REVIEW OF METHODS FOR ASSESSING TRAFFIC CONDITIONS ON BASIC MOTORWAY AND EXPRESSWAY SECTIONS

Motorways and expressways are the core of each country’s road system. Road planning, design and management requires tools to ensure that roads have the right geometry, traffic layout and equipment. These include methods for capacity estimation and assessing traffic conditions. Because the paper focusses on the basic segments of motorways and expressways (sections located between interchanges and outside of their influence), its objective is to review and compare methods used worldwide and establish whether their assumptions or procedures could be used in Polish conditions. Four methods were selected for analysis: US, German, Swedish and Dutch. Theoretical and empirical comparisons were conducted, with the latter using data from sections of motorways and expressways in Poland collected in the RID-2B project. The results of the analyses showed important differences between the methods in terms of procedures for traffic conditions assessment, assumptions, base capacities, traffic conditions measures, factors or speed-flow models. Significant differences were also found when traffic parameter estimates made with particular methods were compared to real data from Polish roads. The results contributed to the development of Poland’s new method, to be prepared as a result of the RID-2B project. It was concluded that none of the analysed methods can be directly adopted to Polish conditions. An important conclusion is the need to include Poland-specific motorway speed limits and procedure for determining freeflow speed, the basis for further analyses.


Introduction
Motorways and expressways (ME roads) are high standard roads which are the core of each country's road network. They are designed to handle large high speed traffic flows and ensure a high level of road safety, high driving comfort and low environmental impact. Decisions to build this type of roads must be well-thought-out and supported with technical and economic analyses. An important element of the analyses is to determine the functionality of the roads by estimating the capacity of the proposed solutions and assessing traffic conditions for forecasted traffic volumes. For this purpose, road traffic conditions assessment methods (RTCA methods) are used of which the best known is the US's HCM method (TRB, 2016). It gives concepts, guidelines and procedures to determine the capacity or assess traffic conditions on various types of roads, including ME roads. HCM is used in many countries, not just the US, although it is usually adapted to local conditions (GDDKiA, 1995; Luttinen and Innamaa, 2000). Other countries elaborate their own methods for determining the functionality of a planned road or assessing the operation of an existing road (FGSV, 2015;Nakamura, 1994;Ravinder et al., the Polish 1995 method still applies, in a completely unchanged form. This problem was noticed by the General Directorate for National Roads and Motorways (GDDKiA) and in 2016, a consortium made up of the Cracow University of Technology, Gdansk University of Technology and Warsaw University of Technology began to work on the RID-2B project, aimed at updating the Polish 1995 method. The first step towards developing a new Polish method for assessing traffic conditions on basic segments of ME roads (which are the sections of ME roads located between interchanges and outside of their influence) was to review existing RTCA methods used worldwide, with particular emphasis on the procedures, models, assumptions and parameters. The aim of the paper is to summarise the findings and to compare the methods using real data from ME roads in Poland. The following research (RQ) and practical (PQ) questions were posed: -RQ1: Are there significant differences between RTCA methods used worldwide? -RQ2: Are the results of the assessment of traffic conditions achieved by different RTCA methods comparable to each other? -RQ3: What is the accuracy of traffic flow parameter estimates obtained with particular RTCA methods in relation to the real data from Polish roads? -PQ1: Which of the analysed RTCA methods can be applied in Polish conditions? -PQ2: What elements of the existing RTCA methods could be adopted in the new Polish RTCA method? -PQ3: What should be the structure of the new Polish RTCA method?

