CHAPTER 4:HIGHWAY CAPACITY

INTRODUCTION

Highway capacity deals with the volume of traffic that can pass over a section of roadunder the prevailing roadway and traffic conditions. Conversely, it relates to the "ease ofmovement" of the vehicles involved, usually referred to as Level of Service (LOS).Traffic can be uninterrupted or interrupted in reference to external influences affectingtraffic movement such as for example, traffic lights and traffic signs. Under uninterruptedtraffic, speed and ease of maneuvering is determined by the dynamics of the traffic flowitself. As a result, uninterrupted traffic can be fairly jammed!, (e.g., a southernCalifornian freeway).

The study of uninterrupted traffic flow can be subdivided into:• capacity of freeways,• capacity of multi-lane highways,• capacity of 2-lane highways,• capacity of their components, (i.e., ramps and weaving areas).The difference between a freeway and a highway is the degree of access control, (i.e., inthe former, intersections are not at-grade while in the latter they are). The study ofinterrupted traffic flow deals primarily with signalized intersections. This Chapter dealsonly with uninterrupted traffic flow and only with the "basic freeway segments" i.e.,segments that are far enough from other highway elements, such as ramps and weavingareas, so they can be treated in isolation, (Fig. 4.1). It should be pointed out from theoutset that all procedures prescribed here are the ones recommended by the 1985,Highway Capacity Manual (TRB SR 209) and are empirical in nature.

Figure 4.1: Definition of a Basic Freeway Segment, (Highway Capacity Manual, 1985).

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DEFINITIONS

LOS: Qualitative measure of operational conditions within a traffic stream and theirperception by motorists (factors include speed/travel time, freedom to maneuver, trafficinterruptions, etc.). LOS is indexed by the letters A, B, ....F, where A stands for free-flowconditions and F stands for "jam" conditions. These conditions are best defined inpictorial terms as shown below:

Level-of-Service A represents free flow. Individual users are virtually unaffected by thepresence of others in the traffic stream. Freedom to select desired speeds and tomaneuver within the traffic stream is extremely high. The general level of comfort andconvenience provided to the motorist, passenger, or pedestrian is excellent.

Level-of-Service B is in the range of stable flow, but the presence of other users in thetraffic stream begins to be noticeable. Freedom to select desired speeds is relativelyunaffected, but there is a slight decline in the freedom to maneuver within the trafficstream from LOS A. The level of comfort and convenience provided is somewhat lessthan at LOS A, because the presence of others in the traffic stream begins to affectindividual behavior.

Level-of Service C is in the range of stable flow, but marks the beginning of the range offlow in which the operation of individual users becomes significantly affected byinteractions with others in the traffic stream. The selection of speed is now affected bythe presence of others, and maneuvering within the traffic stream requires substantial

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vigilance on the part of the user. The general level of comfort and convenience declinesnoticeably at this level.

Level-of-Service D represents high-density, but stable flow. Speed and freedom tomaneuver are severely restricted, and the driver or pedestrian experiences a generallypoor level of comfort and convenience. Small increases in traffic flow will generallycause operational problems at this level.

Level-of-Service E represents operating conditions at or near the capacity level. Allspeeds are reduced to a low but relatively uniform value. Freedom to maneuver withinthe traffic stream is extremely low, and it is generally accomplished by forcing a vehicleor pedestrian to "give way" to accommodate such maneuvers. Comfort and conveniencelevels are extremely poor, and driver or pedestrian frustration is generally high.Operations at this level are usually unstable, because small increases in flow or minorperturbations within the traffic stream will cause breakdowns.

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Level-of-Service F is used to define forced or breakdown flow. This condition existswherever the amount of traffic approaching a point exceeds the amount which cantraverse the point. Queues form behind such locations. Operations within the queue arecharacterized by stop-and-go waves, and they are extremely unstable. Vehicles mayprogress at reasonable speeds for several hundred feet or more, then be required to stop ina cyclic fashion. Level-of-service F is used to describe the operating conditions withinthe queue, as well as the point of breakdown. It should be noted, however, that in manycases operating conditions of vehicles or pedestrians discharged from the queue may bequite good. Nevertheless, it is the point at which arrival flow exceeds discharge flowwhich causes the queue to form, and level-of-service F is an appropriate designation forsuch points.

