Study on Heterogeneous Traffic Flow characteristics of a Two-Lane Road

Abstract The paper presents traffic studies conducted by using a video capturing technique on the uninterrupted heterogeneous mix of vehicles plying on an undivided two-lane road facility. On the basis of the collected data, traffic characteristics pertaining to arrival, headway and speed distributions have been plotted considering suitable mathematical distributions to fit field observed values. The curves representing fundamental traffic flow relationships among three basic variables, namely speed, density and flow have also been established. Thus, a systematic attempt to enable the understanding of heterogeneous traffic flow parameters has been made through this exploratory study.


Introduction
Road tra c in India displays a heterogeneous mix condition wherein vehicles possessing distinguished physical and operational attributes constitute the vehicular ow. e behaviour of homogeneous ows, commonly observed in the developed Western nations, is characterized by a strict lane discipline and single-le motion of vehicles with restricted movement across the lanes. A heterogeneous ow, on the contrary, is di erentiated by the presence of a loose lane discipline and use of the entire road space without any con nements for manoeuvring. e lateral movement of vehicles, apart from usual longitudinal motion, results in mass queue formations that operate two-dimensionally. Furthermore, wide ranging vehicle types moving in these tra c ows add to the dynamic quality of the ow. e behaviour of such tra c is ensued by the existence of ow variables that vary over space and time. Knowledge about these parameters is, therefore, essential for understanding the nature of a heterogeneous tra c mix moving on the road. Information derived from parametric studies can provide a crucial base for accomplishing tasks such as road design, planning and operation.
A large proportion of the transport network in India consists of two-lane roads. e majority of them are undivided road facilities that are uniquely identi ed by the subjection of vehicles to tra c moving on the oncoming lane. us, the behaviour of ows travelling in a particular direction is predominantly in uenced by the prevailing tra c conditions on the opposing lane, as it constrains the passing/overtaking activity of vehicles. In India, these facilities carry a high volume of tra c comprising a variety of public, private and commercial vehicles. ey serve a wide range of tra c requirements concerned with infrastructural potential and indirectly a ect the economy and commerce of the country. e paper hereby aims to examine the tra c ow parameters of the uninterrupted heterogeneous tra c ow on a two-lane undivided road facility. e primary objectives desired to be accomplished through the study are listed as follows: to obtain and extract tra c data from the eld employing a suitable approach; to assess data with respect to arrival patterns, time headway characteristics and vehicle speed distributions; to derive fundamental relationships among key variables -speed, density and ow.

Literature Review
Several empirical studies were performed in the past to evaluate tra c ow characteristics of vehicles and to determine appropriate representations of tra c ow parameters. Katti et al. (1985) found through their study on arterials that for volumes ranging from 500 to 1000 vehicles/hour, negative exponential distribution was suitable for representing headways between vehicles. Mukherjee et al. (1988) evaluated the suitability of negative and shi ed negative exponential distributions to generate vehicles approaching roads at the intersections in Calcutta, India. e suitability of theoretical distributions was judged by using the chi-square test. It was found that the shi ed negative exponential distribution gave a close t for the observed headways. It was suggested that a comparison of theoretical headway distributions along with the observed distributions could be made based on cumulative frequencies. Sahoo et al. (1996) used a 3-second class interval for grouping headway data and compared cumulative frequencies of the observed and theoretical distributions. e maximum tra c volume was about 850 vehicles per hour, and headways were found to t into negative exponential distribution. The authors also found that vehicular speeds tted well to normal distribution with a mean of 42÷45 km/h and a standard deviation of 9÷13 km/h on di erent intercity roads in India. Hossain and Iqbal (1999) attempted to study headway patterns on twolane, two-way highways in Bangladesh. e carried out analysis determined that for the volume of the observed eld ranging between 200 and 708 vehicles / hour, exponential and log-normal distributions were adequate for tting time headways between vehicles. Al-Ghamdi (2001) analyzed the time headways of vehicle arrivals on urban roads in Riyadh based on lane-wise tra c data collected under di erent volume levels. It was found that negative exponential, shi ed exponential and gamma distributions reasonably tted time headways at low and medium ow rates on freeways, whereas the Erlang distribution was found to be appropriate in high tra c ows. An appropriate methodology to extract headway data was suggested by Arasan and Koshy (2003) in their study on a heterogeneous tra c ow on an urban arterial in Chennai, India. ey also recommended Sturges' rule for computing the range of headway classes and established that headway data representing varying ows could be tted as negative exponential distribution. Arkatkar and Arasan (2010) determined that vehicle arrivals could be tted well into the Poisson distribution, whereas inter-arrival times could be tted well into negative exponential distribution. Kadiyali et al. (1981) discovered that free speeds of di erent types of vehicles followed normal distribution. May (1990) suggested choosing the Poisson distribution for modelling vehicle arrivals under low-ow random headway state conditions. He purported that the speeds of the observed speeds could be tted as normal or log-normal distribution based on the traits of their frequency distribution plots. Tseng et al. (2005), as a part of e ort to revise Taiwan Area Highway Capacity Manual, analyzed the collected free-ow speed data at the midpoints of seventy-six multilane rural and suburban highway segments in Taiwan. e analysis regarding the distribution of free ow speeds for di erent vehicle categories showed that free speeds of di erent vehicle categories followed normal distribution. Minh et al. (2005) performed a study to analyze motorcycle behaviour and operation on four selected locations in Hanoi, Vietnam. Speed -ow relationships were developed using the adjustment factor for the presence of vehicles, other than motorcycles, and was based on the motorcycle equivalent unit. Speed data on motorcycles were also plotted as normal distribution. Hall and Montgomery (1993) pointed out the important features of a speed-ow fundamental diagram. Speedvolume relationships employed in the U.K. comprises two-segment linear functions. Speed may remain constant with increasing ow for some considerable range of ows. e break point, at which speed starts decreasing, is somewhere around the two-thirds or three-quarters of maximum ows. Speed at maximum ows, in the absence of congestion (queues), may be 10 to 25 km/h lower than free-ow speed. It is unlikely, that the whole data pertaining to the speed-ow curve can be obtained at any location. Within the bottleneck, data may cover an uncongested segment along with some portion of the queue discharge segment. On the other hand, in the location that experiences queue formation, some portion of the uncongested segment will be observed along with some part of the within queue. Sahoo et al. (1996) studied tra c ow characteristics on National Highway No. 5. e conducted analysis concluded that with an increase in tra c volume, speed decreased. e relationships among speed, ow and density were studied by Kumar and Rao (1998) for road stretches on NH 5 and NH 6 in India. ey established fundamental diagrams based on the collected data and observed it was inadequate to estimate capacity values since the ow of vehicles did not encompass an appropriate regime. However, Haefner et al. (1998) were able to determine capacity, free-ow speeds and critical density from the relationships plotted for tra c data collected from an urban freeway in St. Louis, as a wide range of ow regimes could be identi ed. Akcelik et al. (1999) developed a time-dependent speed-ow model popularly known as Akcelik's function based on queuing theory concepts, providing a smooth transition between a steady-state queuing-delay function for unsaturated conditions and a deterministic-delay function for over saturated conditions. Arasan et al. (2009) modelled a set of speed-ow curves using HETEROSIM simulation so ware for heterogeneous tra c on road spaces having widths of 7.5 m, 11.0 m and 14.5 m. Relationships thus developed were observed to follow the standard pattern indicating the goodness of the simulation model. Van As and Van Niekerk (2004) evaluated the available tra c models for an operational analysis of two-lane highways and proposed an alternative queuing model for platoons in a tra c ow under conditions of South African roadways. It was found that the available models such as those from the Highway Capacity Manual had various limitations and were inappropriate or inadequate for modelling South African road tra c. A new model based on microscopic simulation was proposed and an alternative measure of e ectiveness, named follower density, was introduced which serves as a better indicator of warranting capacity upgrading. Roshandeh et al. (2009) performed spot-speed studies on a Malaysian highway and plotted frequency distribution curves useful for understanding tra c ow characteristics and making speedrelated decisions on a particular roadway system. Speed distribution curves were plotted for eld observed data and basic parameters related to speed were derived for the selected highway with a heterogeneous tra c mix. e importance of speed studies, with respect to tra c engineering, was also discussed. Polus and Cohen (2009) developed and estimated new, theory-based queuing relationships considering the quality of the ow on 15 two-lane rural highways in northern Israel and proposed a new Level of Service (LOS) variable measuring the quality of the ow both inside and between platoons in a tra c ow. e study presented ve ow measures, namely -the platoon ow rate, the average platoon length, tra c intensity, percent-time-spent following and the freedom of the ow. ese measures are highly relevant to estimate ow characteristics on two-lane rural highways. e relationship between the freedom of the ow and two-way ow was also calibrated from trafc observations. LOS thresholds based on the ow and the freedom of the ow were presented and discussed.
e reviewed literature presents that the selection of eld location as well as the application of a suitable approach for collecting and extracting data form a crucial part of tra c studies. Also, various distributions and relationships pertaining to ow parameters take into account the quality of the ow that prevails on road spaces, which subsequently determines the choice and appropriateness of an adequate representation of eld observed variables.

