Lec 5: Capacity and LOS(Ch. 2, p.74-88)

Understand capacity is the heart of transportation issues.

Understand the fundamental flow of diagram Understand how a shock wave is caused Understand capacity analysis was set up for ideal

cases and modifications are made to reflect prevailing conditions

Understand many factors, geometric, traffic, and control characteristics affect the capacity of a facility

Understand capacity and level of service correspond each other directly only for uninterrupted flow

Issues of traffic capacity analysis

How much traffic a given facility can accommodate?

Under what operating conditions can it accommodate that much traffic?

Highway Capacity Manual (HCM)

1950 HCM by the Bureau of Public Roads

1965 HCM by the TRB

1985 HCM by the TRB (Highway Capacity Software published)

1994 updates to 1985 HCM

1997 updates to 1994 HCM

2000 HCM is available

Highway capacity software

Flow-density relationshipsFlow = (density) x (Space mean speed)

sukq Space mean speed = (flow) x (Average space headway)

kd /1dqus where

Average space headway = SMS/(Average time headway)

hud s where qh /3600

Speed, Density, and Flow Rate

A few examples…

Fundamental diagram of traffic flow (flow vs. density)

Flo

w (

q)

Density (k)

Optimal flow or capacity,qmax

Optimal density, ko

Jam density, kj

Mean free speed, uf

Optimal speed, uo

Speed is the slope. u = q/k

Uncongested flow Congested

flow

Fundamental diagram of traffic flow (SMS vs. density & SMS vs. flow)

kj0

uf

Density

SM

S

SMS vs. density

qmax0

uf

Flow

SM

S

SMS vs. flow

Uncongested flow

Congested flow

Fundamental diagram of traffic flow and shock wave

Flo

w (

q)

Density (k) kj

For bottleneck

For upstream

q2

q1

Queue forms upstream of the bottleneck. So we use the diagram of the upstream section

k1k2

Slope gives velocity uw of shock wave for q1

12

12

kk

qquw

Work zone

Capacity concept

Capacity as defined by HCM:

“the maximum hourly rate at which persons or vehicles can be reasonably expected to traverse a point or uniform segment of a lane or roadway during a given time period under prevailing conditions.”

Traffic

Roadway

Control

With different prevailing conditions, different capacity results.

HCM analyses are usually for the peak (worst) 15-min period.

Some regularity expected (capacity is not a fixed value)

Sometimes using persons makes more sense, like transit

Capacity values for ideal conditions

Most capacity analysis models include the determination of capacity under ideal roadway, traffic, and control conditions, that is, after having taken into account adjustments for prevailing conditions.

Freeway, uninterrupted flow

12-ft lane width, 6-ft lateral clearance (right side, 2 ft on left side), all vehicles are passenger cars, familiar drivers, level grade, no heavy vehicles, free-flow speeds (70 mph for urban, 75 mph for rural; if you have a speed limit, it’s a different matter. Capacity used is usually average per lane (e.g. 2400 pcphpl in one direction)

Prevailing condition types

Geometric conditions

Horizontal & vertical alignment, lane width and lateral clearance, grades

Traffic conditions

Directional distribution, lane distribution, heavy vehicles in the traffic stream, turning movements

Control factors

Speed limits, lane use controls, traffic signals, STOP and YIELD signs

Factors affecting: examples

Drivers shy away from concrete barriers

Trucks occupy more space: length and gap

From ideal conditions to real, prevailing conditionsWe use adjustment factors to take into account the effect of prevailing conditions on capacity and level of service. Typically it is like…

IDNLCLWi ffffFFSFFS

)/( pHVp ffNPHFvv

Free-flow speed:

Passenger car equivalent flow rate:

Application of the capacity conceptPrecision Low Used in transportation planning studies

to assess the adequacy or sufficiency of existing highway networks (Traffic volumes are estimates; define targeted LOS first then find the number of lanes)

Medium Used as a design control in the selection of highway type and in determining dimensional needs (Traffic volumes are estimates; define targeted LOS first then find the number of lanes)

High Used in traffic operational analyses: a) Analysis of existing conditions, b) Estimation of operational improvements (For this analysis volume, geometry and control data exist)

Level of service“A level of service is a letter designation that describes a range of operating conditions on a particular type of facility.”

LOS A (best) LOS F (worst or system breakdown)

A Free flow

B Reasonably free flow

C Stable flow

D Approaching unstable flow

E Unstable flow

F Forced flow

MOE in 2000 HCMUninterrupted Fwy: Basic sections Density (pc/mi/ln)

Fwy: Weaving areas Density (pc/mi/ln)

Fwy: Ramp junctions Density (pc/mi/ln)

Multilane highways Density (pc/mi/ln)

Two-lane highways Percent-time spent following

Average upgrade speed

Interrupted Signalized intersections

Approach delay (sec/veh)

Unsignalized intersections

Average total delay (sec/veh)

Arterials Average travel speed

Transit Load factor (pers/seat)

Pedestrians Space (sq ft/ped)

LOS example: freeway basic sectionsBasic freeway segments: Segments of the freeway that are outside of the influence area of ramps or weaving areas.

See Exhibit 23-3.

LOS – density – flow rate - speed

Level of Service: general descriptions

LOS for basic freeway segments

A

B

C

D

LOS for basic freeway segments (cont.)

EF

LOS examples near SLC

LOS C or D

LOS B

LOS A

LOS E or F

Level of service

Density range (pc/mi/ln)

A 0 - 10.0

B 10.1 - 16.0

C 16.1 – 24.0

D 24.1 – 32.0

E 32.1 – 45.0

F > 45.0

Objective of highway design

Create a highway of appropriate type with dimensional values and alignment characteristics such that the resulting design service flow rate is at least as great as the traffic flow rate during the peak 15-min period of the design hour, but not greater enough as to represent extravagance or waste

Why the peak 15-min period? Traffic flow fluctuates, but it is known from previous studies that it is stable for about 15 minutes.

Service flow rates vs. service volumes

What is used for analysis is service flow rate. The actual number of vehicles that can be served during one peak hour is service volume. This reflects the peaking characteristic of traffic flow.

SVi = SFi * PHF

Stable flow

Unstable flow

Density

Flo

w

SFA

SFE

AB

C

D

E F

Design service flow rate vs. design volume

Design volume (DHV, vph)

Hourly volume of traffic estimated to use a certain type of facility during the design year (peak period)

Design service flow rate (vph)

Maximum hour flow rate of traffic that a new facility can serve without the degree of congestion falling below a pre-selected level

)/( pHVp ffNPHFvv

Acceptable degree of congestion

Rural freeway Motorists expect high speed smooth traffic always

Urban arterial Motorists accept few delays because they know there are physical limits for improvements (and budgets)

Balance need (demand) and resources available (supply) to determine the degree of congestion for design.

Targeted LOS