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(1) Senior Lecturer in Transport Studies, University of Salford, Manchester M5 4WT, UK, Email: [email protected], Tel: (+44) 161 2953835, (2) Lecturer in Roads and Transport Studies, University of Al-Qadissia, Iraq.

Drivers’ lane utilization for UK motorways

(1)Saad Yousif, (2)Jalal Al-Obaedi and (1)Ralph Henson

Abstract:

Lane utilization represents how the rate of traffic flow is distributed among the available

number of lanes in a given section. This utilization or split is affected by several factors

including traffic flow rates as well as the presence and amount of heavy goods vehicles within

the traffic. The importance of studying lane utilization comes from the fact that it is one of

the input parameters for any traffic micro-simulation models which are increasingly being

used in order to assess and suggest solutions for traffic problems. This paper uses two

sources of data to model lane utilization including “Motorway Incident detection and

Automatic Signaling” MIDAS data and individual vehicles raw data. The latter source of data

is specifically used to model how heavy goods vehicles (HGVs) are distributed between

motorway lanes as flow increases since MIDAS data does not specify the proportions of

HGVs by lanes. Since the data used to develop the models in this paper are based on a

relatively large set of data (compared with those represented by older models), one could

argue that these models are more representative of current lane utilization on UK motorways.

The development of lane utilization models for HGV traffic will help in providing more

realistic predictions of traffic behavior when represented by micro-simulation models and in

the assessment of such commercial vehicles using the lanes when it comes to pavement

design.

Keywords: flow distribution, heavy goods vehicles, narrow lanes, traffic micro-simulation

Journal of Transportation Engineering. Submitted March 29, 2012; accepted December 2, 2012; posted ahead of print December 4, 2012. doi:10.1061/(ASCE)TE.1943-5436.0000531

Copyright 2012 by the American Society of Civil Engineers

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Introduction and background

Lane distribution (lane utilization or sometimes referred to as lane split) represents how traffic

flow is distributed among the available number of lanes for a directional movement (Highway

Capacity Manual (HCM), 2000). Many studies (see for example, Yousif and Hunt (1995) and

Brackstone et al. (1998)) have dealt with the subject and stated that for motorway segments

far away from merge or diverge sections, vehicles are distributed mainly based on total traffic

flow (q). Locations of merging, diverging and weaving sections may affect lane utilization.

Jin (2010) suggested that lane changing patterns are different at such locations. For example,

at the upstream merge section, drivers in the shoulder lane may change to other lanes in order

to avoid/help merging traffic (Knoop et al. 2010) while in the downstream of the merge

section, drivers in the shoulder lane may keep a “close following behavior” without changing

lanes for a short period (Laval and Leclercq 2008). Nordaen and Rundmo (2009) and

Ozkan et al. (2006) suggested that drivers’ behavior is significantly affected by cultural

differences among countries. This might explains the differences in the pattern of lane

changes for different countries as reported by Ferrari (1989). Gunay (2004) in his study on

Turkish highways, also reported that the lane utilization coefficients are significantly different

from those obtained in developed countries. Gunay explained the reasons behind that

behavior by the so called “untidy lanes” where no marking lines between lanes were present

with poor lane discipline. A “non-lane-based” car following model was also developed for

that purpose by Gunay (2007 and 2009).

The Highway Capacity Manual (2000) suggested that in general, the lane utilization depends

on many factors such as traffic regulation, traffic composition, speed and volume (flow rate),

the number of and location of access points, the origin-destination patterns of drivers and

drivers’ behaviors.



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Some studies (see for example, Knoop et al. 2010 and Lee and Park 2012) considered the lane

utilization as a function of traffic density. However, this approach has the drawback that the

traffic density is not measured directly by loop detectors which are commonly installed on

motorway sections to detect traffic.

One of the parameters used as input data to micro-simulation traffic models is lane utilization.

These traffic micro-simulation models have been widely used to assess traffic problems such

as congestions and safety related issues and to provide better solutions in terms of traffic

management techniques. In most of these models, total section flow was used as input data.

That flow was distributed among the lanes either by determining and inputting these flows per

lane manually or specific equations (models) were used to calculate flows per lane. Also, lane

utilization is one of the parameters used in the validation process of such micro-simulation

models when some studies compare the simulated lane utilization coefficients with real data

(see for example, Wall and Hounsell 2005). Some of these previously used models of lane

utilization are presented and tested in this paper.

