01 Lane Changing Bhargav

8/6/2019 01 Lane Changing Bhargav

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CE-740 Traffic Engineering

Term paper

Lane changing models

(Conceptual framework, Gap acceptance, Lane selection)

Under the guidance ofTom v. Mathew

Submitted by

P.Bhargav venil

10304001


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Contents

1. Introduction 31.1 Process of Lane change

1.2 Classification 4

1.2.1 Based on execution 4

1.2.2 Based on Gap 4

2. Lane changing models 5

2.1 Basic Lane changing model 5

2.2 Mandatory Lane Change and Discretionary Lane Change Model 6

2.2.1 Decision making 6

2.2.2 Gap acceptance 7

2.3 Forced merging model 8

2.4 Cooperative and forced gap acceptance 10

2.4.1 Conceptual framework for cooperative and forced gap acceptance 10

2.4.2 Courtesy yielding 11

3. Gap acceptance 12

4. Delay for Lane change 13

5. Summary 16

6. References 16

7. Advanced topics 17

7.1 Target Lane Selection 17

7.2 Minimizing Overall Braking decelerations Induced by Lane changes 18


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Lane changing models

(Conceptual framework, Gap acceptance, Lane selection)

1. Introduction

The transfer of a vehicle from one lane to next adjacent lane is defined as Lane change.

Lane changing has a significant impact on traffic flow. Lane changing models are

therefore an important component in microscopic traffic simulators, which are

increasingly the tool of choice for a wide range of traffic-related applications at the

operational level. Modeling the behaviour of a vehicle within its present lane is relatively

straightforward, as the only considerations of any importance are the speed and location

of the preceding vehicle. Lane changing, however, is more complex, because the decision

to change lanes depends on a number of objectives, and at times these may conflict.

Gap acceptance models are used to model the execution of lane-changes. The available

gaps are compared to the smallest acceptable gap (critical gap) and a lane-change is

executed if the available gaps are greater. Gaps may be defined either in terms of time

gap or free space.

1.1Process of lane changeThe lane changing process is modeled as a sequence of three steps:

1. Decision to consider a lane change,

2. Choice of target lane,

3. Gap acceptance

Lane changing process is explained using the example which is shown in figure 1.The

subject vehicle in lane 2 makes a decision to consider a lane change and then it selects atarget lane which may be either lane 1 or lane 3. Now this subject vehicle accepts the gap

in the target lane to make a lane change.


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Figure 1: Process of lane change

1.2 Classification of Lane change

The classification of lane changes is done based on

1. Execution of the lane change

2. Gap

1.2.1 Based on execution of Lane change

Mandatory Lane Change (MLC): Mandatory lane change (MLC) occurs when a driver

must change lane to follow a specified path.

E.g.: If a driver wants to make a right turn at the next intersection the he changes to the

right most lane which is referred as Mandatory Lane change.

Discretionary Lane Change (DLC): Discretionary lane change (DLC) occurs when a

driver changes to a lane perceived to offer better traffic conditions, he attempts to achieve

desired speed, avoid following trucks, avoid merging traffic, etc.

E.g.: If a driver perceives better driving conditions in the adjacent lane then he makes a

Discretionary Lane change.

1.2.2 Based on Gap

Gap lane change: Both the lead and trailing vehicle influence the maneuver of subject

vehicle

Retarded lane change: Lane change of the subject vehicle is influenced by lead vehicle.

Conflict lane change: Lane change of the subject vehicle is influenced by rear vehicle.


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Free lane change: Lane change of the subject vehicle is not influenced by lead and rear

vehicle

Most of the models use the classification based on the execution.

2. Lane changing models

2.1 Basic Lane changing model

The basic lane change model is described using the framework shown in figure 2. The

subject vehicle in the current lane tries to change direction either to its left or to its right.

If the gap in the selected lane is acceptable the lane change occurs or else it will remain in

the current lane.