Background
Road performance can be assessed from two perspectives: efficiency and prevailing traffic conditions. Road efficiency tells us how much traffic a given road section can carry. It is measured by capacity, defined as the maximum number of vehicles that may cross a given section of road or lane in an hour in prevailing roadway, traffic and control conditions (TRB, 2016). Traffic conditions are in turn a particularly important aspect for the road user, since they define the quality of travel, and in particular: the freedom to choose the desired speed, the freedom to manoeuvre, the level of traffic interruptions and travel comfort (Pamuła, 2016). Both concepts, capacity and traffic conditions, are interrelated -the traffic conditions that prevail on a given road at a given level of traffic volume strongly depend on its capacity. Therefore, in the traffic conditions assessment procedure for an existing or planned road, two main steps are distinguished: determination of capacity and assessment of traffic conditions on this road at a given traffic volume level, using measures and classification criteria. ) and bad (when < ). In the USA the division of traffic conditions into six classes (A-F) was introduced, called level of service (LOS). The LOS concept first appeared in the HCM published in 1965 (Roess and Prassas, 2014). Since then, classification and interpretation of traffic conditions using a 6-grade LOS scale has been adopted in many countries, i.e. Germany (FGSV, 2015), Scandinavian countries (Luttinen and Innamaa, 2000) (except Sweden), the Netherlands (Heikoop and Henkens, 2016) or China (Zhou et al., 2016). Particular countries, however, use different measures of traffic conditions or assume different threshold values of these measures for particular levels of service (see example in Table 1). Table 1 shows that at a similar level of traffic flow rate or density, the level of service is assessed differently depending on the country. This results from the use of different methods to assess traffic conditions, and, in particular, different assumptions on how measures of traffic conditions are estimated and also different adopted road capacities depending on road class, speed limit or location. Table 2 shows the differences in base capacities of ME roads from country to country, for a four lane (2x2 lanes) rural motorway segment with a speed limit of 110 km/h. Base capacity should be understood as the capacity in conditions of a low heavy vehicles (HV) share, flat terrain, regular lane and right shoulder width.  Table 2 shows a high variation in adopted capacities from country to country. The lowest values are seen in Australia and Germany (3,600-3,800 pc/h) and the highest in the US (4,800 pc/h). It is clear that the difference in this case is even 1,000-1,200 pc/h (500-600 pc/h/lane). As stated by Wu (Wu, 2005) the difference in road capacity values between countries may result, among others, from different legal conditions and traffic rules. For example, in the USA it is common to stay in one lane and overtaking is allowed from any side, while in Germany there is a rule of driving on the right and overtaking only on the left. This may influence driver overtaking and lane selection behaviour, affecting lane distribution and road capacity (Wu, 2005). Similarly, the differences in how traffic rules are enforced may also significantly affect driver behaviour, and as a result, road capacity and traffic conditions. Another reason for the differences in Table 2 is how traffic flow variability within the hour is treated. For example, in the US's HCM method the reference time period for the analysis is a 15-minute intervalthat means that the given capacity corresponds to a maximum 15-minute traffic volume. While in the German HBS method the capacity is given as the maximum traffic volume corresponding to 1-hour time interval. For both values to be comparable, the peak hour factor should be applied. For example, assuming = 0.95 at the capacity flow, the hourly capacity value in the HCM is approx. 4560 pc/h. Similarly, the difference can be partly explained by how heavy vehicles are treated in the analyses and the adopted values of passenger car units (Srikanth and Mehar, 2017). Understood as the capability of a road to carry traffic, the higher the capacity, the higher the volume that can be served. Thus, on similar roads in Germany, Poland or the US, at the same volume levels, drivers can have a different sense of freedom and driving quality. The RTCA method developed e.g. for the USA may not be applicable to ME roads in other countries and should be verified for specific country's conditions before use. This was proved by Pompigna and Rupi (Pompigna and Rupi, 2015), who found that the capacity estimated using the HCM method is even 30% higher than the actual capacity estimated based on empirical data from the A4 motorway in Italy. Thus, using the HCM for the case of Italian motorways may lead to an underesti-mation of traffic conditions assessment. Similar conclusions were drawn by Bertini et al. (Bertini et al., 2006), who compared the capacity obtained using HCM and HBS methods for the A9 motorway section in Germany. He found that the difference depending on the method used is even 20%. This can be a reason why countries work on their own methods or adapt existing ones to their specific conditions. This also justifies why the paper aims to compare RTCA methods and check how they apply to specific Polish conditions.