Lane utilization for heavy goods vehicles (HGVs) traffic has got less attention in previous

research. This may be due to lack of sufficient traffic data to deal with this factor. One of the

earlier reported trials to model the distribution of HGVs per lane was by Hollis and

Evans (1976). Their study was based on video recording of data collected from five

motorway sites in the UK. As a total, 714 hourly flows are used for a period from 1966 to

1973. The distribution of HGVs on motorway lanes was assumed to be a function of the total

HGVs flow (H) only and no HGVs were assumed to be in the third lane or higher.

Turner (1983) included the individual effect of HGVs flow and total directional flow on

HGVs’ lane utilization. Fwa and Li (1995) studied the HGVs’ lane utilization in Singapore

for pavement design purposes. As in Turner’s study, Fwa and Li (1995) considered the

individual effect of total flow and HGVs flow without studying the combined effect of these



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two parameters. The levels of HGVs flows which were considered by Hollis and

Evans (1976) and Turner (1983) were up to 1000 veh/hr. The study by Fwa and Li (1995)

considered HGVs flows up to 200, 400 and 1000 veh/hr for sections with 2, 3 and 4 lanes,

respectively.

In the UK, the Design Manual for Roads and Bridges (as shown in the Highways Agency web

site, 2011) provides charts to predict commercial vehicle (HGVs) lane use for the

nearside (lane 1) based on total commercial vehicle traffic per day (cv/day). These charts

were currently being used in the design of highway pavement thickness to predict the “design

traffic” in million standard axles (msa) for typical commercial vehicles in the “heavily” used

lane (i.e. lane 1) within the design life of the highway.

In summary, previously suggested lane utilization models have some limitations due to the

fact that some were based on relatively old and limited database. Other factors which may

affect lane utilization could be related to the differences in the imposed speed limits used on

such roads in different countries. The cultural differences between countries affecting

drivers’ behavior (as discussed above) and the fact that in some countries, both undertaking

and overtaking are allowed could also affect the lane distribution/utilization. In the UK,

undertaking is prohibited and HGVs are, for example, prohibited from using the third lane on

a three lane motorway. These limitations explain the need to introduce newly developed

models for lane utilization specifically for the UK.

In this paper, new models for traffic lane utilization as well as HGVs lane utilization have

been developed using a large traffic data base taken from different motorway sites. The

development of such models will help in providing more realistic predictions of lane

utilization for use in micro-simulation traffic models and in the assessment of proportions of

commercial vehicles (HGVs) using the lanes for pavement design purposes.



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Methodology and data collection

Motorway Incident Detection and Automatic Signaling - MIDAS data (which are based on

loop detectors positioned at known locations) were used to develop regression lane utilization

models. The data was taken from selected normal sections which are at least 1000 meters

from the nearest merge/diverge section, concentrated on straight segments (i.e. with no

significant horizontal curvature) and with no work zones or incidents present. Data from the

M602 motorway (two lanes) and the M62 motorway (three lanes) were used. In addition,

individual vehicles raw data taken from loop detectors on the M25 motorway were used to

represent lane utilization models for a motorway at a four-lane section. The latter source of

data was also used to check the validity of the models obtained based on the M62 data by

comparing these models with data taken from the M42 (Managed Motorway site). Complete

days and weeks of data have been used as shown in Table 1. The data used were averaged for

intervals of five minutes and a manual filtering process was conducted to remove any

anomalies in the data (e.g. durations of incidents when certain lanes were closed temporarily

for a short period of time associated with a drop in traffic speeds or cases where time

headways taken from loop detectors between two successive vehicles on the same lane and

travelling with the same speed were extremely small, say less than 0.4 seconds, which

represented a trailer rather than two successive vehicles …etc.).

Other scenarios were also checked such as excluding congested periods from the data and

considering smaller time intervals in the analysis (i.e. 1 minute interval instead of 5 minutes)

to try to represent the effect of local traffic density on lane use.

For the HGV lane utilization, the raw data for a full 14 days from both the M25 and the M42

motorway sites were used. The raw data combined all vehicles in all lanes and in both

directions. Equivalent hourly traffic and HGV flows were averaged for intervals of ten

minutes. Five minute intervals were also tested. Using higher interval periods such as 1 hour



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as adopted by Hollis and Evans (1976) was not considered as it might combine different flow

conditions ranging between free and congested situations. Since vehicle type was not clearly

defined in the data with only vehicle length being obtained from the raw data, a similar

approach to that used by the Highway Agency to define HGVs, was considered in this paper.