Maximum Service Flow (MSF): Maximum rate of flow, in pcph, that a facility can carryunder ideal conditions for each LOS. These ideal conditions are defined as:

• 12' minimum traffic lanes• 6' minimum lateral clearance on either side of a lane• Only passenger vehicles in traffic stream• Driver behavior typical of weekday work commuter (uniform).

Hence, there are 5 MSF's, one for each of LOS of A, B, ...and E, respectively. Obviously,there is no MSF for LOS F, because at F nobody moves.

Capacity (C): The maximum flow a road section can carry under LOS E. Under “ideal”conditions (see above), the lane capacity of a freeway ranges between 1,800 and 2,000pcph, depending on its design speed.

The MSFi at a design speed j can be expressed as:

MSF CVCi j

i= � � (4.1)

with units of pcphpl rounded to the nearest 50. Cj is the capacity of a basic freewaysegment with a design speed j, and ( / )V C i is the ratio of volume over capacity for LOSi

called degree of saturation.

Service Flow (SF): It is the adjusted MSF value to account for conditions less than ideal,(e.g., presence of trucks, lanes narrower than 12' and so on), expressed in vph.

Peak Hourly Factor (PHF): It is defined as the ratio of the peak hourly volume dividedby the Service Flow:

PHF = <Peak Hourly VolumeFlow Rate

1 (4.2)

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The operating characteristics of basic freeway segments under ideal conditions are shownin Table 4.1, as a function of level of service and the design speed of the facility.

Table 4.1Operating Characteristics of Basic Freeway Segments

Under Ideal Geometric/Traffic Conditions, (Highway Capacity Manual, 1985).

Note volume / capacity ratios:700

2 0000 35

1 1002 000

0 54

,.

,,

.

=

= , etc.

CAPACITY ANALYSIS

For conditions different than the "ideal" outlined above, the value of MSFi must befactored to yield what is called service flow for LOSi that is SFi . Thus:

SF MSF f f fi i w hv p= ∗ ∗ ∗ (4.3)

In essence, this changes pcph under ideal conditions into vph under prevailing conditions,where:

fw = adjustment factor for lane widths less than 12'fhv = adjustment factor for heavy vehiclesfp = adjustment factor for driver behavior

These factors are tabulated in Tables 4.2, 4.3 and 4.4, respectively, while trafficequivalencies in terms of number of passenger vehicles are given in Table 4.5. Note thatin a multi-lane facility, SFi must be multiplied by the number of lanes to yieldservice flow in each direction.

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Table 4.2Adjustment Factors for Lane Width ( fw), (Highway Capacity Manual, 1985).

Obstructions one side Obstructions on both sidesDistance fromtraveled Lane width (ft)pavement a(ft) 12 11 10 9 12 11 10 9

4-Lane freeway (2 lanes each direction)

>6 1.00 0.97 0.91 0.81 1.00 0.97 0.91 0.815 0.99 0.96 0.90 0.80 0.99 0.96 0.90 0.804 0.99 0.96 0.90 0.80 0.98 0.95 0.89 0.793 0.98 0.95 0.89 0.79 0.96 0.93 0.87 0.772 0.97 0.94 0.88 0.79 0.94 0.91 0.86 0.761 0.93 0.90 0.85 0.76 0.87 0.85 0.80 0.710 0.90 0.87 0.82 0.73 0.81 0.79 0.74 0.66

6- or 8-Lane freeway (3 or 4 lanes each direction)

>6 1.00 0.96 0.89 0.78 1.00 0.96 0.89 0.785 0.99 0.95 0.88 0.77 0.99 0.95 0.88 0.774 0.99 0.95 0.88 0.77 0.98 0.94 0.87 0.773 0.98 0.94 0.87 0.76 0.97 0.93 0.86 0.762 0.97 0.93 0.87 0.76 0.96 0.92 0.85 0.751 0.95 0.92 0.86 0.75 0.93 0.89 0.83 0.720 0.94 0.91 0.85 0.74 0.91 0.87 0.81 0.70

a Certain types of obstructions, high-type median barriers in particular, do not cause any deleterious effecton traffic flow. Judgment should be exercised in applying these factors.Source: TRB, 1985.

