Lecture notes in Traffic Engineering And Management
Date: February 19, 2014
Uncontrolled intersections are the traffic junctions where there is no explicit
traffic control measures are adopted.
The important aspects that will be covered in this chapter are: the concept of
two-way stop controlled intersection, all-way stop controlled intersection, gap
acceptance, critical gap, follow-up time, potential capacity, and delay
These concepts are primarily adopted from Highway Capacity Manual.
An intersection is a road junction where two or more roads either meet or cross
This intersection includes the areas needed for all modes of travel:
pedestrian, bicycle, motor vehicle, and transit.
Thus, the intersection includes not only the pavement area, but typically the
adjacent sidewalks and pedestrian curb cut ramps.
All the road junctions designated for the vehicles to turn to different
directions to reach their desired destinations.
Traffic intersections are complex locations on any highway.
This is because vehicles moving in different direction want to occupy same
space at the same time.
In addition, the pedestrians also seek same space for crossing.
Drivers have to make split second decision at an intersection by considering
his route, intersection geometry, speed and direction of other vehicles etc.
A small error in judgment can cause severe accidents.
It causes delay and it depends on type, geometry, and type of control.
Overall traffic flow depends on the performance of the intersections.
It also affects the capacity of the road.
Therefore, both from the accident perspective and the capacity perspective, the
study of intersections are very important by the traffic engineers.
Intersection design can vary widely in terms of size, shape, number of travel
lanes, and number of turn lanes.
Basically, there are four types of intersections, determined by the number of
road segments and priority usage.
- Priority Intersection: Occur where one of the intersecting roads is
given definite priority over the other.
The minor road will usually be controlled by some form of sing marking, such as
stop or yield sign; thus ensuring that priority vehicles travailing on the main
street will incur virtually no delay.
- Space sharing intersection: Are intended to permit fully equally
priority and to permit continuous movement for all intersecting vehicle flows;
example would be rotaries and other weaving areas.
- Time Sharing Intersection: Are those at which alternative flows are
given the right of way at different point in time.
This type of intersection is controlled by traffic signal or by police officer.
- Uncontrolled intersection: are the most common type of intersection
usually occurs where the intersecting roads are relatively equal importance and
found in areas where there is not much traffic shown in
At uncontrolled intersection the arrival rate and individuals drivers
generally determine the manner of operation, while the resulting performance
characteristics are derived from joint consideration of flow conditions and
driver judgment and behavior patterns.
In simplest terms, an intersection, one flow of traffic seeks gaps in the
opposing flow of traffic.
At priority intersections, since one flow is given priority over the right
of way it is clear that the secondary or minor flow is usually the one seeking
By contrast at uncontrolled intersection, each flow must seek gaps in the other
When flows are very light, which is the case on most urban and rural roads large
gaps exist in the flows and thus few situation arise when vehicles arrive at
uncontrolled intersection less than 10 second apart or at interval close enough
to cause conflicts.
However when vehicles arrive at uncontrolled intersection only a few second
apart potential conflicts exist and driver must judge their relative time
relationships and adjusts accordingly.
Generally one or both vehicles most adjust their speeds i.e. delayed
somewhat with the closer vehicle most often taking the right of way; in a sense,
of course, the earlier arriving vehicle has priority and in this instance
when two vehicles arrive simultaneous, the rule of the road usually indicate
priority for the driver on the right.
The possibility of judgmental in these, informal priority situation for
uncontrolled intersection is obvious.
At an Uncontrolled intersection: Service discipline is typically controlled by
signs (stop or yield signs) using two rules two way stop controlled intersection
(TWSC) and all way stop controlled intersection (AWSC).
Researchers rely on many specific definitions to describe the performance of
traffic operation systems.
The clear understanding of such terminology is an important element is studying
two-way stop-controlled (TWSC) traffic operation system characteristics; defined
as: One of the uncontrolled intersections with stop control on the minor street
shown in Fig. 2.
Example showing uncontrolled intersection
At TWSC intersections, the stop-controlled approaches are referred to as the
minor street approaches; the intersection approaches that are not controlled by
stop signs are referred to as the major street approaches.
A three-leg intersection is considered to be a standard type of TWSC
intersection if the single minor street approach is controlled by a stop sign.
Three-leg intersections where two of the three approaches are controlled by stop
signs are a special form of uncontrolled intersection control.
TWSC intersections assign the right-of-way among conflicting traffic streams
according to the following hierarchy:
Two way stop controlled intersection
- The major street through and right-turning movements are the
highest-priority movements at a TWSC intersection.
This movements shown Fig. 3 are 2, 3, 5, 6, 15 and 16.
- Vehicles turning left from the major street onto the minor
street yield only to conflicting major street through and right-turning
All other conflicting movements yield to these major street left-turning
The movements on this rank are 1, 4, 13, 14, 9 and 12.
- Minor Street through vehicles yield to all conflicting major
street through, right-turning, and left-turning movements.
The movements on this rank are 8 and 11.
- Minor Street left-turning vehicles yield to all conflicting
major street through, right-turning, and left-turning vehicles and to all
conflicting minor street through and right-turning vehicles.
The movements on this rank are 7 and 10.
All-way-stop-controlled intersection (AWSC) are mostly used approaching from
all directions and is required to stop before proceeding through the
intersection as shown in Fig. 4.
An all-way stop may have multiple approaches and may be marked with a
supplemental plate stating the number of approaches.
Traffic flow stream in two way stop controlled intersection
The analysis of AWSC intersection is easier because all users must stop.
In this type of intersection the critical entity of the capacity is the average
intersection departure head way.
Secondary parameters are the number of cross lanes, turning percentages, and the
distribution volume on each approach.
The first step for the analysis of capacity is select approach called subject
approach the approach opposite to subject approach is opposing approach, and the
approach on the side of the subject approach is are called conflicting approach.
AWSC intersections require every vehicle to stop at the intersection before
Since each driver must stop, the judgment as to whether to proceed into the
intersection is a function of traffic conditions on the other approaches.
If no traffic is present on the other approaches, a driver can proceed
immediately after the stop is made.
If there is traffic on one or more of the other approaches, a driver proceeds
only after determining that there are no vehicles currently in the intersection
and that it is the driver’s turn to proceed.
Gap acceptance is one of the most important components in microscopic traffic
The gap acceptance theory commonly used in the analysis of uncontrolled
intersections based on the concept of defining the extent drivers will be able
to utilize a gap of particular size or duration.
A driver entering into or going across a traffic stream must evaluate the
space between a potentially conflicting vehicle and decide whether to cross or
enter or not.
One of the most important aspects of traffic operation is the interaction of
vehicles with in a single stream of traffic or the interaction of two separate
This interaction takes place when a driver changes lanes merging in to a traffic
stream or crosses a traffic stream.
Inherent in the traffic interaction associated with these basic maneuvers is
concept of gap acceptance.
All way stop controlled intersection
The critical gap for movement x is defined as the minimum average
acceptable gap that allows intersection entry for one minor street or major
The term average acceptable means that the average driver would accept or choose
to utilize a gap of this size.
The gap is measured as the clear time in the traffic stream defined by all
Thus, the model assumes that all gaps shorter than are rejected or
unused, while all gaps equal to or larger than would be accepted or
The adjusted critical gap computed as follows.
- Gap means the time and space that a subject vehicle needs to merge
adequately safely between two vehicles.
Gap acceptance is the minimum gap required to finish lane changing safely.
Therefore, a gap acceptance model can help describe how a driver judges whether
to accept or not.
- Gap acceptance: The process by which a minor stream vehicle accepts an
available gap to maneuver.
- Critical gap: The minimum major-stream headway during which a
minor-street vehicle can make a maneuver.