Therefore, a value of 6.6m was used as a threshold value for the length of vehicles between

HGVs and non-HGVs. The filtering process has been carried out using a simple computer

program using Compaq Visual FORTRAN-2005.

Results of lane utilization for motorway traffic

This section provides essential background information on the validity of using previous

models, based on tests with existing data from MIDAS and individual vehicles raw data. It

also highlights the lack of previous information on modeling, for example, four-lane sections

using data from the UK motorways and the effect of HGVs on lane utilization. The main

contribution of this study is that a comprehensive data set has been used to test the validity of

lane utilization models which were previously based on relatively limited and rather relatively

old data sources.

Testing some of the previous models

Regression analysis was used in modeling the available data. Firstly, some of the previously

developed models for lane utilization have been tested using the existing data available for

this work. The reason for doing so was to evaluate the validity of such models in representing

lane utilization for the relatively extensive data available from UK motorways for this paper.

It should be noted here that motorways in the UK have speed limits of about 110 km/hr

(i.e. equivalent to 70 mph) for cars and 100 km/hr (i.e. equivalent to 60 mph) for HGVs. Also

HGV’s are restricted from driving on the offside lane and that drivers are only allowed to



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overtake (rather than undertake) when trying to improve their speeds and positions. These

conditions might differ from other countries and such differences might affect and influence

lane use. Therefore, the comparisons shown in Table 2 are restricted to previous UK studies

and any of the recommended models in this paper should be used with care if applied in other

countries with different driving regulations (as briefly explained in the introduction section).

However, the methods of development of these models may find their use for comparison

reasons of drivers’ behaviors with other countries).

The details of the models and the test results (i.e. coefficient of determination values, r2) are

shown in Table 2. These r2 values were obtained using the Statistical Package for the Social

Sciences (SPSS) software based on the actual and predicted lane utilization coefficients.

For motorways with two-lane sections, it seems that the models developed by Yousif and

Hunt (1995) are still applicable as these models gave good correlations with real

data (i.e. r2=0.93). However, further attempts have been made in this study to test if such

models could be improved using the existing data for two lanes sections.

For motorways with three lanes sections, all the presented models in the table suggested good

correlation between the data and the models for lanes 1 and 3 (i.e. all were higher than 0.80).

However, none of the presented models were capable of modeling lane utilization adequately

for lane 2 (i.e. r2 values were around 0.30 and in the case of Zheng’s (2003) model as low

as 0.02). This could be due to some limitations in the original data available in producing

those models (e.g. sample size might be low for certain levels of flow). Therefore, it was felt

necessary to consider the case of three lanes and attempts were made to model lane utilization

using the existing data. However, the current study adopted a simplifying approach which

modeled flow proportions for 2 of the lanes and assumed the third lane as the residual

proportion. This approach has been adopted in other studies in the literature.



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For four-lane sections, no reliable published work was found in the UK to model lane use.

Therefore, available data on these sections were analyzed for this purpose.

Development of new regression models

For the M602 motorway (two lanes), Fig. 1 shows the lane utilization for both lanes with

corresponding regression models and coefficient of determinations (r2). As the flow rate

increases, the utilization of the inside lane (lane 2) increases rapidly until there is a similar use

of lanes at around 2000 veh/hr. After that, lane 2 will ultimately have around 60% share of

use at flows close to capacity. This is different from the finding of Wu (2006) who suggested

that lane 2 in German autobahn sections (with two lanes) will start carrying flow rates higher

than in lane 1when the total flow exceeds a value of about 1300 veh/hr. This may be due to

the fact there are differences in the way speed limits are implemented in German autobahns

compared with similar UK sites.

Fig. 2 and Fig. 3 show the lane utilization for the M62 motorway (with three lanes section)

and for the M25 motorway (with four lanes section). The Figures indicate that vehicles

usually concentrate on the lower speed lanes for relatively low traffic flows operating under

free flowing conditions (i.e. up to about 500 veh/hr), then other lanes start to have their share

of use as traffic flow increases. When these flows are close to the capacity of the motorway,

more even use of lanes occurs. However, that does not mean that the number of vehicles in

each lane is equal at such levels of flow.

Data from the M42 three-lane sections (Managed Motorways) with narrower lanes than those

for normal three lanes section such as the M62 motorway were also available for comparison.