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Table 4.3Adjustment Factors for Heavy Vehicles ( fhv ), (Highway Capacity Manual, 1985).

Table 4.4Adjustment Factors for Driver Behavior ( fp ), (Highway Capacity Manual, 1985).

Table 4.5Passenger Car Equivalencies of Heavy Vehicles, (Highway Capacity Manual, 1985).

Note that Table 4.5 suggest that 1 truck is equivalent in terms of capacity to 1.7, 4.0 and8.0 passenger vehicles for level, rolling and mountainous terrain, respectively. Theseequivalencies must be used to translate vehicles/hour to passenger cars/hour,vehicles/mile to passenger cars/mile and so on. This is essential because most empirical

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values and relationships in the Highway Capacity Manual refer to passenger cars only(e.g., Table 4.1).

There is a more exact method for calculating fhv as a function of the characteristics of theheavy vehicle and the grade, using the following formula:

fP E P E P Ehv

T T B B R R

=+ − + − + −

11 1 1 1( ) ( ) ( )

(4.4)

Where,Pi = Percentage of trucks, buses and RV's in the traffic streamEi = Heavy vehicle equivalencies obtained from tables as functions of the horse-power ofa truck and its gross vehicle weight. Three truck categories are defined, namely 100, 200and 300 lb./HP. The Et table for the typical (i.e., 200 lb./HP) truck is given next:

Table 4.6:Et for Typical (i.e., 200 lb./HP) Truck

as a Function Truck Percentage and Length of Uphill Grade,(Highway Capacity Manual, 1985).

Passenger-Car Equivalent, ETGrade Length(%) (rni) 4-Lane freeways 6 to 8-LanefreewaysPercent trucks: 2 4 5 6 8 10 15 20 2 4 5 6 8 10 15 20

<1 All 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 20 to 0.5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 20.5-1.0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3>1.0 4 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3

2 0-.25 4 4 4 3 3 3 3 3 4 4 4 3 3 3 3 30.25-0.5 5 4 4 3 3 3 3 3 5 4 4 3 3 3 3 30.5-0.75 6 5 5 4 4 4 4 4 6 5 5 4 4 4 4 40.75-1.0 7 6 6 5 4 4 4 4 7 5 5 5 4 4 4 4>1 8 6 6 6 5 5 4 4 8 6 6 5 4 4 4 4

3 0-.25 6 5 5 5 4 4 4 3 6 5 5 5 4 4 4 30.25-0.5 8 6 6 6 5 5 5 4 7 6 6 6 5 5 5 40.5-1.0 9 7 7 6 5 5 5 5 9 7 7 6 5 5 5 51.0-1.5 9 7 7 7 6 6 5 5 9 7 7 6 5 5 5 5>1.5 10 7 7 7 6 6 5 5 10 7 7 6 5 5 5 5

4 0.-.25 7 6 6 5 4 4 4 4 7 6 6 5 4 4 4 40.25-0.5 10 7 7 6 5 5 5 5 9 7 7 6 5 5 5 50.5-1.0 12 8 8 7 6 6 6 6 10 8 7 6 5 5 5 5>1 13 9 9 9 8 8 7 7 11 9 9 8 7 6 6 6

5 same 8 6 6 6 5 5 5 5 8 6 6 6 5 5 5 510 8 8 7 6 6 6 6 8 7 7 6 5 5 5 512 11 11 10 8 8 8 8 12 10 9 8 7 7 7 714 11 11 10 8 8 8 8 12 10 9 8 7 7 7 7

6 0-.25 9 7 7 7 6 6 6 6 9 7 7 6 5 5 5 50.25-0.5 13 9 9 8 7 7 7 7 1 1 8 8 7 6 6 6 60.5-0.75 13 9 9 8 7 7 7 7 1 1 9 9 8 7 6 6 6>0.75 17 12 12 11 9 9 9 9 13 10 10 9 8 8 8 8

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'If a length of grade falls on a boundary condition, the equivalent for the longer grade category is used. For any grade steeper than thepercentage shown, use the next-higher grade category

Table 4.7:SF per Lane for Use in Planning Analysis, (Highway Capacity Manual, 1985).