Methodology
In order to answer the questions, research was conducted to compare selected RTCA methods. The studies were divided into two segments: -studies based on literature review and examination of existing RTCA methods (Chapter 4), -analytical research using empirical data, based on a comparison of traffic condition assessments with selected RTCA methods and comparing estimated values of traffic condition measures with empirical data (Chapter 5). The research covered those parts of RTCA methods which assess traffic conditions on basic segments of motorways (defined in Introduction). The methods can be applied to assess traffic conditions on basic segments of Polish motorways and expressways. The objective of the theoretical research was to compare RTCA methods for their assumptions, input data, factors, input speed and capacity values. This helped to identify the advantages, disadvantages and gaps that would enable or hinder the use of the analysed methods in Poland. Four foreign methods were selected for the analysis: the US's HCM, Germany's HBS, Sweden's SHCM and the Netherlands' DHCM. The choice of methods was dictated by their originality and availability; as a result, the detailed analysis did not include methods that are a direct adaptation of another method (e.g. HCM) or Asian methods, the manuals of which would be difficult to find and use. The objective of the analytical research was to compare the selected RTCA methods (HCM, HBS, SHCM, DHCM) using empirical data from Polish ME roads.

Data
The analyses use data from traffic measurements carried out within the RID-2B project (RID, 2016).
These included ME road segments selected in a fourstage procedure looking at the technical feasibility of conducting measurements and road and traffic parameters, i.e. cross-section, speed limit, vicinity of interchanges, annual average daily traffic, traffic flow composition or road location. The measurements were carried out with ANPR (automatic number-plate recognition) and MioVision Scout devices for a minimum period of 24 hours, from May to October 2017. Data were obtained such as the speed of individual vehicles and the number of vehicles registered by the measuring devices, with classification by type (passenger car, light truck, heavy truck, bus, etc.). The data was aggregated into 15-minute intervals. Traffic flow and average speed of vehicles (aggregated into two classes: passenger cars, heavy vehicles) data was obtained for each interval. For further analyses, data was extracted only for daytime hours (5:00-21:00) to avoid the impact of lack of natural lighting on the speed of vehicles. Similarly, based on the analyses of video files, intervals involving road incidents and adverse weather conditions were excluded. A collective summary of the survey sites is presented in Table 3. It presents survey site location (urban/rural), road cross-section (2x2 lanes, 2x3 lanes) and the speed limit (90-140 km/h). The total number of measurement hours amounted to 540 h. Figure 1 presents speed-flow charts for empirical data collected at the survey sites. For each of the survey sites, the necessary data were compiled such as the number of lanes, width of lanes and shoulders, speed limits, and interchange density. All analysed sections were situated on flat terrain. In each survey site the free-flow speed was determined as the average speed of passenger cars in low traffic conditions (<1,000 veh/h/lane) and the peak hour factor PHF, as the ratio of one hour traffic flow to four times the maximum traffic volume in the busiest 15 minutes of this hour.

Analyses based on empirical data
For each survey site and 15-minute interval, the measures of traffic conditions were calculated using the selected RTCA methods: average speed of passenger cars and volume-to-capacity ratio. Since the analysed RTCA methods apply to free-flow traffic conditions only (when > ), the intervals in which the speed fell below 80 km/h were excluded from the analysis. Due to the aggregation of traffic volumes into 15-minute intervals, capacity in the case of HBS, DHCM, SHCM (which are based on a 1-hour interval analysis) was reduced to 15-minute values using the factor. Descriptive goodness-of-fit measures were used to assess the accuracy of speed estimation produced by individual RTCA methods. These measures are commonly used to evaluate fit and compare nonlinear models. In each case the lower the value, the better the speed estimate in relation to empirical data. The analysed goodness-of-fit measures included: ( ) where: number of observations, observed value of the analysed variable, ̂value of the analysed variable estimated using the model.
T-test was used to assess whether the difference between empirical and estimated mean speeds is statistically significant. The significance level was set at = 0.05 and < 0.05 was considered to be statistically significant. The tests were conducted for different levels of flow rate, taking into account the speed limit and the number of lanes. Not all RTCA methods use the LOS concept, therefore the assessment of traffic conditions by individual RTCA methods was carried out for the volumeto-capacity ratio , values of which were determined for each survey site and for each time interval with the use of the four analysed methods. The results were analysed by comparing their distributions in 6 classes ( Table 4). The results of the analyses are presented in Chapter 5. . Swedes do not use the LOS. At the road design stage, the use of capacity calculations is to ensure that the newly designed road, for a design hour is characterised by a maximum average speed of 10 km/h below the speed limit, the maximum of a 5minute time loss and the volume-to-capacity ratio of not more than 0.5 (Luttinen and Innamaa, 2000). Japan, which had previously used the HCM, in 1984 published their own method, based on research conducted in the country, without using the LOS to assess traffic conditions. Individual RTCA methods vary in terms of procedure, models, assumptions or factors that may impact speed or capacity. In particular: -different base capacities are adopted in the RTCA methods (Table 2), -the methods are based on a 1-hour or 15-minute interval of traffic conditions analysis, -calculations are made for a lane (e.g. HCM) or cross-section (HBS, Dutch and Swedish methods), -the procedure uses the traffic flow rate expressed in pc/h (e.g. HCM, China, the Netherlands) or veh./h (e.g. HBS, Sweden), -most methods use the LOS concept, except for Sweden, the Netherlands and Japan, -the LOS is usually determined on the basis of density (HCM, Poland) or volume-to-capacity ratio (HBS, China, the Netherlands), the less often used criteria include: congestion probability (the Netherlands) or a decrease in the average speed relative to free-flow speed (China), -the influence of other factors on free-flow speed and capacity (e.g. lane width, weather conditions, road class) is taken into account, -the methods require detailed calculations (HCM) or reading particular measures from tables and graphs (Germany, Sweden). Further in the paper a more detailed analysis and comparison of approaches for motorways were made for the methods: the US's HCM, Germany's HBS, the Netherlands' DHCM and Swedens's SHCM. They are original methods, based on own studies, rather than directly adopting elements of other methods. The instructions for assessing traffic conditions are available (in their respective languages).

The US's HCM
The HCM 6 method assumes that traffic conditions are mostly influenced by: the number of lanes, the width of the lane and obstacle-free right shoulder, ramp density, fluctuations of traffic in the design hour, HV share and the longitudinal gradient of the road section and its length. The HCM also allows for the inclusion of the impact of weather, incidents and driver familiarity with the route in the additional procedure. The starting point is the determination (measurement or estimation) of free-flow speed ( ). This is the speed that occurs under low traffic volume conditions at which there is no interaction between the vehicles. In formula (6), the impact of the relevant factors is considered: right-side lateral clearance ( ), lane width ( ) and ramp density on the analysed segment ( ), reducing the base freeflow speed ( 0 v sw 0 ) due to restrictions. The value of 0 is assumed by default as 120 km/h and the method itself applies to in the range of 90 -120 km/h.
where: ,coefficients of the equation (given in HCM; for speed expressed in mi/h: a=3.22, b=0.84).
Analysing the sensitivity of the model (6) it can be stated that: -lane width below 3.65 m reduces by 3.1-10.6 km/h (the highest reduction for a ≤ 3 m-wide lane), -right-side lateral clearance less than 1.8 m reduces by 0-6 km/h (the highest reduction when ≤ 0.6 m), -each increase in the averaged (10 km) total ramp density per 1.6 km-road by 2 ramps causes a reduction of by approx. 8 km/h. In the HCM method the base capacity 0 is given and varies, depending on , in the range of 2,250 -2,400 pc/h/lane. The flow rate 0 (in pc/h/lane) is determined from the formula (7) by dividing the demand volume expressed in veh./h by the number of lanes (n) and the coefficients taking into account: the impact of irregular traffic distribution in the hour (PHF), the HV share and longitudinal gradient ( ). At the same time: the greater the traffic variability within the hour, the smaller the ; the greater the HV share and the greater the longitudinal gradient, the lower the value. Thus, along with the increase in traffic variability, HV share or gradient, the flow rate 0 increases.
By relating the obtained value of 0 to 0 , it is already possible at this stage to assess the traffic conditions, i.e. to determine whether the cross-sectional capacity has been exceeded (when 0 / 0 ≥ 1). In this case, the procedure ends with the assignment of traffic conditions corresponding to LOS F. Or, the method allows for further calculations, i.e. determining the average travel speed , and the existing LOS, the measure of which is the traffic density 0 (as the ratio of 0 to ). The average speed of passenger cars at the observed traffic volume is determined from the HCM model (8). The model assumes that the speed is constant and equals until the break point flow rate 0, is exceeded, when the speed begins to decrease in accordance with the formula (8). The 0, will be in the range of 1,000 -1,800 pc/h/lane, depending on . For the flow rate in the range of 0, < 0 < 0 the average speed depends on: , 0 , 0, and the 0, density occurring at the flow rate equal to the capacity.  Rakha, 1995), whose parameters were determined empirically and are included in the HBS method, in the section dedicated to motorways (Geistefeldt, 2016). Another way to determine the average speed for the given parameters, which change depending on the HV share, road location, gradient and speed limit, is the application of the model (9): where: 0 , 0 , 0 are model parameters given in the HBS. Figure 3 shows an example of v(q) curve graphs for a rural section of a motorway, with a speed limit of 120 km/h, flat terrain and 2 lanes, with varying percentages of HV share.