An attempt was made to check the validity of the proposed lane utilization models for the

M42 motorway data and to compare them with that of the M62 motorway data in order to see

if narrow lanes had a significant effect on lane use. The best fitting model for the M42 data

gave r2 values of 0.946, 0.708 and 0.956 for lanes 1, 2 and 3 respectively. Similar r2 values



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were obtained by applying the models derived from the M62 data on the data taken from the

M42 motorway. In this case, the r2 values were 0.946, 0.672 and 0.952 for lanes 1, 2 and 3

respectively indicating the validity of the developed regression models from the M62 with

other sections. This also indicates that the effect of having narrow lanes, such as in the case

of the M42 motorway, has a negligible effect on lane utilization.

In order to exclude the effect of congested periods (i.e. when queues were formed and stop-

start conditions occurred), the existing data were filtered to eliminate such periods. This was

done by deleting data associated with periods when there was a drop in traffic speeds. The

results show that there was no significant change in r2 values or to the regression model

parameters which have already been presented earlier for the cases without excluding

congested periods. This could be due to the fact that data points representing those periods of

congestion were relatively small when compared with the whole data representing non-

congested conditions.

An attempt was also made to analyze the data based on one minute intervals rather than five

minutes (i.e. by considering the effect on local traffic density rather than using an aggregated

average speed and density for a relatively longer time interval). The results of this scenario

gave more scatter and produced lower r2 values than those reported above. Therefore and for

practical reasons, only total flow has been considered and the above reported regression

models are suggested for use.

Lane utilization for congested conditions

In order to represent the effect of congestion on lane utilization, data were filtered for those

cases when speeds on all lanes started to drop below a certain value (chosen as

below 60 km/hr). This threshold was suggested and used based on the work by Hounsell and

McDonald (1992) which investigated traffic breakdown at motorway sections. Average one

minute data was used in order to avoid mixing cases of short durations of congestion with non



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congested flow conditions. For the M602 motorway with two lanes section, the available data

do not include any congested cases. Therefore, this part of the analysis was only limited to

three and four lane motorway sections.

For motorways with three lanes sections (i.e. M62 motorway), data for congested situations

are presented in Fig. 4. The data revealed that when flows are in the region of 5000

to 6000 veh/hr (i.e. at capacity with speed values below the threshold), lane 3 carries

around 40% of traffic compared with 25% for lane 1 and 35% for lane 2. This could be due to

the fact that HGVs are normally restricted to lanes 1 and 2, with lane 1 carrying the majority

of HGVs.

Fig. 5 shows data for motorways with four lanes sections (i.e. M25 motorway). At congested

conditions with flow rates between 7000 and 8000 veh/hr, average lane usages are 22%, 25%,

25% and 28% for lanes 1, 2, 3 and 4, respectively. This suggests that the offside lane (i.e.

lane 4) still carries more vehicles. However, the presence of HGVs in other lanes (especially

in lanes 1 and 2) could be the reasons for that (i.e. similar to observations from a three-lane

section).

Results of lane utilization for HGVs

Testing some of the previous HGV lane utilization models

Some of the developed models for HGV lane utilization in previous research have been tested

in this paper using data from the M42 and M25 motorway sites. The details of these models

and the test results (i.e. coefficient of determination values, r2) are shown in Table 3. The

Table suggests that these models need to be refined in order to get better representation of the

real, more recent, data (especially noting that some of these previous models are based on old

data taken two to three decades ago).



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Fig. 6 compares lane utilization coefficients obtained from the M42 motorway data with the

models by Hollis and Evans (1976) and Turner (1983) with respect to HGV flows. The

Figure shows that Evans and Hollis’ models give better representation of the current data

compared with those models developed by Turner (1983). The effect of total motorway flow

on the lane utilization factors based on the M42 motorway data is presented in Fig. 7. The

figure shows that the concentration of HGVs in lane 2 increases with an increase in traffic

flow. The models by Turner (1983) as shown in the same figure (i.e. Fig. 6) suggested that

lanes 1 and 2 will have the same proportion of HGVs when motorway flow reaches a value of

about 3000 veh/hr. After that, lane 2 will start to carry higher proportions of HGVs. In fact,

the real data presented in Fig. 6 suggested that HGVs in lane 1 are always higher than those

on lane 2 even at higher flow rates approaching motorway capacity.

Development of new models

Based on the discussion in previous sections, the presence of HGVs within traffic flow has an

effect on lane use and some of the models used for this purpose are based on old data. Also,

the reliance on the Motorway Incident Detection and Automatic Signaling (MIDAS) data

which is widely used in the UK will not help in estimating the proportions of HGVs in each

lane, since this data source (i.e. MIDAS data) does not specify the percentage (or number) of

HGVs by lane. Therefore, there is a need to develop new models for HGVs lane utilization to

provide more realistic applications for this sort of data (i.e. MIDAS data) in micro-simulation

traffic models which are widely used to assess and evaluate solutions to current traffic

problems. These models are also useful in the assessment of commercial vehicles (HGVs)

using the lanes when it comes to pavement design.

The new models have been developed based on simple linear regression analysis using SPSS

software. Factors which are considered in this study are HGVs flow (H), total flow (q) and

average speed (V). Although traffic density (or traffic occupancy) may affect the



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instantaneous use of lanes, the effect of traffic density is presented through taking the effects

of traffic flow and speed parameters. It should be noted that the ranges of HGV flow for the

data used are (0 to 1200) and (0 to 1500) veh/hr for the M42 and the M25 motorways,

respectively. It should be noted here that a trial has been made to see whether or not there is a

strong correlation between HGVs flow (H) and total flow (q). The results in Fig. 8, shows a

typical example from the M42 which suggests that there is a wide scatter indicating that the

correlation between these two variables is not strong. Such a scattered relationship is not

unexpected, given the different trip purposes associated with HGVs compared to other vehicle

types and the effect that this has on typical flow profiles. For example, with the development

of just-in-time freight distribution, HGVs flow may reach a maximum even when the other

vehicle flow is low (e.g. at night) indicating that there is no clear correlation between these

two variables.

The results from the regression analyses with respect to the selected parameters (i.e. total

flow, total HGV flow and speed) are shown in Table 4 for both the M42 and M25 motorway

sites. In general and by considering the effect of each selected parameter separately using a

stepwise regression analysis, the results suggest that the total flow is the most important factor

in modeling HGV lane utilization. In addition, using the HGV flow only as a parameter gave

better r2 values than using the average speed. Combining the effect of total flow and HGV

flow parameters would significantly enhance the r2 values. Moreover, the effect of these three

parameters (all together) also makes the r2 values more reliable especially in the case of the

M25 motorway. Speed and flow variables are likely to be associated in practice, so models

which contain both of these as independent variables need to be treated with caution.

However, speed has been included at this stage of the modeling, because the underlying

reason why a driver selects a particular lane may be based on individual attitudinal factors

(e.g. driving style, attitude to risk, …etc.) and speed is a proxy variable which captures these

effects. This aspect of the study justifies further research.



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For practical reasons and since speed data might not always be available and may contravene

the assumptions of independence, the developed models, which consider the combined effects

of total flow and total HGVs flows, are recommended pending further study.

It should be noted that these new developed models are based on average 10 minutes intervals

of data. Using lower time intervals such as 5 minutes data have also been tested and have

given lower reliable models (due to higher scatter in the data).

Summary and conclusions

This paper used real traffic data taken from loop traffic detectors in order to study drivers’

lane utilization (distribution) behavior on UK motorways. Different motorway sections were

selected carrying different flow rates ranging from free flowing to congested situations. Some

of the previous lane utilization models have been tested using the current data which provided

evidence regarding the need to develop new models. The developed models for a motorway

with a three-lane section were tested with real data taken from the M42 narrow lanes site and

the results showed that there was no significant differences in lane use behavior when

compared with normal motorway lane widths. In addition, individual vehicles’ raw traffic

data taken from detectors on the M42 and the M25 motorway sites has been used in

developing new lane utilization models for heavy goods vehicles (HGVs). Stepwise

regression analysis was used in developing new models for lane utilization (as suggested in

Figures 1, 2 and 3 for motorways with 2, 3 and 4 lanes, respectively). For HGVs lane

utilization, the developed models showed that considering the combined effect of the total

flow and total HGV flow could give more reasonable representation of lane utilization (as

suggested by Model 4 in Table 4, or even Model 5 if speed data are available). This study has

successfully updated previous models so that they more accurately reflect current UK

motorway circumstances based on selected motorway locations. Although one should be



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reasonably confident in implementing such models for other UK motorways due to the

relatively large database used in developing such models, however, there are limitations and

assumptions which require further study if the findings are to have a general application

across the full range of possible locations. Some of these developments could relate to

extending the database to look at other motorways with varying degrees of HGVs for various

flow levels. Also, looking at day vs. night driving effects, weather conditions (wet vs. dry)

and effects of presence of speed limit controls and other variable message signs. Therefore, it

is recommended that further work is needed to extend the database and include other

motorways in order to give a wider application and better representation for lane utilization on

UK motorways.

References

Brackstone, M., McDonald, M. and Wu, J. (1998). “Lane changing on the motorway: Factors

affecting its occurrence, and other implications.” 9th International Conference on Road

Transport Information and Control, No. (454), 160-164.

Ferrari, P. (1989). “The effect of driver behavior on motorway reliability.” Transportation

Research Part B, 23(2), 139-150.

Fwa, T. F. and Li, S. (1995). “Estimation of lane distribution of truck traffic for pavement

design.” Journal of Transportation Engineering, 121(3), 241-248.

Gunay, B (2004). “An investigation of lane utilization on Turkish highways.” Proceeding of

the Institute of Civil Engineering (ICE), Transport 157, 43-49.

Gunay, B (2007). “A methodology on the automatic recognition of poor lane keeping.”

Journal of Advanced Transportation, 42(2), 129-149.



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Gunay, B (2009). “Rationality of a non-lane-based car-following theory.” Proceeding of the

Institute of Civil Engineering (ICE), Transport 162, 27-37.

Transportation Research Board (2000). “Highway Capacity Manual .” Washington, D.C.

Hollis, E. and Evans, R. (1976). “Motorway traffic patterns.” Transport and Road Research

Laboratory, TRRL Laboratory Report 705, UK.

Hounsell, N. and McDonald, M. (1992). “ An investigation of flow breakdown and merge

capacity on motorways.” Transport Research Laboratory, Contractor Report 338, UK.

Jin, W. (2010). “A kinematic wave theory of lane-changing traffic flow.” Transportation

Research B, 44(8-9), 1001 - 1021.

Knoop, V. L., Duret, A., Buisson, C. and Arem, B. V. (2010). “Lane distribution of traffic

near merging zones influence of variable speed limits.” Proceeding of the 13th

International IEEE Conference on Intelligent Transportation System. 485-490.

Laval, J. A. and Leclercq, L. (2008). “Microscopic modeling of the relaxation phenomenon

using a macroscopic lane-changing model.” Transportation Research B, 42(6), 511 - 522.

Lee, J. and Park, B. (2012). “Determining lane use distributions using basic freeway segment

density measures.” Journal of Transportation Engineering, 138(2), 210-217.

Nordaen, T. and Rundmo, T. (2009). “Perceptions of traffic risk in an industrialized and a

developing country.” Transportation Research Part F, 12(1), 91-98.

Ozkan, T., Lajunen, T., Chliaoutakis, J., Parker, D. and Summala, H. (2006). “Cross-cultural

differences in driving behaviors: A comparison of six countries.” Transportation

Research Part F, 9(3), 227-242.

Turner, D. J. (1983). “Traffic characteristics of a rural motorway.” Traffic Engineering +

Control, 24(5), 248-251.



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Wall, G. T. and Hounsell, N. B. (2005). “Microscopic modeling of motorway diverges.”

European Journal of Transport and Infrastructure Research, 5(3), 139-158.

Wu, N. (2006). “Equilibrium of lane flow-distribution on motorways.” Transportation

Research Board, No. 1965, 48–59.

www.standardsforhighways.co.uk/dmrb/vol7/ (Giving details on road design as part of the

Design Manual of Roads and Bridges Volume 7 - Accessed January2011).

Yousif, S. and Hunt, J. (1995). “Modeling lane utilization for British dual-carriageway roads:

effect of lane changing.” Traffic Engineering + Control, 36(12), 680-687.

Zheng, P. (2003). “A microscopic simulation model of merging operation at motorway on-

ramps”. PhD Thesis, University of Southampton, UK.