Figure 2: Conceptual Framework

Most models classify lane changes as either mandatory or discretionary lane change. This

separation implies that there are no trade-offs between mandatory and discretionary

considerations. For example, a vehicle on a freeway that intends to take on of-ramp will

not overtake a slower vehicle if the distance to the off-ramp is below a threshold,

regardless of the speed of that vehicle. Furthermore, in order to implement MLC and

DLC model separately, rules that dictate when drivers begin to respond to MLC


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conditions need to be defined. However, this point is unobservable, and so only

judgment-based heuristic rules, which often are defined by the distance from the point

where the MLC must be completed, are used.

The model shown in Figure 2 integrates MLC and DLC into a single utility model.

Variables that capture the need to be in the correct lanes and to avoid obstacles and

variables that capture the relative speed advantages and ease of driving in the current lane

and in the lanes to the right and to the left are all incorporated in a single utility model

that captures the trade-offs among these variables. An important goal that affects drivers'

lane changing behavior in this model is following the travel path. This goal is captured by

a group of variables that capture the distance to the point where drivers have to be in

specific lanes and the number of lane changes that are needed in order to be in these lanes

2.2 MLC and DLC Model

The lane changing model structure is shown in Figure 3. The MLC branch in the top level

corresponds to the case when a driver decides to respond to the MLC condition.

Explanatory variables that affect such decision include remaining distance to the point at

which lane change must be completed, the number of lanes to cross to reach a lane

connected to the next link, delay (time elapsed since the MLC conditions apply), and

whether the subject vehicle is a heavy vehicle (bus, truck, etc..,). Drivers are likely to

respond to the MLC situations earlier if it involves crossing several lanes. A longer delay

makes a driver more anxious and increases the likelihood of responding to the MLC

situations. And finally, due to lower maneuverability and larger gap length requirement

of heavy vehicles as compared to their non heavy counterparts, they have a higher

likelihood of responding to the MLC conditions.

2.2.1 Decision making

The MLC branch corresponds to the case where either a driver does not respond to an

MLC condition, or that MLC conditions do not apply. A driver then decides whether to

perform a discretionary lane change (DLC). This comprises of two decisions: whether the

driving conditions are satisfactory, and if not satisfactory, whether any other lane is better


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than the current lane. The term driving conditions satisfactory implies that the driver is

satisfied with the driving conditions of the current lane. Important factors affecting the

decision whether the driving conditions are satisfactory include the speed of the driver

compared to its desired speed, presence of heavy vehicles in front and behind the subject,

if an adjacent on ramp merges with the current lane, whether the subject is tailgated etc.

If the driving conditions are not satisfactory, the driver compares the driving conditions

of the current lane with those of the adjacent lanes. Important factors affecting this

decision include the difference between the speed of traffic in different lanes and the

driver's desired speed, the density of traffic in different lanes, the relative speed with

respect to the lag vehicle in the target lane, the presence of heavy vehicles in different

lanes ahead of the subject etc.

In addition, when a driver considers DLC although a mandatory lane change is required

but the driver is not responding to the MLC conditions, changing lanes opposite to the

direction as required by the MLC conditions may be less desirable. If a driver decides not

to perform a discretionary lane change (i.e., either the driving conditions are satisfactory,

or, although the driving conditions are not satisfactory, the current is the lane with the

best driving conditions) the driver continues in the current lane.

Otherwise, the driver selects a lane from the available alternatives and assesses the

adjacent gap in the target lane. The lowest level of ovals in the decision tree shown in

Figure 2 corresponds to the gap acceptance process. When trying to perform a DLC,

factors that affect drivers' gap acceptance behavior include the gap length, speed of the

subject, speed of the vehicles ahead of and behind the subject in the target lane, and the

type of the subject vehicle (heavy vehicle or not). For instance, a larger gap is required

for merging at a higher travel speed. A heavy vehicle would require a larger gap length

compared to a car due to lower maneuverability and the length of the heavy vehicle.

2.2.2 Gap acceptance

In addition to the above factors, the gap acceptance process under the MLC conditions is

influenced by factors such as remaining distance to the point at which lane change must


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be completed, delay (which captures the impatience factor that would make drivers more

aggressive) etc. Note that, delay cannot be used as an explanatory variable except for

very specialized situations, for example, merging from an on ramp. This is because the

very inception of an MLC condition is usually unobserved.