- Lag: Time interval between the arrival of a yielding vehicle and the
passage of the next priority stream vehicle (Forward waiting time).
- Headway: The time interval between the arrivals of two successive
Headway differs from gap because it is measured from the front bumper of the
front vehicle to the front bumper of the next vehicle.
- Minimum Headway: The minimum gap maintained by a vehicle in the major
- Follow-up time: Time between the departure of one vehicle from the
minor street and the departure of the next vehicle using the same gap under a
condition of continuous queuing.
- Delay: The additional travel time experienced by a driver, passenger or
- Conflicting movements: The traffic streams in conflict at an
- Capacity: The maximum hourly rate at which persons or vehicles can
reasonably be expected to traverse a point or uniform section of a lane or a
roadway during a given time period under prevailing roadway, traffic, and
is the critical gap for movement ``'',
is the base critical gap from Table. 1
is the adjustment factor for heavy vehicles
is the proportion of heavy vehicles
is the adjustment factor for grade
is the percent grade divided by 100,
is the adjustment factor for each part of a two-stage gap acceptance process, and
is the critical gap adjustment factor for intersection geometry.
The follow up time for movement ``'' is the minimum average
acceptable time for a second queued minor street vehicle to use a gap large
enough admit two or more vehicles.
Follow-up times were measured directly by observing traffic flow.
Resulting follow-up times were analyzed to determine their dependence on
different parameters such as intersection layout.
This measurement is similar to the saturation flow rate at signalized
Table. 1 and 2 shows base or
unadjusted values of the critical gap and follow up time for various movements.
Base critical gaps and follow up times can be adjusted to account for a number
of conditions, including heavy - vehicle presence grade, and the existence of
two stage gap acceptance.
Adjusted Follow up Time computed as:
is the follow-up time for minor movement
is the base follow-up time from table 1
is the adjustment factor for heavy vehicles, and
is the proportion of heavy vehicles for minor movement.
Base critical gap and follow up times
||Base Critical Gap,,base (s)
|Left turn from major
|Right turn from minor
|Through traffic on minor
|Left turn from minor
The traffic flow process at un-controlled intersection is complicated since
there are many distinct vehicular movements to be accounted for.
Most of this movements conflict with opposing vehicular volumes.
These conflicts result in decreasing capacity, increasing delay, and increasing
potentials for traffic accidents.
Consider a typical four-legged intersection as shown in
The numbers of conflicts for competing through movements are 4, while competing
right turn and through movements are 8.
The conflicts between right turn traffics are 4, and between left turn and
merging traffic are 4.
The conflicts created by pedestrians will be 8 taking into account all the four
Diverging traffic also produces about 4 conflicts.
Therefore, a typical four legged intersection has about 32 different types of
Adjustments to base critical gap and follow up times
||Two-lane major streets
||Four-lane major streets
||Movements 9 and 12
||Movements 7,8,10 and 11
||First or second stage of two-stage process
||For one-stage process
||Minor-street LT at T-intersection
||Two-lane major streets
||Four-lane major streets
Conflicts at an intersection are different for different types of intersection.
The essence of the intersection control is to resolve these conflicts at the
intersection for the safe and efficient movement of both vehicular traffic and
The movements for determining conflict in four legged intersection are:
Conflicts at four legged intersection
Through this movements the conflict volume () for the given movement
is can be computed.
As an example the formula of conflict volume for movement 7 for three legged
intersection shown in Fig. 6 computed as:
- Major street left turns seek gaps through the opposing through
movement, the opposing right turn movement and pedestrians crossing the far side
of the minor street.
- Minor street right turns seek to merge in to the right most lane of the
major street, which contains through and right turning vehicles.
Each right turn from the minor street must also cross the two pedestrians path
- Through movements from the minor street must cross all major street
vehicular and pedestrians flows.