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Table captions

Table 1 Summary of the selected sites

Table 2 Testing of some previous lane utilization models (using existing traffic data)

Table 3 Testing previous models of HGVs lane utilization using data from the M42 and

M25 motorway

Table 4 Regression models for HGVs lane utilization

Figure captions

Fig. 1. Lane utilization for the M602 motorway (two lanes)

Fig. 2. Lane utilization for the M62 motorway (three lanes)

Fig. 3. Lane utilization for the M25 motorway (four lanes)

Fig. 4. Lane utilization for the M62 at congested conditions


Fig. 6. HGVs lane utilization for the M42 with respect to HGV flow compared with

Hollis and Evans (1976) and Turner (1983) models

Fig. 7. HGVs lane utilization for the M42 with respect to total flow compared with

Turner (1983) models

Fig. 8. A scatter plot showing total flow (q) and HGVs flow (H) based on data from the

M42



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Fig. 1. Lane utilization for the M602 motorway (two lanes)

P2 =1-P1 r² = 0.94

P1 = -1.2E-11q3 + 1.13E-07q2 - 0.000397q + 0.9294 r² = 0.94

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000

Lane

uti

lizat

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fact

or

Total flow (veh/hr)

Lane2

Lane 1

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Fig. 2. Lane utilization for the M62 motorway (three lanes)

P1 = 1.732E-15q4 - 2.75E-11q3 + 1.67E-07q2 - 0.000485q + 0.8412

r² = 0.92

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000 6000 7000

Lane

uti

lizat

ion

fact

or

Total flow (veh/hr)

Lane1

P1 = 2.14E-19q5 - 4.91E-15q4 + 4.68E-11q3 - 2.2E-07q2 + 0.000449q + 0.1588

r² = 0.65

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000 6000 7000

Lane

uti

lzat

ion

fact

or

Total flow (veh/hr)

Lane2

P3= 1-P1-P2 r² = 0.97

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000 6000 7000

Lane

uti

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fact

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Total flow (veh/hr)

Lane3




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Fig. 3. Lane utilization for the M25 motorway (four lanes)

P1 = -2.62E-12q3 + 4.67E-08q2 - 0.000253q + 0.54 r² = 0.84

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Lane

uti

lizat

ion

fact

or

Total traffic flow (veh/hr)

Lane1

P2 = 6.27E-09q2 - 7.64E-05q + 0.46 r² = 0.73

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Lane

uti

lizat

ion

fact

or


Lane2

P3 = -8.79E-16q4 + 1.775E-11q3 - 1.29E-07q2 + 0.000377q r² = 0.81

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Lane

uti

lizat

ion

fact

or


Lane3

r² = 0.96

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Lane

uti

lizat

ion

fact

or


Lane4

P4 = 1-P1-P2-P3

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0

0.1

0.2

0.3

0.4

0.5

0 1000 2000 3000 4000 5000 6000

Lane

uti

lizat

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fact

or

Total flow (veh/hr)

Lane1

Lane2

Lane3




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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 2000 4000 6000 8000

Lane

uti

lizat

ion

fact

or

Total flow (veh/hr)

Lane1

Lane2

Lane3

Lane4




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Fig. 6. HGVs lane utilization for the M42 with respect to HGV flow compared with Hollis

and Evans (1976) and Turner (1983) models

0

0.2

0.4

0.6

0.8

1

0 300 600 900 1200

HG

Vs

lane

uti

lizat

ion

HGVs flow (veh/hr)

Lane 2

Lane 1

Hollis and Evans-Lane1

Turner-Lane 1

Hollis and Evans-Lane2

Turner-Lane 2




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Fig. 7. HGVs lane utilization for the M42 with respect to total flow compared with Turner (1983) models

0

0.2

0.4

0.6

0.8

1

0 2000 4000 6000

HG

vs la

ne u

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Total flow (veh/hr)

Lane 1

Lane 2

Turner-lane1

Turner-lane 2




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Fig. 8. A scatter plot showing total flow (q) and HGVs flow (H) based on data from the M42

0

200

400

600

800

1000

1200

0 1000 2000 3000 4000 5000 6000 7000

HG

Vs

flow

(veh

/hr)

Total flow (veh/hr)




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Table 1 Summary of the selected sites Site No. of lanes Date Duration Purpose

M602 2 14/6/2010 to 18/6/2010 5 days

Lane utilization for motorway traffic

M62 3 1/6/2010 to 7/6/2010 7 days

M42 3 22/8/2002 to 4/9/2002 14 days

M25 4 4/5/2002 to 18/5/2002 14 days

M42 3 22/8/2002 to 4/9/2002 14 days HGVs lane utilization

M25 4 4/5/2002 to 18/5/2002 14 days




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Table 2 Testing of some previous lane utilization models (using existing traffic data)

Reference Number of motorway

lanes

Applicable flow range

(veh/hr)