Figure 3: Conceptual Framework

2.3 Forced merging model

If the gap on the target lane is not acceptable then the subject vehicle forces the lag

vehicle on the target to decelerate until the gap is acceptable. This process is known as

Forced merging. The tree diagram in Figure 4 summarizes the proposed structure of the

forced merging model. As before, the ovals correspond to the latent part of the process

that involves decisions and the rectangles correspond to the events that are directlyobservable.At every discrete point in time, a driver is assumed to (a) evaluate the traffic environment

in the target lane to decide whether the driver intends to merge in front of the lag vehicle

in the target lane and (b) try to communicate with the lag vehicle to understand whether


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the driver's right of way is established. If a driver intends to merge in front of the lag

vehicle and right of way is established, the decision process ends and the driver gradually

move into the target lane. We characterize this instant by state M, where M denotes start

forced merging. This process may last from less than a second to a few seconds. This is

shown by the arrow below the left `same lane' box. If right of way is not established, the

subject continues the evaluation/communication process (i.e., remains in state M) during

the next time instant.

Figure 4: Framework for Forced merging model

We assume that a driver has decided to change to the adjacent lane as shown in Figure 5.

The merging process involves the driver's decision as to whether he/she intends to merge

into the adjacent gap and perception as to whether his/her right of way is established, and

finally moving into the target lane. An adjacent gap is defined as the gap behind the lead

vehicle in the target lane. Establishment of right of way means that an understanding

between the subject and the lag vehicle in the target lane hasbeen reached such that thelag vehicle would allow the subject to be in front of it.


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Figure 5: Definition of adjacent gap

2.4 COOPERATIVE AND FORCED GAP ACCEPTANCE

The models discussed so far assume that lane changing is executed through gap

acceptance. However, in congested traffic conditions acceptable gaps may not be

available, and so other mechanisms for lane changing are needed. For example, drivers

may change lanes through courtesy and cooperation of the lag vehicles on the target lane

that will slow down in order to accommodate the lane change. In other cases, some

drivers may become impatient and decide to force in to the target lane and compel the lag

vehicle to slow down.

2.4.1 Conceptual framework for cooperative and forced gap acceptance

The model shown in Figure 6, which was developed for a merging situation, integrates

courtesy and forced merging mechanisms with "normal" gap acceptance. The integrated

model captures the transitions from one type of merging to the other. In this model, the

merging driver first evaluates whether or not the available adjacent gap is acceptable.

This decision is modeled with standard gap acceptance models, which compare the lead

and lag gaps with the corresponding critical gaps. If the available gap is acceptable the

driver merges to the mainline. If the available gap is not acceptable, the driver anticipates

what the magnitude of the adjacent gap is going to be in a short time horizon. The


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anticipated gap is evaluated based on the magnitude of the available gap and the current

speed and acceleration of the lag vehicle.

The time horizon over which the driver anticipates the gap may vary across the driver

population to capture difference in perception and planning abilities among drivers. Theanticipated gap reflects the drivers' perception of the courtesy or discourtesy of the lag

vehicle. The driver then evaluates whether the anticipated gap will be acceptable or not.

An acceptable anticipated gap implies that the lag vehicle is providing courtesy to the

merging vehicle, and so the driver can initiate a courtesy merge. If the anticipated gap is

not acceptable the lag is not providing courtesy, and so the merging driver may choose

whether or not to begin forcing its way to the mainline and compel the lag vehicle to slow

down.

2.4.2 Courtesy yielding

A driver that has initiated courtesy yielding or forced merging completes the merge when

the available gap is acceptable. Thus, the lane change may not be completed when it is

initiated, but take more time. However, the model assumes that a driver that has initiated

a courtesy or forced merge would continue to use this mechanism until the lane change is

complete, or if unsuccessful until the gap it is adjacent to is no longer available (e.g. the

lag vehicle has overtaken it). Critical gaps for courtesy or forced merging may differ

from the ones used in normal lane changing.