Data Collection
For the purpose of collecting tra c data, a 500 m long road stretch on National Highway (NH) No 11 corridor between Sikar and Jaipur cities situated in the western part of India was selected. It is an undivided two-lane two-way road with an overall uniform carriageway width of 7.5 m and paved shoulder width of 1.25 meters in each direction. e width of the unpaved shoulder, made of gravels and stones, ranges from 2 to 2.5 m in each direction; however, it had no e ect on the movement of tra c as vehicles travelled on the road pavement. e chosen tra c plying on the study section is not in uenced by any nearby intersections or road geometry such as a gradient. e conditions prevailing on the study section thus ensured an uninterrupted ow of tra c.
Data was collected within the period of two hoursfrom 4 p.m. to 6 p.m. Four observation points were chosen for installing video cameras: two in each direction, for recording the entry and exit of vehicles. e recordings were synchronized so that extraction errors due to time lag could be avoided. Discernible markings were made on the unpaved shoulder that functioned as reference points. A verbal recording of vehicle categories and license plate numbers was also done to assist the data extraction process. In this manner, continuous data was collected on the two-lane roadway ramp without any loss of information pertaining to the vehicles crossing the road section.

Data Extraction
Tra c data collected from the eld section was extracted using the FMV6 (Full Motion Video) player. Mpeg format video les were played on a computer screen a er copying recordings from each camera on compact discs. e FMV6 player is capable of fragmenting video into frames, which can then be noted down by stopping playback and navigating forward and backward to obtain frame reading when the vehicle just crosses the reference point. e frame numbers can be changed to time values by applying a simple conversion of the unitary method. Time thus computed is denoted in seconds and has the accuracy of up to two decimal places. Careful consideration was given to obtain the exact frame number as, in many instances, more than one vehicle crossed the reference point almost together. is was observed in cases where an overtaking manoeuvre took place near the reference points.
Four observation recordings were processed one at a time. Certain key features such as the number of passengers in case of open vehicles, vehicle-model descriptions etc., were noted down so that the identi cation of a vehicle could be facilitated when the other recording for the same direction was processed. e videos were also repeatedly played at normal speeds around the instances when the vehicle crossed the reference point, so that information from verbal recording could also be obtained for veri cation. e data incurred from video recordings was tabulated as in-time and out-time values ranging from 0 to 7200 and denoted in seconds. Time headways and speeds for vehicles in each direction were calculated by operating on time values. e hourly volume of vehicles travelling towards Jaipur and Sikar was found to be about 733 vehicles / hour and 654 vehicles / hour respectively.
Within the period of two hours considered for the study, there were a few vehicles for which the in-time and out-time values could not be accounted either because they had been already present on the road section when the recording began, or the recording ended before they could exit the study section. However, single time values obtained for these vehicles were retained as they were needed for examining parameters measured at a point such as arrival and headway. Vehicles for which both intimes and out-times were within the period of two-hours were accounted during speed calculations. A number of vehicle types were observed on the study section and then broadly grouped into nine categories, namely: 1) motorized 2-wheeler; 2) motorized 3-wheeler; 3) bus; 4) car; 5) light commercial vehicle (L.C.V.); 6) truck; 7) tractor; 8) bicycle; 9) other (tricycle, animal-pulled cart). Tra c composition for each direction at the study section is illustrated in Table 1.
It can be noticed that motorized 2-wheelers dominated in the tra c ow. It can also be seen that non-motorized vehicles such as bicycles, tricycles and camel carts were found to comprise the heterogeneous tra c ow.

Evaluation of Tra c Flow Characteristics
ree main evaluated tra c characteristics taken from the extracted data include arrival patterns, headway characteristics and speed distributions. e corresponding results obtained from the data analysis procedure are discussed in the following sub-sections.

Arrival Pattern
e uninterrupted heterogeneous tra c ow observed on the selected study section had vehicles mostly travelling independently of each other and resulting in a random arrival pattern. erefore, for the conditions observed on the road section, the Poisson distribution was determined to be a suitable choice for modelling arrival data. e probability mass function for the Poisson distribution is given by: ! r m m e P r r .
In the above equation, P(r) is the probability of vehicles r arriving in time t and m is the average vehicle arrivals per time interval.
Vehicle arrival is point-based measurement, and hence, the arrival pattern was analyzed separately for four observation points in the study section. Vehicles entering the study section were marked as in-vehicles and vehicles exiting the study section were marked as out-vehicles. e vehicles examined for evaluating arrival characteristics were, therefore, grouped as J In (invehicles travelling towards Jaipur), J Out (out-vehicles travelling towards Jaipur), S In (in-vehicles travelling towards Sikar) and S Out (out-vehicles travelling towards Sikar). A combined arrival pattern was also examined by taking into account vehicles arriving at a point on the road section from both directions. e point where in-vehicles travelling towards Jaipur and out-vehicles travelling towards Sikar arrive was labelled as J In S Out , whereas the point where out-vehicles travelling towards Jaipur and in-vehicles travelling towards Sikar arrive was labelled as J Out S In .
For each case, an appropriate time interval was chosen and the number of vehicles arriving in each of these time intervals was counted in order to obtain grouped data on vehicle arrivals. e chi-square test was performed to assess the goodness-of-t of eld observed data as the Poisson distribution. e results of analyses have been summarized in Tables 2, 3 and 4.
Degrees of freedom (df) have been computed by the formula given below: In the above formula, df refers to the number of degrees of freedom, I is the number of class intervals being compared during analysis and p is the number of parameters estimated for de ning the distribution. For the Poisson distribution, the value of p is 1, as only 'm' referring to the average arrival of vehicles per class interval is estimated for de ning the distribution.
us, the generic equation evaluating degrees of freedom (df) becomes: Depending on the number of arrival time intervals (I) being compared during analysis in each case, the value of df is obtained and the corresponding critical chi-square value is checked from the chi-square table for a user-speci ed level of signi cance.
In all cases, the calculated chi-square value (F 2 [calc.]) is found to be less than critical chi-square value (F 2 [c]) obtained from the chi-square table corresponding to the computed degrees of freedom and having the signi cance level of 0.05. is indicates a good t of the observed arrival values as the proposed distribution. us, for all cases, arrival data was successfully modelled as the Poisson distribution and the hypothesis was ascertained by evaluating chi-square tests.

Headway Characteristics
Vehicles constituting the uninterrupted tra c ow moving on the study section were travelling independently of each other and resulting in random headway distribution. erefore, for the conditions observed in the eld study section and based on literature review, negative exponential distribution was selected as the mathematical model to t the observed headway data. Unlike the Poisson distribution which is discrete distribution considering the counts of vehicles, a negative exponential model is a continuous curve taking into account frequency class interval. It describes times between events in the Poisson process and can be derived from the equation of probability mass function for Poisson. e function is then given as: In the equation, P(h ≤ t) is the probability of time headways equal to or less than time t. O is a parameter involved in estimating theoretical distribution and is denoted as the inverse of the mean time headway.
Similar to vehicle arrivals, time headway is pointbased measurement, and therefore a headway pattern was analyzed separately in light of`four observation points in the study section. As mentioned in the previous section, vehicles entering the study section were marked as in-vehicles and vehicles exiting the study section were marked as out-vehicles. e vehicles examined for evaluating headway characteristics were, therefore, grouped as J In (in-vehicles travelling towards Jaipur), J Out (out-vehicles travelling towards Jaipur), S In (invehicles travelling towards Sikar) and S Out (out-vehicles travelling towards Sikar). A combined headway pattern was also examined by combining the headways of in-vehicles and out-vehicles for each direction. e combined headway data for vehicles travelling towards Jaipur was labelled as J In J Out , whereas for vehicles moving towards Sikar, the combined data was labelled as S In S Out .
A sample data set representing di erent ow-levels was selected for each case and an appropriate range of time interval was chosen using the Sturges' rule expressed as: In the equation, I is the range of class interval, R is the total range of the observed values and N is the number of observations. As exclaimed by Arasan et al. (2003), the Sturges' rule only gives an estimate of the range of class intervals. Several di erent range values around the computed range should be tried out and the smallest one that gives a smooth histogram must be selected. A desirable way is to interpret the histogram plot of headway data by statistically mapping the eld measured values, and select bin range for which a smooth graph of a negative exponential curve is obtained. For this study, MINITAB was used to plot the data set of the headway sample. e selection of an appropriate class interval is a vital step for beginning the analysis process as the selected range will decide the capability of the observed values tting into the proposed mathematical distribution.
A er selecting the range, the chi-square test was performed to assess the goodness-of-t of eld measured data as negative exponential distribution. e results of analysis for each case are summarized in Tables 5 and 6. e tables show that minimum headways were recorded to be as low as 0.01 seconds, and in some cases, even zero time headways were observed. is can be attributed to the fact that on many occasions, vehicles engaged in overtaking manoeuvres near the observation points only if tra c on the opposing lane was very light or negligible in order to allow the pass. In some cases, two smaller vehicles such as motorized 2-wheelers were involved in overtaking activity; however, owing to their small sizes, it could be executed on the same one-way lane without being moderated by tra c moving over the oncoming lane.
Degrees of freedom have been computed by the formula given in the previous sub-section. Even for headway analysis, the value of p is 1 as only O referring to the inverse of the mean time headway is estimated for de ning the distribution. us, the generic equation for evaluating degrees of freedom becomes: In the equation, 'I' pertains to the number of class intervals being compared.
In all cases, the calculated chi-square value (F 2 [calc.]) is found to be less than critical chi-square value (F 2 [c]) obtained from the chi-square table, corresponding to the computed degrees of freedom and having the signi cance level of 0.05. is indicates a good t of the observed headway values as the proposed distribution. us, for the cases, headway data was successfully modelled as negative exponential distribution and the hypothesis was ascertained by evaluating chi-square tests.

Speed Distributions
Speed is a qualitative measure of tra c ow. In a tra c ow, vehicles move with di erent individual speeds. Instead of having single characteristic speed, a tra c mix has the distribution of speeds that can then describe the behaviour of vehicle movements on the road facility. e basic speed measures, as observed for the vehicles plying on the study section, are illustrated in Tables 7 and 8 for each vehicle category and for both directions. Max/Min refer to maximum and minimum speeds recorded for the vehicle category. P is the mean and V is a standard deviation of the observed speed values.
e Tables indicate that high speed values were recorded for cars, whereas vehicle categories such as a motorized 3-wheeler, tractor, bicycle etc., were found to traverse the road section with considerably lower speeds. As a result, these categories had lower mean speeds while high mean values were detected for cars. Also, a maximum deviation of speed values from the mean was observed for cars since they were found to travel with wide ranging speeds, for example, in the range of 85.82 km/hr for cars moving towards Jaipur. Motorized 2-wheelers, buses and L.C.V. 's were also noticed to have substantially high standard deviation values. e reason for this occurrence can be attributed to the various models or types of these vehicle categories having di erent power capacities and operational capabilities plying on the road. For example, certain models of motorcycles can be accelerated to higher speeds, whereas scooters that fall under the same motorized 2-wheeler category have comparatively low acceleration capabilities. e same observation can also be ascribed to the age of the vehicle, since old vehicles will have lower performance. Comparatively smaller deviation values have been identi ed for motorized 3-wheelers, trucks and tractors as operational variation in models is comparatively less.
Sample data sets from vehicle categories with the size above 30 observations were analyzed for each direction. A combined data set was also created by uniting vehicle samples from each vehicle category moving in each direction, and analyzed for evaluating speed characteristics. For starting the analysis process, an appropriate speed class interval was computed from the Sturges' rule described in the previous sub-sections. By supplying various bin range values around the computed range, the observed speeds were plotted as frequency histograms in MINITAB. erefore, for these categories, normal distribution was selected to represent the eld values. In order to ease calculations, standard normal distribution was opted, which has the sample mean set at zero with dispersion on either side of y-axis. e probability density function for a standard normal curve is given by: In the equation, z is a parameter computed as z = (x -P)/V, where x is an observation of the investigated speed, P is the mean of the sample and V is a standard deviation from the sample.
In the case of motorized 2-wheelers, the histogram plots revealed that the distribution was unimodal and asymmetric around the mean with a considerably long tail extending to the right. e plot indicated that the mean was located at a lower side with respect to the wide spread of the observed speeds. is behaviour is typical of a log-normal curve. erefore, log-normal distribution was selected as a suitable model to represent data sets for motorized 2-wheelers. e probability density function for a log-normal curve is expressed by the following equation: In the above equation, x refers to the investigated speed value; μ ln is the mean of the natural logarithm of speed values and V ln is a standard deviation the natural logarithm of speed values.
A er selecting a suitable range to group the eld values, the chi-square test was performed to assess the goodness-of-t of eld measured data as the proposed distribution. e results of the analysis of each vehicle category that were travelling towards Jaipur and Sikar are summarized in Tables 9 and 10 respectively. e results incurred from the combined data analysis are summarized in Table 11. In the Tables, L.C.V. refers to Light Commercial Vehicles. Degrees of freedom have been accounted for by the formula given in the 'arrival pattern' sub-section. For a standard normal curve, the value of p is 2 as z value, estimated for each speed observation, considers mean (P) and standard deviation (V) for de ning the distribution. In case of a log-normal curve, the value of p is also 2, since a mean and standard deviation from natural logarithms of speed (P ln and V ln ) are two parameters determined for de ning the distribution. us, a generic equation for evaluating degrees of freedom for both distributions is given by: In the equation, 'I' refers to the number of compared class intervals.
In all cases, the calculated chi-square value (F 2 [calc.]) is found to be less than critical chi-square value (F 2 [c]) obtained from the chi-square table corresponding to the computed degrees of freedom and having the signi cance level of 0.05. is indicates a good t of the observed speed values as the proposed distribution. us, for all cases, data on speed was successfully modelled as log-normal for motorized 2-wheelers and normal distribution for the rest of vehicle categories. e hypothesis was ascertained by evaluating chi-square tests.

Fundamental Tra c Flow Relationships
Empirical relationships among three basic variablesspeed, density and ow -can be explained on the basis of fundamental diagrams of tra c ow. It is a macroscopic theoretical model which is an eminent indicator of the operational capability of road facility. On the basis of the data collected from the eld for this study, three primary relationships have been established and discussed in the following sub-sections.

Speed-Density
According to the theoretical diagrams of tra c ow, linear relationship exists between the density and speeds of vehicles travelling on the road (May 1990). Density is space measurement accounted for a particular instant of time. erefore, in order to explain the same phenomenon for the observed tra c data, a total of 36 random control points were evaluated separately for each direction. Data on a two-hour period was extracted identifying time (in seconds) at which vehicles crossed observation points. Hence, the times of entry and exit ramps ranging between 0 and 7200 seconds were obtained.
ese time values were plotted in MINITAB by supplying speci c bin values and the regions of varying ows were identi ed. Control points were selected within the identi ed classes and density was computed by counting the number of vehicles present on the road section at those instants of time. e average speed of vehicles constituting density was then calculated as space mean speed. On the basis of the obtained values, graphical plots between speed, as kilometres per hour and density, as vehicles per kilometre, were mapped and regressiont analysis was performed to examine how well data points approximated to a linear model. For vehicles travelling towards Jaipur and Sikar, speed-density linear plots were found to incur R 2 values of 0.810 and 0.745 respectively. is indicates a decent t of data points as a linear model. Both tted line plots are illustrated in Figs 1 and 2 along with the equation for the regression line. e obtained tted linear plots were extrapolated in order to determine axis intercepts on x-axis and y-axis representing jam-density and free-ow speeds of vehicles respectively. For vehicles travelling towards Jaipur, jam density and free-ow speeds were estimated to be 109.75 vehicles/km and 68.88 km/hr respectively. In case of vehicles moving towards Sikar, jam density and free ow speeds were determined to be 106.88 vehicles/km and 69.02 km/hr respectively.
It may be noted that these parameters have been estimated utilizing an empirical approach, and this exercise was conducted to gain some basic understanding of such relationship.
Control points selected for both directions were united to obtain a combined plot of 72 data points. Regression-t analysis was performed to examine the goodness-of-t of the linear model. e R 2 value of the combined plot was found to be 0.796 indicating a decent t. e tted line was extrapolated to obtain jam density and free-ow speed determined to be 109.07 vehicles/ km and 68.89 km/hr respectively. e regression-t plot for a combined data set is illustrated in Fig. 3 along with the equation for the regression line.
In all the plots, free-ow speeds are the space mean speed of vehicles. e established relationships reveal that the average speed of vehicles decreases with an increase in density since the movement of vehicles on the road gets impeded. According to the linear model, this trend continues until density reaches jam condition wherein vehicles come to a complete stop. e same phenomenon was explained for the tra c ow plying on the selected two-lane road stretch.
Data on tra c collected from the study site represents an uninterrupted vehicular ow. e ow of vehicles on the road did not reach the capacity level at any point of time during the study. us, only the uncongested regime was obtained for the relationship and region at and beyond capacity ow could not be mapped. However, some basic idea about tra c behaviour as well as linear relationship that exists between the speed and density of vehicles was acquired through the plots.

Speed-Flow
According to the theoretical diagrams of tra c ow, a parabolic relationship exists between the ow and speeds of vehicles in a tra c ow (May 1990;Highway Capacity Manual 2000). e ow is point-based measurement accounted for a time period usually shorter than an hour. However, it is expressed as a measure of vehicles per hour. For data collected from the study on the two-lane section, tra c regimes at and beyond capacity ow could not be mapped as behaviour observed for an uninterrupted ow was insu cient for evaluating relationships during congested condition. In order to explicate the uncongested regime, in total, 36 control intervals of 1 minute length were evaluated separately for each direction. ese intervals of varying ow-levels were identi ed a er plotting in MINITAB. e ow of vehicles and the average speed of vehicles constituting the ow were computed for each time interval. e average speed represents the space mean speed of vehicles. Graphical plots between speed, as kilometres per hour, and the ow, as vehicles per hour, were mapped for each case as shown in Figs 4 and 5. Regression-t analysis was performed to analyze the approximation of data points as a quadratic model. For vehicles travelling towards Jaipur and Sikar, speed-ow quadratic model plots were found to incur R 2 values of 0.630 and 0.631 respectively. ese values indicate a decent t of eld observed data as a quadratic relationship model. Regression curve equations are also displayed in the gures.
A combined data set of 72 values, a er uniting control points from each direction, was also created. e speed vs. ow graph for combined values is presented in Fig. 6 along with the equation for the regression curve. Flow and speed values were plotted in MINITAB and regression-t analysis was conducted to assess the goodness of the quadratic model. For a combined data plot, R 2 value was observed to be 0.592 which indicated a decent t of data points as the quadratic model. e established relationships disclose that the average speed of vehicles decreases gradually with an increase in ow. is occurs due to the fact that along with a rise in the ow, the number of vehicles moving on road facility increases thus impeding the free movement of vehicles. e same phenomenon was explained for the tra c ow plying on the selected section of the twolane road. According to the theoretical model, this trend continues until capacity ow is reached wherein vehicles travel with critical speed. Beyond this point, the ow decreases gradually along with speed under congested conditions. Data on tra c collected from the study site represents an uninterrupted vehicular ow. e ow of vehicles on the road did not reach the capacity level at any point of time during the study. us, as mentioned earlier in this section, only the uncongested regime was obtained for the relationship and region at and beyond capacity ow could not be mapped. However, some basic idea about tra c behaviour as well as quadratic relationship that exists between the speed and ow of vehicles was acquired through the plots.

Flow-Density
e relationship between ow and density follows a parabolic curve according to the theoretical models of tra c ow (May 1990;Highway Capacity Manual 2000). Associating these two variables for tra c data collected from the study section was a bit tricky, since the ow is measured over a time interval while density is accounted for an instant of time. e obtained data discloses that minimum time taken by a vehicle to cross the road section of 500 meters, considered for the study, was a bit more than 15 seconds. Hence, a time interval of 15 seconds was chosen for computing the ow of vehicles entering the road section. e end point of these 15 second intervals was selected as the instant of time for calculating density. By selecting a period of the remarked length of time, it was ensured that whatever vehicles constituted the ow could also be accounted for density measurement. e vehicles that may have been present on the road section before the start of the interval and remained on stretch for the entire 15 seconds were also included in density measurements. is can be justi ed by the fact that vehicles already moving in a tra c ow also have an in uence on the in ow of vehicles.
For data collected from the two-lane study, trafc regimes at and beyond capacity ow could not be mapped as the behaviour observed for an uninterrupted ow was insu cient for evaluating relationships during the congested condition. In order to explicate the uncongested regime, a total of 36 control intervals of 15 seconds were considered and evaluated separately for each direction. ese intervals of varying ow-levels were identi ed from the plots obtained through MINIT-AB. e ow and density of vehicles were computed for each time interval. e graphical plots between the ow, as vehicles per hour, and density, as vehicles per kilometre, were mapped in MINITAB and regression-t analysis was performed to examine the approximation of data points as a quadratic model. For vehicles travelling towards Jaipur and Sikar, the plots of the ow-density quadratic model were found to incur R 2 values of 0.788 and 0.845 respectively. Two graphs, along with the equation for the regression curve, are displayed in Figs 7 and 8.
A combined relationship was also established with respect to ow-levels related to both directions by considering a separate set of 50 class intervals of 15 seconds. For a particular time period of 15 seconds, the ow from both directions was aggregated and noted down. Similarly, taking the end point of these intervals as an instant of time, the total density of vehicles on the entire road section was computed. e relationship between ow and density for the combined data was plotted and regression t analysis was conducted to assess the goodness-of-t of data points as a quadratic model. e R 2 value of the tted line plot was determined to be 0.704, which indicates a decent t of the observed data points for a quadratic plot. e graph along with the equation for the regression curve is shown in Fig. 9.
e established relationships indicate that the density of vehicles on the road increases gradually with an increase in the ow. is is attributed to the fact that along with a rise in the ow, the number of vehicles us- ing the road facility increases, thus subsequently raising density measure. e same phenomenon has been explained while discussing the tra c ow plying on the selected section of the two-lane road. According to the theoretical model, this trend continues until capacity ow is reached wherein vehicles reach critical density. Beyond this point, the ow decreases gradually while density keeps increasing as more vehicles enter the road section resulting in the congested ow. Tra c data collected from the study site represents an uninterrupted vehicular ow. e ow of vehicles on the road did not reach the capacity level at any point of time during the study. us, only the uncongested regime was obtained and relationship with the region at and beyond capacity ow could not be mapped. However, some basic idea about tra c behaviour as well as a quadratic relationship existing between the ow and density of vehicles was acquired through the plots.