Lane number

Lane utilization model

(%) r2

Yousif and Hunt (1995) 2

0-4000

1 P1=87.04 - 0.036q + 5.91E- 6q2 0.93

2 P2=100 – P1 0.93

Yousif and Hunt (1995) 3

0-5000

1 P1=608.84q-0.39 0.86

2 P2=100 - P1 - P3 0.34

3 P3=0.034 + 0.0179q - 1.85E-6q2 0.92

Brackstone et al. (1998) 3

1500-5500

1 P1=1756.5q-0.5253 0.82

2 P2=385.47q-0.2699 0.32

3 P3=0.0244q0.8791 0.96

Zheng (2003) 3

1000-5250

1 P1=67.106-2.4168E-2q-2.9302E-6q2 0.89

2 P2=47.95 - 1.052E-3q - 3.018E-7q2 0.02

3 P3=-15.061+2.522E-2q+2.6284E-6q2 0.92




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Table 3 Testing previous models of HGVs lane utilization using data from the M42 (3-

lane motorway) and M25 (4-lane motorway)

Reference Lane number HGVs lane utilization model

r2 M42 M25

Hollis and Evans (1976)

1 PH1 = 1200/(1200+H) 0.586 0.574

2 PH2 = H/(1200+H) 0.552 0.382

Turner (1983) taking the effect of HGVs flow

1 PH1 = (H+129.76)/(2.17H) 0.206 0.268

2 PH2 = (H-139.49)/(1.73H) 0.20 0.265

Turner (1983) taking the effect of total flow

1 PH1 = (174.44-15.57 ln q)/H 0.526 0.52

2 PH2 = 1 - PH1 0.498 0.325

Fwa and Li (1995) taking the effect of HGVs flow

1 PH1 = (45.1+0.608H+0.000308H2)/H 0.09 0.05

2 PH2 = 1 - PH1 0.09 0.042

Fwa and Li (1995) taking the effect of total flow

1 PH1 = (174.4+0.082q-0.0000125q2)/H 0.21 0.347

2 PH2 = 1 - PH1 0.2 0.232

Note: H represents the total HGVs flow in veh/hr




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Table 4 Regression models for HGVs lane utilization using data from the M42 (3-lane

motorway) and M25 (4-lane motorway) Motorway Lane Model parameters used r2 Remarks

Model 1 (HGVs flow only)

M42 1 PH1=0.949 - 0.00034225H 0.58 Simple models

which could be used (3 lanes) 2 PH2=1 - PH1 0.52

M25 1 PH1=0.878-0.00083H+3.87E-7H2 0.54

Ignore (low r2 values)

2 PH2=0.138+0.00049H-2.489E-7H2 0.39 3 PH3=1- PH1- PH2 0.48

Model 2 (Total flow only)

M42 1 PH1=0.951 - 0.000047q 0.58

Simple models which could be

used (for 3 and 4 lanes)

2 PH2=1- PH1 0.52

M25 1 PH1=0.841 - 0.00005694q 0.60 2 PH2=0.165 + 0.00003102q 0.42 3 PH3=1 - PH1 - PH2 0.45

Model 3 (speed only)

M42 1 PH1=0.0439 + 0.004V 0.16

Ignore (low r2

values)

2 PH2=0.558 - 0.004V 0.16

M25 1 PH1=-0.005 + 0.00606V 0.42 2 PH2=0.624 - 0.00328V 0.29 3 PH3=1 - PH1 - PH2 0.34

Model 4 (HGVs flow and total flow)

M42 1 PH1=0.976 - 0.0002044H - 0.0000285q 0.70

Recommended models to be used

(for 3 and 4 lanes)

2 PH2=1 - PH1 0.63

M25 1 PH1=0.862 - 0.0002007H -0.00003943q 0.67 2 PH2=0.154 + 0.00011H + 0.00002143q 0.46 3 PH3=1 - PH1 - PH2 0.51

Model 5 (HGVs flow, total flow and speed)

M42 1 PH1=0.812 - 0.00019H - 0.00002722q +

0.0015V 0.72

Recommended models to be used

(for 3 and 4 lanes)

2 PH2=1 - PH1 0.65

M25

1 PH1=0.488 -0.00017H - 0.0000303q + 0.00315V

0.75

2 PH2=0.354 + 0.000096H + 0.0000165q - 0.0017V

0.52

3 PH3=1 - PH1 - PH2 0.60

Note: H represents the total HGVs flow in veh/hr

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