- Minor street left turns must deal not only with all major street
traffic flow but with two pedestrians flows and the opposing minor street
through and right turn movements.
Capacity is defined as the maximum number of vehicles, passengers, or the like,
per unit time, which can be accommodated under given conditions with a
reasonable expectation of occurrence.
Potential capacity describes the capacity of a minor stream under ideal
conditions assuming that it is unimpeded by other movements and has exclusive
use of a separate lane.
Three legged intersection conflicts volume determination for movement 7
Once of the conflicting volume, critical gap and follow up time are known
for a given movement its potential capacity can be estimated using gap
The concept of potential capacity assumes that all available gaps are used by
the subject movement i.e.; there are no higher priority vehicular or pedestrian
movements and waiting to use some of the gaps it also assumes that each movement
operates out of an exclusive lane.
The potential capacity of can be computed using the formula:
is the potential capacity of minor movement (veh/h),
is the conflicting flow rate for movement (veh/h),
is the critical gap for minor movement , and
is the follow-up time movement .
Vehicles use gaps at a TWSC intersection in a prioritized manner.
When traffic becomes congested in a high-priority movement, it can impede
lower-priority movements that are streams of Ranks 3 and 4 as shown in
Fig. 4 from using gaps in the traffic stream, reducing
the potential capacity of these movements.
The ideal potential capacities must be adjusted to reflect the impedance effects
of higher priority movements that may utilize some of the gaps sought by lower
This impedance may come due to both pedestrians and vehicular sources called
The movement capacity is found by multiplying the potential capacity by an
The adjustment factor is the product of the probability that each impeding
movement will be blocking a subject vehicle.
is the movement capacity in vph,
is the potential capacity movement x in vph,
is the probability that impeding vehicular movement is not blocking
the subject flow; (also referred to as the vehicular impedance factor for
is the probability that impeding pedestrian movement is not blocking
the subject flow; also referred to us the pedestrian impedance factor for the
Priority 2 vehicular movements LTs from major street and RTs from minor street
are not impeded by any other vehicular flow, as they represent the highest
priority movements seeking gaps.
They are impeded, however, by Rank 1 pedestrian movements.
Priority 3 vehicular movements are impeded by Priority 2 vehicular movements and
Priority l and 2 pedestrian movements seeking to use the same gaps.
Priority 4 vehicular movements are impeded by Priority 2 and 3 vehicular
movements, and Priority 1 and 2 pedestrian movements using the same gaps.
Table. 3 lists the impeding flows for each subject
movement in a four leg.
Generally the rule stated the probability that impeding vehicular movement
is not blocking the subject movement is computed as
is the demand flow for impeding movement , and
is the movement capacity for impeding movement vph.
Pedestrian impedance factors are computed as:
One of the impeding effects for all the movement is pedestrians movement.
Both approaches of Minor-street vehicle streams must yield to pedestrian
Table. 3 shows that relative hierarchy between
pedestrian and vehicular streams used.
A factor accounting for pedestrian blockage is computed by
Eqn. 7 on the basis of pedestrian volume, the pedestrian
walking speed, and the lane width that is:
is the pedestrian impedance factor for impeding pedestrian movement ,
is the pedestrian flow rate, impeding movement in peds/hr,
is the lane width in m, and
is the pedestrian walking speed in m/s.
The capacities of individual streams (left turn, through and right turn) are
If the streams share a common traffic lane, the capacity of the shared lane is
then calculated according to the shared lane procedure.
But movement capacities still represent an assumption that each minor street
movement operates out of an exclusive lane.
Where two or three movements share a lane its combined capacity computed as:
Relative pedestrian/vehicle hierarchy
||Must Yield to
||Impedance Factor for
is the shared lane capacity in veh/hr,
is the flow rate, movement sharing lane with other minor street flow, and
is the movement capacity of movement sharing lane with other minor
Delay is a complex measure and depends on a number of variables it is a measure
of driver discomfort, frustration, fuel consumption, increased travel time etc.
Total delay is the difference between the travel time actually experienced and
the reference travel time that would result during base conditions, in the
absence of incident, control, traffic, or geometric delay.
Also, Average control delay for any particular minor movement is a function of
the Capacity of the approach and The degree of saturation.
The control delay per vehicle for a movement in a separate lane is given by:
is the average control delay per vehicle for movement in s/veh,
is the capacity of movement or shared lane in veh/hr,
is the analysis period h (15 min=0.25 h), and
is the demand flow rate, movement or shared lane in veh/hr.
Four measures are used to describe the performance of TWSC intersections:
control delay, delay to major street through vehicles, queue length, and v/c
The primary measure that is used to provide an estimate of LOS is control delay.
This measure can be estimated for any movement on the minor (i.e., the
By summing delay estimates for individual movements, a delay estimate for each
minor street movement and minor street approach can be achieved.
For AWSC intersections, the average control delay (in seconds per vehicle)
is used as the primary measure of performance.
Control delay is the increased time of travel for a vehicle approaching and
passing through an AWSC intersection, compared with a free flow vehicle if it
were not required to slow or stop at the intersection.
According to the performance measure of the TWSC intersection, LOS of the
minor-street left turn operates at level of service C approaches to
Level of service criteria for TWSC intersection
|Level of Service
For a three legged intersection given in figure 7
determine the control delay and level of service for movement 7.
The total volume of both pedestrian and vehicular traffic at each movement is
given in the figure itself.
Following data is also given:
Three legged intersection
- The speed of the pedestrians is 1.2m/s
- All flows contains 10% trucks
- The percentage of the grade is 0.00
- Ignore moments coming from south bound
- The analysis period is 15 min. (T=0.25)
This chapter focuses on theoretical analysis of capacity at uncontrolled
First the gap acceptance theory and follow time was described; including
conflict volume determination through the hierarchy of priorities for two ways
stop controlled intersection.
Second, after determining the potential capacity using the computed value and
then prepare an adjustment for this capacity.
Finally, computation of the delay to determine the level of service (LOS) of the
given intersection is also described.
- Compute the critical gap and follow up time:
- Critical gap
From table. 1 and
table. 2 we have
= 7.1 s , = 0.2, = 0.0, = 0.0.
Then at movement 7 computed as:
= 7.1 + 1.0 0.1+0.2 0.0 - 0.0 - 0.0 = 6.50 sec
- To compute the Follow up time:
From table. 1 and
table. 2 we have
= 3.5 s , = 0.9.
Then at movement 7 computed as:
= 3.5 + 0.9 0.1 = 3.59 sec.
- Compute the conflicting flow rate:
- Determining potential capacity:
- Determine the impudence effect of the movement capacity for movement 7:
From the given figure movement 7 is impeded by vehicular movement 4 and 1 and
pedestrian 13 and 15.
- Pedestrian impedance probability computed as:
- Vehicular impedance probabilities are:
- Once the pedestrian and vehicular impedance is determined, the moment
capacity is computed as:
- Delay computation:
The delay is Calculated by using the formula
The delay of movement 7 is 18.213 sec/veh.
- Determine the level of service:
From the computed delay (18.213 se) in step 5 the level of service is
LOS C obtained from HCM table.
I wish to thank my student Mr. Birara Tekeste for his assistance in developing
the lecture note, and my staff Ms. Reeba in typesetting the materials.
I also wish to thank several of my students and staff of NPTEL for their
contribution in this lecture.
- Highway Capacity Manual.
Transportation Research Board.
National Research Council, Washington, D.C., 2000.
- W S Homburger.
Fundamentals of traffic engineering.
12th Edition, pp 5-1 to 5-5.
- William R McShane, Roger P Roesss, and Elena S Prassas.
Prentice-Hall, Inc, Upper Saddle River, New Jesery, 1998.
Prof. Tom V. Mathew