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Chapter 30
Uncontrolled Intersection
30.1 Introduction
An intersection is a road junction where two or more roads either meet or cross at grade. 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.
30.1.1 Categories of Intersection
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 Fig. 30:1. 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 gaps”. By contrast at uncontrolled intersection, each flow must seek gaps in the other opposing flow. 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 intersec- tion 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).
STOP STOP
STOP
Four−leg intersection T−intersection
Rank Traffic stream Rank Traffic stream
4
32
1 7, 10
1, 4, 13, 14, 9, 128, 11 2, 3, 5, 6, 15, 16 32
1 7
4, 13, 14, 92, 3, 5, 15
121110
2
7 8 9
6 4 2
(^54)
7 9
16 13
15
14
13 14 (^315)
1
5
3
Figure 30:3: Traffic flow stream in two way stop controlled intersection source[1]
Flow at TWSC Intersections
TWSC intersections assign the right-of-way among conflicting traffic streams according to the following hierarchy: Rank 1 - The major street through and right-turning movements are the highest-priority movements at a TWSC intersection. This movements shown Fig. 30:3 are 2, 3, 5, 6, 15 and 16. Rank 2 - Vehicles turning left from the major street onto the minor street yield only to conflicting major street through and right-turning vehicles. All other conflicting movements yield to these major street left-turning movements. The movements on this rank are 1, 4, 13, 14, 9 and 12. Rank 3 - 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. Rank 4 - 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.
30.1.3 All-Way-Stop-Controlled Intersection (AWSC)
AWSC Intersection are mostly used approaching from all directions and is required to stop before proceeding through the intersection as shown in Fig. 30:4. An all-way stop may have multiple approaches and may be marked with a supplemental plate stating the number of approaches.
STOP
STOP STOP
STOP
A
B
Figure 30:4: All way stop controlled intersection(source [5])
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.
Characteristics of AWSC Intersections
AWSC intersections require every vehicle to stop at the intersection before proceeding. 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 drivers turn to proceed.
30.2 Gap Acceptance and Follow up Time
Gap acceptance is one of the most important components in microscopic traffic characteristic. 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
larger than tcx would be accepted or used. The adjusted critical gap tcx computed as follows.
tcx = tcb + tcHV P HV + tcGG − tc,T − t 3 ,LT (30.1)
where, tcx = critical gap for movement “x”, tcb = base critical gap from Table. 30: tcHV = adjustment factor for heavy vehicles PHV = proportion of heavy vehicles tcG = adjustment factor for grade G = percent grade divided by 100, tcT = adjustment factor for each part of a two-stage gap acceptance process t 3 LT =critical gap adjustment factor for intersection geometry
30.2.3 Follow up Time
The follow up time tf x for movement “x” 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 intersection. Table. 30: and 30:2 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:
tf x = tf b + tf HV PHV (30.2)
where, tf x = Follow-up time for minor movement x tf b = Base follow-up time from table 1 tf HV = Adjustment factor for heavy vehicles PHV = Proportion of heavy vehicles for minor movement
30.3 Conflicts
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
Table 30:1: Base critical gap and follow up times source[1] Base Critical Gap,tc,base (s) Vehicle Movement Two-Lane Four-Lane Base Follow-up Time, MajorStreet Major Street tf,base (s) Left turn from major 4.1 4.1 2. Right turn from minor 6.2 6.9 3. Through traffic on minor 6.5 6.5 4. Left turn from minor 7.1 7.5 3.
