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Modeling time mean speed and spacemean speed for heterogeneous trafficconditionsPadma Seetharaman a , Madhu Errampalli a , VelmuruganSenathipati b , Anuradha Shukla c & Subhamay Gangopadhyay da Scientist, Transport Planning & Environment Division, CentralRoad Research Institute (C.R.R.I.) , New Delhi, 110025, Indiab Scientist, Traffic Engineering & Safety Division, Central RoadResearch Institute (C.R.R.I) , New Delhi, 110025, Indiac Head of the Division, Transport Planning and Environment,Central Road Research Institute (C.R.R.I.) , New Delhi, 110025,Indiad Central Road Research Institute (C.R.R.I) , New Delhi, 110025,IndiaPublished online: 15 Nov 2011.

To cite this article: Padma Seetharaman , Madhu Errampalli , Velmurugan Senathipati , AnuradhaShukla & Subhamay Gangopadhyay (2011) Modeling time mean speed and space mean speed forheterogeneous traffic conditions, Transportation Planning and Technology, 34:8, 823-838, DOI:10.1080/03081060.2011.613593

To link to this article: http://dx.doi.org/10.1080/03081060.2011.613593

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Modeling time mean speed and space mean speed for heterogeneoustraffic conditions

Padma Seetharamana*, Madhu Errampallia, Velmurugan Senathipatib,

Anuradha Shuklac and Subhamay Gangopadhyayd

aScientist, Transport Planning & Environment Division, Central Road Research Institute(C.R.R.I.), New Delhi-110025, India; bScientist, Traffic Engineering & Safety Division, CentralRoad Research Institute (C.R.R.I), New Delhi-110025, India; cHead of the Division, TransportPlanning and Environment, Central Road Research Institute (C.R.R.I.), New Delhi-110025,

India; dDirector, Central Road Research Institute (C.R.R.I), New Delhi-110025, India

(Received 13 April 2010; accepted 8 August 2011)

This paper analyzes vehicular speeds at a micro level and studies the relationshipsbetween the important elements of speed, namely space mean speed (SMS) andtime mean speed (TMS) under heterogeneous traffic conditions. Vehicular speeddata were collected at selected road stretches around Delhi, India, in an attemptto understand and model the type of relationships between SMS and TMS underheterogeneous traffic conditions. To demonstrate the superiority of the proposedmodels, comparisons are made with existing traditional models. The results revealthat the proposed models are consistent in predicting speeds with high accuracy.

Keywords: time mean speed (TMS); space mean speed (SMS); variance;heterogeneous traffic; Delhi

Introduction

Speed, a primary element in the area of traffic engineering, has a wide range of

applications. For instance, it has a vital role in determining capacity of roads through

speed-flow relationships, geometric design of roads, implementation of traffic control

measures to improve safety, fuel consumption, and associated vehicle operating cost

components for economic evaluation of road projects, evaluation of performance

through journey speed, etc. The mean vehicular speed on roads is generallyrepresented in two forms, namely time mean speed (TMS) and space mean speed

(SMS). TMS is defined as the arithmetic average of speeds of vehicles observed

passing a point on a highway and is also referred to as the average spot speed.

Individual speeds of vehicles passing a point are recorded and are arithmetically

averaged (HCM 2000) as shown below:

�UT ¼P

ni¼1ui

n(1)

where UT is TMS in Km/h; ui is spot speed of ith vehicle in Km/h; n is the total

number of vehicles traversing in the defined period of time.

*Corresponding author. Email: padmaseetharaman5@gmail.com

Transportation Planning and Technology

Vol. 34, No. 8, December 2011, 823�838

ISSN 0308-1060 print/ISSN 1029-0354 online

# 2011 Taylor & Francis

http://dx.doi.org/10.1080/03081060.2011.613593

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Space mean speed is a statistical term frequently used to denote an average speed

based on the average travel time of vehicles to traverse a segment of roadway. Because

of this it is called SMS where average travel time is weighted according to the length

of time each vehicle spends in the defined roadway segment or space (HCM 2000) asshown below:

�US ¼d

1n

Pn

i¼0 ti

(2)

where US is SMS in Km/h; d is the length of the selected stretch in Km; ti is time

spent by ith vehicle in defined stretch of roadway in hours; n is total number of

vehicles traversing in the defined period of time.