Figure 6: model for cooperative and forced gap acceptance


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3. Gap acceptance

A gap is defined as the gap in between the lead and lag vehicles in the target lane (see

Figure 7). For merging into an adjacent lane, a gap is acceptable only when both lead and

lag gap are acceptable. Drivers are assumed to have minimum acceptable lead and lag

gap lengths which are termed as the lead and lag critical gaps respectively. These critical

gaps vary not only among different individuals, but also for a given individual under

different traffic conditions. Most models also make a distinction between the lead gap

and the lag gap and require that both are acceptable. The lead gap is the gap between the

subject vehicle and the vehicle ahead of it in the lane it is changing to. The lag gap is

defined in the same way relative to the vehicle behind in that lane. The critical gap for

driver n at time t is assumed to have the following relation.

Gng,cr

(t) = exp[Xng

(t)g

+ gvn + n

g(t)]

Gng,cr

(t)= critical gap measure for gap G perceived by driver n

at time step t

Xng

(t) = explanatory variable used to characterize mean Gng,cr

(t)

n = random term follows log normal distribution

g

= parameter of driver specific random term vn

Figure 7: Definition of gaps

Assuming ),0()( 2gNtg

n i.e., the critical gap lengths are log normally distributed, the

conditional probability of acceptance of a gap is given by:


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4. Delay for Lane change

If we assume that the drivers gap acceptance policy does not change with time then the

individual waiting periods is given by the probability.

P(n) = pn(1-p) n= 1,2,3

P(n) is the probability of a driver having a wait for n intervals each less than T sec

f(t) is the distribution of gaps

E(n) is expected number of intervals a driver has to wait

The blockage length and the average delay for the lane change are calculated based on

the following formulae.

=

==

lag

nleadlag

tn

laglag

tn

lead

nleadlead

tn

leadlead

tn

lag

tncr

lag

tn

lead

tncr

lead

tn

lag

tncr

lag

tn

lead

tncr

lead

tn

vXGvXG

GGPGGP

GGGGP

,,

,,

,,

-)ln(*

-)ln(=

))ln(>)(ln())ln(>)(ln(

)>and>(=

)acceptablegapP(lag)acceptablegapP(leadaccepted)aregapslagandProb(lead

accepted)isgapProb(a

=

=

T

T

dttf

dttf

p

pnE

)(

)(

1)( 0

=


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Where

T = Total time of headways rejected

BL = blockage length

Vs = stream velocity

Vr= relative velocity

Example 1:

In a two lane, one way stream of 1000 vph with 360 vehicles in Lane A and the

remaining vehicles in lane B. 8% of the vehicles in lane A have gaps less than 1 sec and

18% of the vehicles in lane A have gaps less than 2 sec. Compute the time during which

vehicles in Lane B may not change to Lane A in 1 hour.

Assume driver requires one second ahead and behind in making a lane change

Solution:

0 to 1 second Gaps = 8% of 360 = 29

1 to 2 second Gaps = (18-8) % of 360 = 36

Total = 65 Gaps

Time spent in Gaps 0 to 1 second = 29 x .5 = 14.5 sec

Time spent in Gaps 1 to 2 second = 36 x 1.5 = 54.0 sec

As 57 Gaps are rejected, Acceptable Gaps are (360-65) = 295 Gaps


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In this 295 Gaps clearance time = 295 x 2 = 590 sec.

Time lost in rejected gap = 14.5+54=68.5

Therefore,

Total time left in one hour to accept Gap=(3600 590 68.5) = 2941sec.

Vehicle can change lane in (2941/3600) = 81.7% of the Total time.

Vehicle is prevented from changing lane in 18.3% of the time

Example 2:

In a two lane, one way stream of 1000 vph with 360 vehicles in Lane A and the

remaining vehicles in lane B. 8% of the vehicles in lane A have gaps less than 1 sec and

18% of the vehicles in lane A have gaps less than 2 sec. Compute the average waiting for

the driver to make a lane change. Assume driver velocity in lane B = 40 kmph and stream

velocity = 50 kmph

Solution:

The average length of headways and portions of head ways of insufficient length for a

lane change, which may be considered as general blockages moving in the stream.

Division of this Blockage length by the relative speed determines potential total delay

time of the blockade. Finally since a delayed vehicle is as likely to be at the head as at the

tail of such a blockade at the moment of desired lane change, the total delay must be

divided by 2 for average delay time.