Sweden's SHCM
The procedure in SHCM distinguishes two classes of motorways, depending on the percentage of sections with visibility over 500 m and type of terrain. Class 1 is technically superior to class 2. The procedure includes the following steps: (1) gathering input data, (2) selecting from the manual a table referring to a given cross-section, speed limit, road class and location, (3) reading the values of capacity and average speed of vehicles from the table, taking their class into account. The base capacity is defined for a cross-section. The model (10) helps to determine the (irregular) distribution of traffic into lanes.
where: traffic flow in the right lane, ,model parameters (5).
The Swedish method, like the HBS, does not require complex calculations but involves reading the data from the appropriate tablesan example is shown in Table 5.  The average speeds and break point traffic flows depending on the cross-section, speed limit and road class were determined empirically. Table 5 should be understood as follows: in point 0, vehicles travel at free-flow speed; after exceeding point 1 the traffic flow begins to affect the speed of the vehicles; after exceeding point 2 this effect intensifies; in point 3 road capacity is achieved, while point 4 represents theoretical traffic flow equal to 1.2 times capacity, used in economic analyses. These relationships can also be presented in a graph as broken lines with break point values specified in the tables (Figure 4).

The Netherland's DHCM
In the Dutch method traffic conditions are assessed using two indicators: volume-to-capacity ratio and congestion probability, i.e. the maximum probability of a driver coming across congestion (in the Netherlands this is defined as the state of motorway traffic when the speed drops below 50 km/h). Capacity (in pc/h) is defined for the so-called typical sections of motorway, i.e. sections with a speed limit of 100 or 120 km/h, 15% of HV share, with no obstacles or roadside elements to distract drivers, flat terrain (<2.5%), good quality surface, equipped with a traffic management system, where measurements are taken in good weather conditions and in daylight. In this case, the capacity depends on the number of lanes only. For a four lane motorway the capacity is 4300 pc/h, in the case of a six lane motorway it is 6200 pc/h (the given values correspond to the total capacity of a roadway in one direction of traffic). The obtained capacity is adjusted for the impact of: -weather conditions (adjustment factor equals: 1.00 for good weather conditions, 0.95 for light precipitation and 0.90 for heavy precipitation), -lighting conditions (adjustment factor equals: 1.00 for daylight, 0.97 for lit roads, 0.95 for unlit roads). The research conducted for the purposes of the Dutch HCM showed no impact on the capacity of lane width, right-side lateral clearance, presence of emergency lanes and speed limits. As a result, these factors are not taken into account in the analysis. The last step in the procedure is to assess traffic conditions. The method does not use the classification of traffic conditions according to LOS. Traffic conditions are assigned to one of the five classes based on the volume-to-capacity ratio and the corresponding congestion probability (Table 6).