In developed countries where homogeneous traffic conditions and traffic lane

discipline prevails, SMS data is usually collected by automatic methods using

induction loops, infrared scanners, etc. (Han et al. 2010). But in these situations, thelength of the stretch is very small. TMS is usually collected employing laser- and

radar-based techniques. However, in India, the presence of induction loops, etc. to

measure spot speeds/TMSs, which can be used as the primary input to the

calculation of travel times, are close to negligible. Hence the travel time/SMS

calculations are carried out based on manual methods such as the registration plate

method, moving car method, etc. The processes involved in these methods are very

tedious and require a huge level of manpower. Various studies carried out in the past

have determined relationships between these speeds, namely, TMS and SMS. Thesestudies primarily emphasized the calculation of one speed from other, because of

which, the data collection process gets simplified as there is no need to collect both

types of speed data.

The state-of-the-art in developing TMS and SMS models is discussed in detail in

the next section, where the formulated objectives of the study are also presented after

critically reviewing these models. In order to develop TMS and SMS models, the

traffic data collected at selected road sections is presented in ‘Data collection and

analysis’ section. The development of the TMS and SMS models exclusively forheterogeneous traffic conditions is presented in ‘Model development’ section.

Finally, the conclusions drawn from this study are given in ‘Conclusions’ section.

State-of-the-art � TMS and SMS models

As discussed in the previous section, many studies have been conducted to study the

relationships between TMS and SMS over the years. The conventional and most

popular model which explains the relationship between SMS and TMS follows

Wardrop (1952):

�UT ¼ �US þr2

S

�US

(3)

where UT is TMS in Km/h; US is SMS in Km/h; r2S is variance of SMS Km2/h2.

Mikhalkin et al. (1972) derived the SMS of vehicles detected by single loop by

developing unbiased minimum mean square error estimators of their speed. The

study stated that the SMS should be performed for individual vehicles and not from

some arbitrarily fixed sampling period. Further, the estimators derived were checked

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with the simulation techniques and thereby their superiority over the conventional

SMS estimation techniques was established.

Hall and Persaud (1989) focused on the calculation of speed from single loop

data based on the following relationship:

�US ¼F

OCC � L(4)

where F is flow in number of vehicles passing a point in unit time; OCC is occupancy

in number of vehicles occupied in defined stretch of length; L is a constant to convert

units to similar values and is related to mean vehicle length.

This study states that as both speed and occupancy are indicators of traffic

conditions and since speed is the parameter of interest of the study, occupancy hasbeen taken as the variable to assess the consistency of the L value. It also finds that

L tends to be more scattered as the percentage occupancy increases. The study also

found that the categorization of L as a constant is erroneous and may lead to biased

results as its value varies for various percentages of occupancy. Hall and Persaud

(1989) stated that though L was not found to be a constant during the study,

according to conventional traffic flow theory L should be a constant. The reasons

behind such an occurrence could be possibly due to either measurement errors and/

or assumptions made in the conventional theory and the extent to which theyare contradicted in practice. The reasons were studied in detail and the studies have

revealed that the measurement errors were not responsible for the varying L value

but the assumptions made in the conventional traffic flow theory and their

contradictions in the practical applications were the main reasons.

The US Highway Capacity Manual (HCM 2000) proposes a typical linear

relationship between TMS and SMS as follows:

SR ¼ 1:026 � ST � 3:042 (5)

where SR is SMS in Km/h; ST is TMS in Km/h.

The data used to arrive at Eq. (5) were collected from the Chicago Area

Expressway Surveillance Project, which comprised 1224 one-minute observations.

The relationship between these speeds is found to be dictated by the method of data

collection. The data collection by single loop detectors brought about a factor of

vehicular dimension in the estimation of SMS as the trap lengths in these cases are

very small. The conventional relationship does not account for vehicular dimensions

and is applicable for the data collected over a larger trap length.Wang and Nihan (2003) proposed a SMS model considering flow and

occupancies as follows:

�SSðiÞ ¼NðiÞ

TOðiÞg(6)

where i is time integral index; �SS is SMS in km/h; N is vehicles per interval; O ispercentage of time that the loop is occupied per interval (lane occupancy); T is time

per interval; g is a factor to convert occupancy into density.

The effect of vehicle length on speed values was considered in Eq. (6) by

introducing the factor g which was used to compute SMS by converting lane

occupancy to traffic density. The above model was calibrated using data collected

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over every 20 seconds by single loop outputs, which were consolidated into five

minute intervals. To calculate the correct value of g, the mean vehicle length in real

time is necessarily required. The study proposed the g value as a function of vehicle

length which varies with time (Wang and Nihan 2003):

gðiÞ ¼ 52:8

lðiÞ(7)

where lðiÞ � mean effective length of vehicles.

Wang and Nihan (2003) justified the need for calculation of the g value for each

time interval as a function of observed effective vehicle length and also discussed

ways to estimate the mean vehicle length from single loop outputs.

Coifman et al. (2003) discussed the effect of vehicle dimension in the calculation

of speed. The study introduced an aggregate methodology to estimate the velocity of

the vehicle and reduce the impact of longer dimension vehicles on the velocity

estimates. The study argued that the mean vehicular dimension tends to produce abiased result in the calculation of velocity in comparison with the median vehicular

dimension which tends to be less sensitive toward the presence of a vehicle of higher

dimension. The study showed that the estimated SMS using the refined equation

utilizing the median value gave a lesser measure of variance in comparison with the

conventional method of computing SMS.

Contradicting the findings of Hall and Persaud (1989), Coifman et al. (2003)

were able to prove that a single mean vehicle length is enough in the case of high

flows for the calculation of SMS using TMS values. However, significant erroroccurred in the mean value of the vehicle lengths during low flow conditions as the

variance in the vehicle length values increased. Subsequently, they proposed that an

optimal time period is representative of both long and small vehicles which was

found to be sufficient for the estimation of speed of the traffic stream.

Rakha and Zhang (2005) highlighted the fact that it is relatively difficult to

collect SMS values compared to TMS values. Considering this, a derived relationship

was proposed between these parameters which enabled SMS to be estimated from

TMS values. The relationship between SMS and TMS was as follows:

�US � �UT �r2

T

�UT

(8)

where r2T �variance of TMS in Km2/h2.

It was found that the estimated SMS from Eq. (8) fell within the margin of error

from 0 to 1% with R2 values about 0.99. The study further stated that the distance

used as a trap length was so chosen that the differences in vehicle lengths could be

ignored in computing vehicle speed.

Li (2009) has highlighted that the estimated values of SMS using the single loop

output are biased as they replace the harmonic mean value with arithmetic meanvalues. The time taken by a vehicle to traverse a short distance is assumed to follow a

gamma distribution. By developing a statistical model for SMS, a Bayesian analysis

was undertaken to estimate the vehicular speed by combining prior data with current

data. The model thus developed was then incorporated in a statistical model for

SMS.

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Han et al. (2010) have approximated the value of the expectation operator Eðv2i Þ

using TMS values. This was then used for the computation of SMS using the

following equation:

SMS ¼3 � TMSþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 � TMS2 � 8Eðv2

i Þq

4(9)

After critically reviewing the available literature, it can be inferred that if the trap

lengths are small then a dynamic vehicular dimensional variable has to be

introduced. It can be clearly observed from these conventional models that thevariance of speed plays a vital role in the estimation of speeds. The variance in speeds

for homogeneous traffic is relatively less in comparison to the variance in the speeds

of heterogeneous traffic within a defined period of time. Therefore, the application of

these models might not yield realistic results under heterogeneous traffic prevailing

on Indian roads. Hence, there is a clear need for assessing the validity of these

conventional models for heterogeneous traffic and to propose an appropriate model

which is suitable exclusively for heterogeneous traffic conditions. In view of these

aspects, the objective of our study was formulated mainly to model SMS and TMSconsidering heterogeneous conditions. In this process, the present study also

proposes to validate the conventional and most popular Wardrop (1952) and Rakha

and Zhang (2005) models under heterogeneous traffic conditions. In order to achieve

this objective, the data collection, the data collection methods, and type of data

collected are described in detail in the next section.

Data collection and analysis

Traffic surveys were conducted to collect data at the following four road sectionsaround the city of Delhi:

(1) Greater Noida Expressway near Lotus Valley School;

(2) Greater Noida Expressway near Panchsheel Bal Inter College;

(3) Delhi�Gurgaon Expressway near Mahipalpur;

(4) National Highway 1 near Sonepat.

The locations were chosen such that there was no interference from cross traffic. Thetraffic surveys at the above locations mainly included: traffic volume counts; spot

speed measurements, and SMS measurements for a period of eight hours at each of

the road sections. The surveys were carried out to capture the characteristics of both

the traffic coming into Delhi and going away from Delhi. The classified traffic

volume count was undertaken using the manual method. The vehicle types

considered for this study were:

(1) Cars(2) Two Wheelers (TW)

(3) Buses

(4) Auto Rickshaws

(5) Light Commercial Vehicles (LCV)

(6) Two Axle and Multi Axle Heavy Commercial Vehicles (HCV).