Where T = 3600 X 18.3 % =658.8

Vs = 50 kmph

N = acceptable gaps

VsTBL

=

rV

BLayAveragedel =

2

1


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0 to 2 second Gaps = 18 % of 360 = 65

Therefore N = 360-65 = 295

6.111295

508.658

=

=BL

In the above figure the vertical lines are the centre line of the cars and gr , ga represents

the acceptable and rejected gaps respectively.

5. Summary

Lane changing is an important component of microscopic traffic simulation model, and

has significant impact on the results of analysis that uses these tools. In recent years,

interest in the development of lane changing models and their implementation in traffic

simulators have increased dramatically. There is a lot of scope for the improvement of these

lane change models like integrating acceleration behavior, impact of the buses, bus stops, traffic

signals and queues that form due to lane change maneuver

6. References

1. Ahmed K.I. (1999), Modeling drivers acceleration and lane changing behaviors,PhD thesis,Department of Civil and Environmental Engineering, MIT.

2. Choudhury C.F., (2007), Modeling driving decisions with Latent plans, PhD thesis,Department of Civil and Environmental Engineering, MIT.

sec58.5)4050(

6.111

2

1. =

=DelayAvg


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3. Drew D.R.,(1968)Traffic Flow Theory and Control McGraw-Hill Book, NewYork,. Pages (173-190).[chapter 9]

4. Matson., Theodore M.,(1955)Traffic Engineering McGraw-Hill Book, New York,.Pages (136-145).[chapter 7]

7. Advanced topics

7.1 Target Lane Selection

Target lane is the lane the driver perceives as most desirable to drive in, depending upon

the prevalent conditions and his immediate destination.

Figure 8: Hypothetical scenario

Figure 9: Framework for hypothetical scenario


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In the above framework of figure 9, the first decision task for a driver involves the

selection of a target lane. A random utility-based framework is used to model this

decision, where the driver considers different aggregate lane-specific variables as well as

his individual path plan in estimating utilities of all available lanes. The selection of the

target lane among the available lanes follows a multinomial logit choice process. Subject

to the location of the selected target lane with respect to the drivers current lane, the

driver considers changing lane into the right or left adjacent lane (also termed his

immediate target lane), moving laterally in the direction of the target lane. The next step

in this process is the evaluation of the available adjacent gap in the lane that the driver

considers moving into based on his target lane selection. The gap acceptance model is

employed for this purpose, and the decision outcome results in the drivers final

observable action regarding lane change. If the adjacent gap is rejected, the driver does

not enact a lane change, while a lane change is exhibited on acceptance of the adjacent

gap.

7.2 Mobil (Minimizing Overall Braking decelerations Induced by Lane changes)

Lane changes takes place, if

the potential new target lane is more attractive, i.e., the "incentive criterion" issatisfied,

and the change can be performed safely, i.e., the "safety criterion" is satisfied.In lane change model MOBIL, We base both criteria on the accelerations on the old

and the prospective new lanes.

Model equations:

The safety criterion is satisfied, if the IDM braking

deceleration acc'=acc'IDMimposed on the back vehicleB'of the target lane after a

possible change does not exceed a certain limit bsave, this means, the safety criterion


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acc' (B') > - bsave

is satisfied. In this formula, the dash of the acceleration acc'=acc'IDM stands for "after

a possible change", while the dash of the back vehicle labelB'stands for "on the

target lane".

The lane-change model MOBIL has the following main features:

While other lane-change models typically assume purely egoistic behaviour, i.e.,p=0,

we can model different behaviours by varying this factor:

p > 1 => a very altruistic behaviour. p in ]0, 0.5] => a realistic behaviour: Advantages of other drivers have a lower

priority, but are not neglected: Notice that this feature means that yielding to

"pushy" is included into MOBIL.

p=0 => a purely selfish behaviour. Notice that also selfish drivers do not ignorethe safety criterion!

p a malicious personality who takes pleasure in thwarting other driverseven at the cost of own disadvantages. This may have some interesting game-

theoretic consequences. Of course, even those mischief makers do obey the

safety criterion.

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