Table 30:2: Adjustments to Base critical gap and follow up times source[1] Adjustment Values(s) Factor tcHV 1.0 Two-lane major streets 2.0 Four-lane major streets tcG 0.1 Movements 9 and 12 0.2 Movements 7,8,10 and 11 1.0 Otherwise tcT 1.0 First or second stage of two-stage process 0.0 For one-stage process T 3 LT 0.7 Minor-street LT at T-intersection 0.0 Otherwise tf HV 0.9 Two-lane major streets 1.0 Four-lane major streets
13 14
15
3
2
7 9
4
5
STOP
Figure 30:6: Three legged intersection Conflicts volume determination for movement 7 (source [4])
puted. As an example the formula of conflict volume for movement 7 for three legged intersec- tion shown in Fig. 30:6 computed as:
Vc7 = 2Vc4 + Vc5 + +Vc2 + 0. 5 V 3 + V 13 + V 15 (30.3)
30.4 Potential Capacity
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. 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 acceptance models. 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:
cpx = vcx × e
−vcx tcx/ 3600 1 − e−vcx tf x/^3600 (30.4)
where, cpx = potential capacity of minor movement x (veh/h)
vcx = conflicting flow rate for movement x (veh/h) tcx = critical gap for minor movement x tf,x = follow-up time movement x.
30.5 Movement Capacity and Impedance Effects
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. 30:4 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 priority movements. This impedance may come due to both pedestrians and vehicular sources called movement capacity. The movement capacity is found by multiplying the potential capacity by an adjustment factor. The adjustment factor is the product of the probability that each impeding movement will be blocking a subject vehicle. That is
Cmx = Cpx × ΣPvi × Ppi (30.5)
where, Cmx = movement capacity, movement x, vah/hr Cpx = Potential capacity movement x, vah/hr Pvi = probability that impeding vehicular movement “i” is not blocking the subject flow; (also referred to as the vehicular impedance factor for movement “i” Ppi = probability that impeding pedestrian movement “j” is not blocking the subject flow; also referred to us the pedestrian impedance factor for the movement “j”
30.5.1 Vehicular Movements
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. 30:3 lists the impeding flows for each subject movement in a four leg.
Table 30:3: Relative pedestrian/vehicle hierarchy (source [1]) Vehicle Stream Must Yield to Impedance Factor for Pedestrian Stream Pedestrians, Pp,x V 1 V 16 Pp, 16 V 4 V 15 Pp, 15 V 7 V 15 , V 13 (Pp, 15 )(Pp, 13 ) V 8 V 15 , V 16 (Pp, 15 )(Pp, 16 ) V 9 V 15 , V 14 (Pp, 15 )(Pp, 14 ) V 10 V 16 , V 14 (Pp, 16 )(Pp, 14 ) V 11 V 15 , V 16 (Pp, 15 )(Pp, 16 ) V 12 V 16 , V 13 (Pp, 16 )(Pp, 13 )
Vy = flow rate, movement “y” sharing lane with other minor street flow Cmy = movement capacity of movement “y” sharing lane with other minor street
30.6 Determining Control Delay
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:
dx =^3600 Cmx
+ 900T
( Vx Cmx
√√ √√ ( Vx Cmx
− 1)^2 +
3600 Cmx
Vx Cmx 450 T
+ 5 (30.9)
where, dx = average control delay per vehicle for movement x, s/veh Cmx = capacity of movement or shared lane x, veh/hr T = analysis period, h(15min=0.25h) Vx = demand flow rate, movement or shared lane x, veh/hr
Table 30:4: Level of service criteria for TWSC intersection (source [1]) Level of Service Control delays(s/veh) A 0- B > 10- C > 15- D > 25- E > 35- F > 50
30.6.1 Performance Measures
Four measures are used to describe the performance of TWSC intersections: control delay, delay to major street through vehicles, queue length, and v/c ratio. 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 stop-controlled) street. 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 B.
30.7 Example and Question
30.7.1 Example
For the given three legged intersection of above figure the total volume pedestrian and vehicular at each movement is given in the fig itself. Taking the following:
- The speed of the pedestrians 1.2m/s
- All flows contains 10% trucks
- The percentage of the grade is 0.