Summary and Conclusions
e study discussed in this paper was performed in order to understand primary tra c parameters and their features pertaining to vehicle behaviour on the two-lane road. Tra c data on a long road section of 500 meters was collected and extracted for a period of two hours. A suitable methodology was incorporated in the process that ensured the collection of a wide range of tra c plying on the study site without any loss of information and the development of accurate readings for evaluating tra c variables. e obtained tra c data was utilized to compute arrival, headway, speed, ow and density parameters analyzed using statistical methods for studying tra c characteristics and fundamental relationships of the vehicle ow moving in both directions on the road section. e outcomes of the procedures performed in this study are listed below: 1) Arrival patterns of vehicles were tted as the Poisson distribution and chi-square test analysis validated the likelihood of eld values conforming to the proposed distribution. 2) Headway characteristics were modelled as negative exponential distribution and the choice was con rmed by conducting the analysis of the chisquare test.
3) Speed distributions of di erent vehicle types observed on the road section were tted for a normal curve, except the speed distributions for motorized 2-wheeler that were modelled as lognormal distribution. e performed chi-square test analysis validated the likelihood of the observed speed values approximating to the proposed distributions. 4) Speed vs. density plots were established for tra c data that revealed a linear relationship between the two ow parameters. Regressiont analysis was carried out to verify the linear model. Jam density and free-ow speeds were estimated through the plots. 5) Speed vs. ow plots were developed for the observed values and a quadratic relationship between the two parameters was veri ed through regression-t analysis. 6) Flow vs. density plots were established for the observed data which revealed a quadratic relationship between the two tra c ow parameters. e model was veri ed conducting regression-t analysis. us, for an uninterrupted heterogeneous tra c ow moving on the two-lane road section selected for the survey, parameter distributions and fundamental relationships among the key variables were examined and ascertained through this exploratory study.
In the case of density measurements, it should be noted that the executed methodology is su cient only for gaining a basic understanding of parameters. In this study, the density of vehicles formulated for the road section was adequate for accomplishing the basic task of presenting the fundamental relationships of the tra c ow. erefore, jam densities and free-ow speeds evaluated from speed-density tted line plots are only estimated empirical values derived through a methodology that enables understanding of primary ow attributes.
One principal limitation of the study pertains to the vehicle composition quality of the tra c ow. e conducted two-hour survey presented only a snapshot of tra c ow properties of the composition observed during the stipulated period. However, vehicular trafc ow is a dynamic attribute and keeps changing over time. In case of a heterogeneous mix, where a variety of vehicle-types with distinguished physical and operational characteristics comprise the tra c ow, the composition becomes a major determinant as it in uences the parametric properties of tra c ow. Hence, observations made between two di erent periods of the study may not develop exactly the same results. Also, data points evaluated from the study could only present ow regimes for an uninterrupted tra c ow. e region pertaining to the over-saturated ow could not be obtained as the conditions persisting on the study section were not su cient to plot the related relationship. However, tra c studies, such as the one explained in this paper, can provide a basic understanding of the nature and behaviour of vehicle ows moving on the road facility. Real-time headways and speed measurements computed for a tra c ow can also be regenerated on computer via simulation so ware that requires three main inputs for recreating the observed tra c ow, including vehicle generation, vehicle placement and vehicle movement. Headways and arrivals account for the rst two input variables, whereas speed values can determine the movement of vehicles. Simulated tra c can then be studied by dealing with various parameters and observing e ects on the nature of the ow. In this way, consequences of changing the behaviour of the tra c ow can be evaluated and certain key factors with respect to design considerations can be determined. Using data information taken from this study, tra c simulation exercises can be performed as further research on widening the scope of understanding the behaviour of the vehicular ow for a heterogeneous mix.
Tra c is a stochastic quantity and it varies from place to place depending on local factors and driver's behaviour. erefore, tra c studies are important for acquiring knowledge about the nature of vehicular ows. e information acquired assists in building better, safer and e cient road facilities. Roads are a part of the infrastructure and tra c that ows through them determines the aesthetic as well as economic value of the country. Hence, tra c engineering plays a vital part in ensuring that the vehicles travelling on the road facilities can reach their intended destinations with comfort and ease and without compromising safety issues.