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The composition of vehicles along the study stretches as shown in Figure 1 on

average were 59% cars, 30% two wheelers, 2% buses, 3% auto rickshaws, 3% LCVs,

and 3% HCVs with significant differences in terms of dimensions, speeds, etc. The

hourly variations of traffic volume at the enumerated locations are presented in

Figure 2, where it can be seen that the flow of traffic was highest on the

Delhi�Gurgaon expressway. It can also be seen that the peak hours for each of

the study stretches varied. On the Greater Noida expressway in front of Lotus Valley

School the peak hour was 9.30�10.30 am, whereas on the Greater Noida Expressway

in front of Panchsheel Bal Inter College the peak hour was 14.00�15.00 pm. At the

same time, on the Delhi�Gurgaon Expressway and National Highway 1 � near

Sonepat, the peak hour was between 9.00�10.00 am.

The spot speeds were collected using radar/laser speed guns whereas the SMS was

calculated from the data obtained through the registration plate method where the

registration number plates of vehicles were noted manually during the survey and

matched at the entry and exit of the trap length. The trap length selected at each test

section ranged from 352 to 1240 metres and the segment length was chosen so that

the vehicle dimensions did not contribute significantly to the calculation of SMS.

The time of entry and exit of the vehicles were noted using synchronized stop watches

and the speed was computed from the formula of distance and time taken to traverse

the segment. The computation of TMS and SMS was done by grouping the entire

data for an interval time period of 15 minutes. The sample size collected for Spot

Speed was about 6260, whereas the sample size for SMS was 1350 vehicles. The value

of TMS and SMS and variance of speeds for different vehicles at selected locations

are given in Tables 1 and 2, respectively. From Table 1, it can be clearly seen that the

TMS of various vehicles along the Delhi�Gurgaon road is the least when compared

with other study stretches.

From Table 2, it can be clearly seen that the average SMS of various vehicles is

lower than the TMS and the variance is also high in comparison with the

corresponding TMS variances for various study stretches.

Model development

Conventional models

To understand the characteristics of the data collected, a correlation between the

observed TMS and SMS was established. The R2 values indicated that the observed

values of SMS and TMS do not have a strong correlation: the Pearson product

moment correlation coefficient gave a value of 0.21 for the observed set of speeds,

indicating a weak linear relationship. It was found that for a specified time period,

TMS was the average speed of the fast moving vehicles whereas the SMS was the

harmonic mean of the slow moving vehicles.

In accordance with the objective of the study, TMS was estimated using the

Wardrop equation shown in Eq. (3) (Wardrop 1952) and SMS was estimated using

the Rakha and Zhang equation given in Eq. (8) (Rakha and Zhang 2005).

Correlation plots between measured and estimated values of TMS and SMS were

made as shown in Figure 3 using these models. Figure 3 highlights the poor estimates

of TMS and SMS obtained using these conventional models. In the case of TMS

estimation from the Wardrop equation, all the points lie below the 45 degree line

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Figure 1. Observed hourly traffic variation at different locations.

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indicating under-prediction of TMS as shown in Figure 3(a) whereas Figure 3(b)

shows the over-predictions of SMS from the Rakha and Zhang equation as all the

points lie above the 45 degree line.The poor performance of these conventional models can be attributed to high

variance of speeds due to the heterogeneous traffic conditions that exist on Indian

roads. From these results, it becomes imperative to modify these models to represent

the heterogeneous traffic conditions with sufficient accuracy. The development of our

proposed speed model is described in the next sections.

TMS model

Both Wardrop (1952) and Rakha and Zhang (2005) considered variance terms in

their speed models developed under homogeneous traffic conditions. According tothese models, TMS and SMS would become the same under zero variance conditions

and TMS would always be more than or equal to SMS under any given condition. It

is to be noted that the homogeneous traffic conditions have the same amount of

variance of speeds for the same vehicle type due to the varying vehicular

characteristics (vehicle dimensions, performance, etc.), varying operation speeds,

varying driver behavior characteristics, etc. Eventually, the influence of such

parameters would diminish resulting in low variance of speeds for homogeneous

traffic conditions. However, these parameters have a significant role in creating highvariance in speeds under heterogeneous traffic conditions. From Figure 3 it was also

evident that the conventional models under-predicted in the case of TMS. To predict

TMS values for heterogeneous conditions, the estimated values have to be necessarily

modified by applying appropriate multiplication factors which can overcome the

Figure 2. Observed Vehicular Composition at Different Locations.