Step 2 Compute the conflicting flow rate
Vc 7 = 2 V 4 + V 5 + V 13 + V 2 + 0. 5 V 3 + V 15 = 40 + 400 + 15 + 200 + 0. 5 × 30 + 30 = 700 Conf licts/hr
Step 3 Determining Potential Capacity
Cpx = vcx^ e
−(vcxtcx /3600) 1 − e−(vcx^ tf x/3600) = 700 e
−(700× 6. 5 /3600) 1 − e−(700×^3.^59 /3600) Cp 7 = 394 V ph
Step 4 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
Ppi = 1 −
vj ×
[ (^) w Sp
]
3600
Pp 13 = 1 −
15 ×
[ (^6)
- 2
]
3600
Pp 15 = 1 −
30 ×
[ (^4). 5
- 2
]
3600 = 1^ −^0 .03125 = 0.^969
- Vehicular impedance probabilities are Pvi = 1 − (^) Cvi mi Pv 4 = 1 − 20 /394 = 0. 949
- Once the pedestrian and vehicular movement is determined the moment capacity is com- puted as
Cmx = CpxP Pvi × Ppj Cm 7 = 394 × (0.949)(0.969)(0.958) = 347V eh/hr
Step 5 Delay computation The delay is Calculated by using the formula
d 7 = (^3600) C mx
+ 900T
( Vx Cmx^ −^ 1) +
√√ √√ ( (^) CVx mx
− 1)^2 +
3600 Cmx
Vx Cmx 450 T
+ 5
+ 900 × 0. 25
(^75 347
√ (^75 347
− 1)^2 +
3600 347
75 347 450 × 0. 25
(^) + 5
= 18. 213 se/veh
The delay of movement 7 is 18.213se/veh
Step 6 Determine the level of service From the computed delay (18.213 se) in step 5 the level of service is LOS“C”
30.7.2 Question
STOP
Vehicle Movement
Pedestrians Movement (^9)
200(2)
12
30(16)
30(15)
15(13) (^) 15(14) (^7)
30(1)
30(3) 75(8) 75(7) 100(9)
20(4)
400(5)
STOP 20(6)
In Fig. ?? the amount of volume for the pedestrians, volume vehicles and the width of the lane in (m) at each movement are given. Taking the following:
- The speed of the pedestrians 1.2m/s
- All flows contains 8% trucks
- The percentage of the grade is 0.
- Ignore moments coming from south bound
Step 3 Determining Potential Capacity
Cpx = vcx^ e
−(vcxtcx /3600) 1 − e−(vcx^ tf x/3600) = 760
e−(760×^7.^18 /3600) 1 − e−(760×^3.^59 /3600) Cp 7 = 312 V ph
Step 4 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
Ppi = 1 −
vj ×
[ (^) w Sp
]
3600
Pp 13 = 1 −
15 ×
[ (^6)
- 2
]
3600
Pp 15 = 1 −
30 ×
[ (^4). 5
- 2
]
3600 = 1^ −^0 .03125 = 0.^969
- Vehicular impedance probabilities are Pvi = 1 − vi Cmi Pv 4 = 1 − 20 /394 = 0. 949
- Once the pedestrian and vehicular movement is determined the moment capacity is com- puted as
Cmx = CpxP Pvi × Ppj Cm 7 = 312 × (0.949)(0.969)(0.958) = 296V eh/hr
Step 5 Delay computation The delay is Calculated by using the formula
d 7 = (^3600) C mx
+ 900T
( Vx Cmx^ −^ 1) +
√√ √√ ( (^) CVx mx
− 1)^2 +
3600 Cmx
Vx Cmx 450 T
+ 5
+ 900 × 0. 25
(^75 296
√ (^75 296
− 1)^2 +
3600 296
75 296 450 × 0. 25
(^) + 5
= 21. 24 se/veh
The delay of movement 7 is 21.24se/veh
Step 6 Determine the level of service From the computed delay (21.24 se) in step 5 the level of service is LOS“C”
30.8 Conclusion
This term paper focuses on theoretical analysis of capacity at uncontrolled intersections. First the gap acceptance theory and follow time was described; including conflict volume determina- tion 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, compute the delay to determine the level of service (LOS) of the given intersection. Left-turn movements (7) will generally experience longer control delays than other movements because of the nature of priority of the movement. At TWSC intersections this movement (7), may control the overall performance of the intersection. Level-of-Service C describes at or near free-flow operations. The above given intersection is operating at acceptable levels, No changes in control and any Design Operation are recommended.
30.9 Acknowledgments
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.