General comparison
A comparison of the selected RTCA methods in terms of the data they require, the initial parameters or factors considered in the analysis ( Table 7), shows that the methods are highly varied, both in terms of the initial values, procedures, and the factors reflecting real road and traffic conditions. The HCM is particularly complex as it has the most complicated procedure and considers the highest number of factors. * Estimated for a very low HV share ** The given values correspond to the total flow on a roadway in one direction of traffic There are also differences in the assumed base capacitiesthese values differ by up to 1,000 pc/h for four lane and 1,800 pc/h for six lane motorways. The range of input speeds in the analysis may constrain the use of the methods in other countries. For example, in the case of the HBS, DHCM and SHCM, traffic conditions may be assessed for specified speed limits only (e.g. 100 km/h, 120 km/h); in the HCM, roads with higher than 120 km/h are not assessed for traffic conditions. That is the case with Polish motorways, where the speed limit is 140 km/h, as a result will most likely be higher than 120 km/h. In this case, none of the methods allows for the assessment of traffic conditions or the correct estimation of the average speed of traffic flow. Although some of the methods are not based on the LOS concept, each may determine the volume-tocapacity ratio which is the basis for comparing traffic conditions estimated with different methods. A significant difference occurs when permissible or free-flow speed are treated as the initial speed. In the case of the HCM, the starting point is the determination of free-flow speed, which is then introduced as a variable into the v(q) model. The v(q) curve will consequently originate exactly from the determined free-flow speed. In the case of a different approach used in the HBS and SHCM, where curves are determined separately for roads with similar roadway and traffic conditions, it is assumed that, on roads with the same cross-section, class, location (type of area), speed limit and similar traffic composition, drivers behave similarly. The question arises whether this behaviour will be similar in a country different from the one for which the method was developed. Chapter 2 suggests that in each country there are some differences e.g. in the traffic rules, traffic management or traffic rules enforcement, therefore, driver behaviour differs as well. This difference may be reflected e.g. in the average speed of traffic flow. Fig. 5 shows the distribution of the estimated volume-to-capacity ratio returned by the HCM, HBS, SHCM and DHCM methods for the analysed survey sites. Sections with a speed limit of 140 km/h were excluded from the comparison because, as demonstrated in Chapter 4, none of the methods analysed provide for the possibility of assessing traffic conditions for roads with a speed limit of 140 km/h or free-flow speed over 120 km/h. Based on the results presented in Figure 5 it follows that:  20 Romanowska, A., Jamroz, K., Olszewski, P., Archives of Transport, 52(4), [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]2019 Analyses were conducted in order to compare the observed speeds of passenger cars with RTCA method estimates. For each data point (15-min. time interval at a particular survey site) the speed was estimated using HCM, HBS and SHCM methods (calculations were not made for DHCM as it does not provide a procedure for average speed estimation). Formulas given in Chapter 3 were used to assess the accuracy of estimated speeds against the real data.

Empirical comparison
The results are given in table 8. It was found that the smallest errors in speed estimation occur for the HCM method, while the largest errors in speed estimation are returned by the SHCM. For the HCM method, the estimated speed deviates by 3.8 km/h on average from the actual value (RMSE error), while in the HBS the deviation is more than 2 times greater and in the SHCM more than 4 times greater. Similar conclusions can be drawn comparing the speed values estimated using the methods on the v(q) graphs ( Figure 6). Based on the results of the speed comparison, it can be observed that for both four lane (2x2 lanes) and six lane (2x3 lanes) roads with a speed limit of 100 km/h, 110 km/h and 120 km/h, visually the best fit is the HCM method. Where the SHCM applies (100 km/h and 110 km/h speed limits), the speed is evidently underestimated. The HBS method (applicable to speed limits of 100 and 120 km/h) gives good results when the actual average speed in the conditions of low traffic (up to 1000 veh/h/lane) does not differ significantly from free-flow speed (Figure 6a). If there is a significant difference between the two speeds (e.g. Figure 6c,d), the speed estimate by the HBS is less accurate than by the HCM. Given that the initial speed parameter in HCM is free-flow speed, and in the other two methods the relationships are derived for the given speed limit, for the data from Polish ME roads much better results are obtained when the relationship is derived for the given free-flow speed rather than the speed limit. In order to assess whether the difference between observed and estimated speeds is statistically significant, t-tests for equity of means were conducted.
The tests compared observed vs. estimated mean speeds for roads with similar characteristics (crosssection, speed limit, location) at given traffic flow levels (table 9). Table 10 presents the results of ttests for HCM, HBS and SHCM method.
The results in table 10 indicate that there is a statistically significant difference ( < 0.05) between the observed mean speed and the mean speed estimated with the use of HBS or SHCM method, regardless of the volume level. In case of HCM, almost in all cases it was impossible to state that the means are significantly different.