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Table 1. Observed TMS values for different vehicle types.

TMS (Km/h)

Location Car TW Bus Auto LCV HCV

1 Greater Noida

Expressway (near Lotus

Valley School)

95.28 (259.52, 384) 79.1 (384.73, 201) 63.78 (184.64, 82) 47.87 (61.57, 45) 60.33 (114.85, 55) 59.69 (154.53, 140)

2 Greater Noida

Expressway (near

Panchsheel Bal Inter

College)

91.14 (432.37, 477) 76.42 (429.58, 231) 67.23 (289.84, 112) 49.82 (336.05, 38) 62.82 (415.1, 50) 65.44 (375.05, 103)

3 Delhi Gurgoan

Expressway (near

Mahipalpur)

63.06 (94.44, 1096) 53.43 (102.21, 816) 47.17 (56.38, 372) 44.02 (31.83, 208) 43.88 (49.7, 223) 43 (33.7, 99)

4 National Highway 1

(near Sonipat)

83.77 (157.58, 908) 62.16 (192.57, 179) 70.56 (55.17, 179) 44.73 (30.67, 72) 48.97 (355.07, 105) 56.54 (120.25, 196)

Note: Values in parentheses represent variance of speeds followed by sample size.

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Table 2. Observed SMS values for different vehicle types.

SMS (Km/h)

Location Car TW Bus Auto LCV HCV

1 Greater Noida Expressway

(near Lotus Valley School)

67 (824.1, 38) 46.39 (364.07, 51) 53 (461.06, 35) 46.51 (144.36,8) 53.88 (420.43, 68) 44.3 (316.03, 53)

2 Greater Noida Expressway

(near Panchsheel Bal Inter

College)

58 (597, 74) 47.68 (355.26, 32) 58.20 (348.19, 56) � 61.32 (341.62, 34) 53.17 (432.36, 58)

3 Delhi Gurgoan Expressway

(near Mahipalpur)

50.69 (358.6, 29) 41.51 (282.17, 72) 48.65 (216, 137) 29.36 (360.78, 3) 44.31 (254.56, 61) 42.55 (213.47, 35)

4 National Highway 1 (near

Sonipat)

69.25 (537.1, 126) 41.86 (164.85, 110) 58.78 (755.05, 71) � 44.93 (714.61, 50) 46.05 (583.24, 98)

Note: Values in parentheses represent variance of speeds followed by sample size.

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under-prediction problem. Moreover, TMS should always be more than or equal to

SMS under any variance of speed conditions. Considering these aspects, various

trials in terms of different models in linear and non-linear forms were undertaken.

The proposed models for estimation of TMS are as follows:

TMS 1 : �UT ¼ a �US þ br2

S

�US

(10)

TMS 2: �UT ¼ �USð Þaþ r2S

�US

!b

(11)

where a and b are model parameters to be estimated.

These models � TMS 1 and TMS 2 � were calibrated and model parameters wereestimated using SPSS software. The calibration process was carried out using the

data collected at three test sections on the Greater Noida Expressway and

Delhi�Gurgaon Expressway whereas National Highway 1 data were used for

validation purposes. The estimated statistical results along with Root Mean Square

Error (RMSE) values from TMS modeling are shown in Table 3.

Figure 3. Correlation between observed and estimated speeds. (a) TMS from Wardrop model.

(b) SMS from Rakha and Zhang model.

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From Table 3, it can be observed that both TMS 1 and TMS 2 models have

produced good statistical validity in terms of low RMSE values. The very lowstandard error of the parameters has further reinforced the good accuracy of the

developed TMS models. These models were then validated using data from National

Highway 1 and the percentage of error and RMSE values were calculated from

observed and estimated values. These models were further compared with the

Wardrop model (1952) to demonstrate their accuracy in considering heterogeneous

traffic conditions and the results presented in Table 4.

From Table 4, it can be clearly inferred that both TMS 1 and TMS 2 models are

far better than the Wardrop model and TMS 1 model has a high level of accuracy interms of lower RMSE and percentage error values compared to TMS 2 model.

Further, to show the prediction capability of these models, the goodness of fit

between the observed and estimated values of TMS was plotted as shown in Figure 4.

From Figure 4, it can be observed that predicted values from TMS 1 model are

very close to the 45 degree line compared to other models. From all these results, it

can be said that the TMS 1 model would predict more realistic values of TMS under

heterogeneous traffic conditions.