Percent trucks a Type of Level of terrain service 0 5 10 15 20

. _

Level A 700 650 650 600 600 B 1100 1050 1000 950 950 C 1550 1500 1450 1350 1300 D 1850 1800 1700 1600 1550 E 2000 1900 1850 1750 1700

Rolling A 700 600 550 500 450 B 1100 950 850 750 700 C 1550 1350 1200 1050 1000 D 1850 1600 1400 1300 1150 E 2000 1750 1550 1400 1250

Mountainous A 700 500 400 350 250 B 1100 800 650 SS0 400 C 1550 1150 900 750 550 D 1850 1350 1100 900 650 E 2000 1500 1200 1000 700

Base assumptions: 70-mph design speed; all heavy vehicles are trucks; lane vndthsare 12 ft; lateral clearances > 6 ft.a AII values rounded to the nearest 50 veh/hr/ln.Source: TRB, 1985.

Three types of capacity analysis can be conducted:

• Operational: Given known or projected geometric and traffic conditions to estimateLOS, speed and density. Useful in estimating impacts of alternative designs.

• Design: Given a forecast volume with known design standards and a desired LOS,determine the number of lanes.

• Planning: Given a forecast demand volume, determine the number of lanes. This isa preliminary estimate based on assumed conditions.

Examples for each are given next.

Example Problem of Operational Analysis:

Older 4-lane freeway facility60 mph design speedDirectional peak hourly volume of 2,100 vph (6% trucks)PHF = 0.9511-foot lanes with obstructions on both sidesRolling terrain.Determine the LOS.

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Calculate V C/ = Directional Peak Hourly Vol/ PHFSFat LOS E

With SF MSF f f fw hv pat LOS E = ⋅ ⋅ ⋅ per lane. Calculate all adjustment factors:

fhv = + − =1 1 0 06 4 1 0 85/ . ( ) .

fw = 0 79. (Table 4.4) for 11' lane and 0 clearance from traveled pavement

fp =1 Don't specify otherwise

Hence:

SF vph laneat LOS E = ⋅ ⋅ ⋅ =2 000 0 85 0 79 1 1 343, . . , /

2 lanes/direction. Therefore, SF vphat LOS E = 2 686,

Directional peak hourly vol PHF vph/ = , / . =2 100 0 95 2 210,

V C LOS V C/ = 2,210 / 2,686 = 0.823 D ( / between 0.69 0.84)→ →

Example Problem of Design Analysis:

Level terrainUrban areaDDHV (Directional Design Hour Volume) = 4,050 veh/hr10 % trucksPHF = 0.95Driver Population = daily commutersDetermine the number of lanes to operate at LOS C for a 70 mph facility.

Peak flow rate = 4 0500 95

4 263,.

, /= veh hr

Max V/C for LOS C to be 0.77 for a 70 mph design speed (0.77 upper end of LOS C).

Assume 12' lanes with no lateral obstructions.

SF = 4,263 veh/hrCj = 2,000V/C = 0.77fw = 1.00f p = 1.00

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f HV = + − =1 1 0 10 1 7 1 0 93/ . ( . ) . (Table 4.6)

N = 4,263/(2000 x 0.77 x 1.00 x 0.93 x 1.00) = 2.98 ≅ 3 lanes

Example Problem of Planning Analysis:

Freeway planned for bypass of an urban areaAADT = 70,000 veh/day (2 directions)15% trucksPHF = 0.90Rolling TerrainDetermine the number of lanes at LOS C

DDHV = AADT x k x D

Assume k = 0.09 % AADT occurring in peak hourD = 0.55 % of peak hour traffic in direction of heaviest traffic

DDHV = 70,000 x 0.09 x 0.55 = 3,465 veh/hr

N DDHVSF PHF

=⋅

From Table 4.7, where 15% trucks and LOS = C and rolling terrain, SF = 1,050

N =⋅

= →3 4651 050 0 90

3 67,, .

. 4 lanes

Fortunately, there is no need to conduct short-hand all these tedious calculations, becausecomputer software have been developed which can do so very effectively. They can befound in the LAN server under D:\HCM\. Typical printouts for the three examplespresented above are given next:

Example of software output for operational analysis:

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Example of software output for design analysis:

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Example of software output for planning analysis: