlation between the estimated and actually realized DHV values. The value of the Pearson’s correlation coefficient (r) for all four models is approximately 0.99, which indicates a significant correlation between the analyzed values. In addition, the coefficient of determination (R²) shows that more than 98% of the variance of the calculated DHVs was explained by the actually realized DHV values. The best results were obtained in the model for calculating the DHVs for the 200th hour (R² = 0.9941), while the poorest (but still extremely reliable) model was the model for calculating DHVs for the 30th hour (R² = 0.9871). When it comes to the correlation according to road type, the highest value was obtained for the roads with predominantly long-distance and summer recreational travel, while the poorest but still high correlation was recorded on the roads with predominantly winter recreational travel. This can be a consequence of the small sample of these sections in the Republic of Serbia.

Figure 3.

Dependence between the predicted and observed design hourly volume (DHV) values.

An additional analysis was conducted to consider the dependence between the obtained DHV values and their corresponding AADT values on the observed road sections. Namely, all calculated DHV values for each of the models were compared with the corresponding AADT values. The graphic representation of the established correlation is provided in Figure 4.

Figure 4.

Dependence between the predicted design hourly volume (DHV) values and annual average daily traffic (AADT).

The figure shows that there is a strong correlation between the analyzed values. It can be seen in the diagram that the linear dependence between DHV and AADT is dominant at the lower AADT values, while the increase in AADT changes this tendency. In other words, the rise of AADT leads to the gradual decrease of the dependence strength. This indicates that traditional models, which serve predominantly as a function of the linear dependence between DHV and AADT, can lead to significant deviations of DHVs on the sections with higher traffic volumes.

The results of the conducted comparative analysis of DHVs expressed as percentage of AADT and the AADT values showed that the rise of AADT by up to 5,000 vehicles per day (vpd) resulted in the decrease of DHV. However, DHV was rather insensitive to any further increase in AADT (Figure 5). The determined dependence was noticed in the results of all the presented models.

Figure 5.

Dependence between the predicted design hourly volume (DHV) values expressed in % and annual average daily traffic (AADT).

Figure 5 shows that the largest DHV dispersion is on the road sections where the AADT values range from 3,500 to 7,000 vpd. The reason for this might be the function of the analyzed roads in the Serbian road network. Namely, the AADT values are within the mentioned range on the largest number of the roads in the Serbian road network. The perceived standard deviation is expected since among the observed roads with similar traffic volume there are roads with absolutely different functions in the network—from recreational to rural roads with predominantly commuter travel. A similar phenomenon is seen on the sections with AADT ranging from 13,000 to 18,000, such as state roads class I (motorways and two-lane roads). Apart from the predominantly long-distance traffic flows, these roads also contain routes with a high share of tourist or recreational flow. This is the reason why the diagram contains roads with similar traffic volumes and different DHV values, which explains the increased variance.

To determine the percentage of deviation of the calculated DHV values on the observed road sections from the actually realized values, the comparison of the mentioned values on the observed sections was conducted. For each analyzed section and for each model separately the percentage of deviation was calculated, that is, the MAPE of the obtained DHVs in comparison with the DHVs from ATCs. The graphic representation of the analysis can be seen in Figure 6, while the deviation values per deviation class for each of the models are provided in Table 1.

Table 1.

The Percentage of Deviation of the Predicted Design Hourly Volume (DHV) Values from the Actual DHV Values

% of deviation	≤5%	5%–10%	10%–15%	15%–20%	20%–25%	25%–30%	≥30%
Number of deviations
DHV 30th	64	50	25	13	0	1	4
DHV 50th	69	54	21	8	1	0	4
DHV 100th	80	55	15	4	0	0	3
DHV 200th	91	54	6	3	2	1	0

Figure 6.

The percentage of deviation of the predicted design hourly volume (DHV) values from the actual DHV values.

The positive values in the diagram show that the DHVs obtained by applying the model have lower values than the actually realized DHVs, while the negative deviation shows the opposite. The mean absolute values of the percentage of deviation of the calculated DHVs in comparison with the DHVs read from ATCs for all four models (DHV 30th, 50th, 100th, and 200th) amount to 7.84%, 7.11%, 6.03%, and 4.86% respectively, while the maximum values amount to 53.08%, 44.66%, 37.35%, and 26.46%, respectively. It should be mentioned that all deviations between the analyzed values greater than 30% are mostly related to the road sections with increased traffic volume in the winter season. This is the consequence of the small sample of these sections (in the development of the model) on the roads in the Republic of Serbia. A more thorough analysis of the percentage of deviation of the calculated values from the actual values confirmed that the most precise model was the model of DHV prediction for the 200th hour, while the least accurate was the 30th hour model. This result is expected, since the volume variations are lower if a greater hour of the chronologically arranged hourly volumes for the period of the whole year is observed.

Namely, the 200th hour model shows that, out of the total number of the analyzed DHV values (157 sections), as many as 92% (or 145 calculated values) are within the error range of up to 10%, which can be clearly seen in the table shown above. On the other hand, out of the total number of analyzed DHV values in the 30th hour model, 73% of the predicted volumes (or 114 calculated values) are within the error range of up to 10%.

The descriptive statistics parameters of the analyzed data are presented in Table 2.

Table 2.

Descriptive Statistics of the Analyzed Parameters

		Mean value	Median	Min.	Max.	Standard deviation	Standard error
DHV 30th	Predicted (vph)	809.92	707	98	2,662	538.53	42.98
DHV 30th	Observed (vph)	781.26	695	129	2,529	485.14	38.72
DHV 50th	Predicted (vph)	777.57	687	92	2,555	513.71	41.00
DHV 50th	Observed (vph)	753.34	674	123	2,433	467.31	37.30
DHV 100th	Predicted (vph)	730.93	648	85	2,411	477.58	38.11
DHV 100th	Observed (vph)	712.90	648	114	2,293	442.27	36.30
DHV 200th	Predicted (vph)	681.37	615	76	2,259	439.12	35.05
DHV 200th	Observed (vph)	669.20	609	101	2,173	414.60	33.09

Note: DHV = design hourly volume; vph = vehicles per hour; Min. = minimum; Max. = maximum.

It can be clearly seen from the table that the mean DHV values obtained in the proposed models do not deviate to a great extent from the mean values calculated on the basis of the actually realized DHV values. In all the models, the mean values of the calculated values are slightly higher than the mean values of the actually realized volumes in all the cases. When comparing the minimum and maximum DHV values read from the ATCs and the volume values obtained in the models, it can be noticed that the models provide slightly lower values in relation to the minimum volumes. On the other hand, when it comes to the maximum values, the models predict slightly higher volumes than the actually realized volumes. This dependence is found in all four analyzed models. When it comes to the standard deviation values and standard error values, the calculated DHV values also do not deviate from the values of the actually realized volume values to a large extent. However, in all the presented models, the standard deviation and standard error values are slightly higher for the calculated DHV values than for the actually realized DHV values.

Conclusions and Recommendations

On the basis of the conducted research in this paper and the review of the relevant literature from the subject field, it can be concluded that DHV prediction without traffic detectors represents a very complex task. The problem complexity is reflected in defining the appropriate parameters which are primarily related to the traffic volume variations over time during a year. On the other hand, developing a model which will solve this problem is required for high-quality and reliable analyses when developing road project designs.

Consequently, as opposed to traditional models, the model developed in this paper was not based on the direct dependence of DHV and AADT. On the contrary, it was based on the volume variations during design days in design months in relation to AADT. This approach avoided the classification of the road network, which can sometimes be a very demanding process, particularly on the sections with superimposed traffic flows of different characteristics. This enabled the examination on different road routes, since all variations were included in the ratio of the volume on design days to AADT. The comparison of the volume on design days recommended for traffic counts and AADT leads to adequate DHV prediction regardless of the observed road’s function in the network or the traffic flow characteristics. The above-mentioned fact represents the basic advantage of the proposed model.

Similarly to most of the DHV prediction models found in the literature, the model presented in this paper has to include the DHV values which represent the input parameters. This model is based on traffic data. Thus, for the application of the model, it is necessary to possess the estimated (interpolated) AADT values on the analyzed section and to conduct two control 24-h traffic counts on a working day (Tuesday, Wednesday, or Thursday) and a day of the weekend (Saturday) in the period of the second half of July and the first half of August. Otherwise, a model without the input parameters would not be able to operate.

The study results show that, in addition to its simple application and calibration in local conditions, the developed model provides reliable and accurate DHV prediction. According to the testing of the models for the characteristic hours (DHV 30th, 50th, 100th, and 200th) on 157 road sections with different traffic flow characteristics, the coefficients of determination between the predicted and actually realized DHV values (R² is above 0.98 for all four models) confirm a significant compatibility and high quality of the models. The results of the DHV and AADT comparative analysis show that the increase in AADT leads to the decrease of the correlative dependence strength, which indicates the limitation of traditional models which only observe the dependence between DHV and AADT. This conclusion completely corresponds to the conclusions of Ghanim et al. ( 12 ). The results of the conducted comparative analysis of DHV values expressed in percentage of AADT and the AADT values showed that the increase in AADT by up to 5,000 vpd resulted in the decrease of DHV, while any further AADT increase significantly decreased DHV sensitivity. It was also perceived that there was a rise of DHV dispersion for roads of specific traffic volume values, which is a consequence of different functions of the observed road routes in the state road network of the Republic of Serbia, that is, the consequence of different traffic flow characteristics on the roads with similar AADT values. The analysis of the deviations of the estimated DHV values from the actually realized values showed that the mean error ranged from 4.86% to 7.84% depending on the number of hours for which DHV was predicted. Out of the total number of the analyzed DHV values (157 sections), 73% of the calculated DHV values were in the error range of 10% when calculating DHV for the 30th hour, whereas 92% of the values were in the error range of 10% when calculating the 200th hour DHV. These results undoubtedly indicate the reliability of the suggested model. The results of the descriptive statistics also confirm the validity of the proposed and developed model, since the average values of design DHV, median, standard deviation, and standard error of the predicted and actually realized DHVs were mainly compatible.

On the basis of the above-mentioned, the main advantages of this paper are the following:

the development of the model which can be simply conducted (it is necessary only to count the traffic during one design working and weekend day, while previously knowing the AADT values),

it does not require the classification of road sections on the basis of the traffic flow characteristics, which can represent a significant problem on numerous road sections in the network which contain traffic flows of different characteristics,

the possibility of adapting the model for calculating DHVs for different hours, and

the application of the model on roads which have all functions in the network, that is, roads with different traffic flow characteristics.

This model represents a universal model for DHV prediction which can be applied on the road networks of different countries. Therefore, future research should increase the sample used in the process of the model development. This primarily means including the sections of predominantly winter recreational character, that is, tourist traffic flow in the winter season. These data are insufficient in the paper because of the non-existence of ATC on the winter tourist routes in the Republic of Serbia. This problem should be overcome by conducting the analysis on the road networks of countries with a larger share of winter recreational roads.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: M. Petković, V. Tubić; data collection: M. Petković, N. Stepanović; analysis and interpretation of results: M. Petković, V. Tubić, N. Stepanović; draft manuscript preparation: M. Petković, V. Tubić, N. Stepanović. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This paper is an outcome of the research within the project of the Ministry of Education, Science and Technological Development of the Republic of Serbia, Project No. TR36027.

Data Accessibility Statement

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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