SMS model

In the same way, various trials were carried out to formulate different SMS models in

linear and non-linear forms. The proposed models for estimation of SMS were as

follows:

SMS 1: �US ¼ c �UT � dr2

T

�UT

!(12)

where c and d are model parameters to be estimated.

Table 4. Validation results of different TMS models.

Model Percentage of error RMSE value Sample size

Wardrop model 23.76% 17.14 33

TMS 1 model �6.47% 14.35 33

TMS 2 model �6.20% 15.23 33

Table 3. Parameter estimates of different TMS models.

Model parameter

Model a b RMSE value Sample size

TMS 1 model 1.368 (0.050*, 27.401a) 1.091 (0.169*, 6.454a) 13.62 78

TMS 2 model 1.080 (0.008*, �a) 1.040 (0.044*, �a) 14.12 78

at-value.*Standard error.

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As in the case of TMS modeling, the above SMS 1 model was also calibrated and

model parameters were estimated using SPSS software using the data collected at the

three test sections on the Greater Noida Expressway and Delhi�Gurgaon Express-

way. The estimated statistical results along with RMSE values from SMS modeling

are shown in Table 5.

From Table 5, it can be observed that SMS 1 model has a good statistical validity

in terms of high R2 and low RMSE values. The very low standard error of

parameters has further reinforced the good accuracy of the developed SMS model.

The model was then validated using data from National Highway 1 and the

percentage of error and RMSE values calculated from observed and estimated

values. The model was further compared with Rakha and Zhang’s model (Rakha and

Zhang 2005) to demonstrate the accuracy in prediction considering heterogeneous

traffic conditions, as shown in Table 6.

From Table 6, it can be clearly inferred that SMS 1 is far better than the Rakha

and Zhang model. Further, to show the prediction capability of the model, the

goodness of fit between the observed and estimated values of SMS was plotted as

shown in Figure 5.

From Figure 5 it can be observed that predicted values from the SMS 1 model are

very close to the 45 degree line compared to other models. From all these results, it

Figure 4. Validated results of TMS models.

Table 5. Parameter estimates of different SMS models.

Model parameter

Model c d R2 RMSE value Sample size

SMS 1

model

0.694 (0.050*, 13.783a) 1.343 (0.634*, 2.120a) 0.9 10.04 78

at-value.*Standard error.

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can be said that the SMS 1 model would predict more realistic values of SMS under

heterogeneous traffic conditions of India.

Sensitivity analysis

The TMS values have been estimated from both the Wardrop model and TMS 1

model for homogeneous and heterogeneous traffic conditions, respectively for

different variances ranging from 0 to 50 km2/h2 and shown in Figure 6.

In the same way, SMS values have been estimated from the Rakha and Zhangmodel and SMS 1 model for homogeneous and heterogeneous traffic conditions,

respectively for different variances ranging from 0 to 50 km2/h2 and shown in Figure 7.

From these results, it can be inferred that speed characteristics are clearly

different for homogeneous and heterogeneous traffic conditions and variance of the

speeds have a significant role in estimating speeds.

Conclusions

From the present study, it was found that the conventional and popular Wardrop

(1952) and Rakha and Zhang (2005) models developed basically under homogeneoustraffic conditions did not yield appropriate results for a heterogeneous mix of traffic.

Accordingly, TMS and SMS models were developed based on the collection of actual

speed data in heterogeneous traffic conditions. After making a critical comparison

Figure 5. Validation results of SMS models.

Table 6. Validation results of different SMS models.

Model Percentage of error RMSE value Sample size

Rakha and Zhang model �53.29 22.81 33

SMS 1 model �12.97 11.06 33

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with conventional models, the superiority of the proposed models was demonstrated.

It can be concluded based on this study that conventional models as such cannot be

used for traffic conditions to be found in countries like India and, therefore, the

proposed TMS 1 and SMS 1 models are found to be better estimators and consistent

in predicting speeds with high accuracy especially for heterogeneous traffic

conditions.

References

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Hall, F.L. and Persaud, B.N., 1989. Evaluation of speed estimates made from single-detectordata from freeway traffic management systems. Transportation Research Record 1232.Washington, DC: Transportation Research Board, National Research Council.

Figure 6. TMS relationship with SMS under homogeneous and heterogeneous traffic

conditions.

Figure 7. SMS relationship with TMS under homogeneous and heterogeneous traffic

conditions.

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