Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

8.4 Flow of Traffic 213

In Equation (8.4),qrepresents the traffic flow in terms of number of vehicles per hour,nis the

number of vehicles passing a known location during a time durationTin seconds. Another

useful variable of traffic information is density — how many cars occupy a stretch of a highway.

Density is defined by

(8.5)

wherekis density and represents the number of vehicles per kilometer, andnis the number

of vehicles on a stretch of highway,d, measured in meters.

Knowing the average speed of cars also provides valuable information for the design

of road layouts and the location and timing of traffic control devices. The average speed

of cars is determined from

(8.6)

In Equation (8.6),uiis the speed of individual cars (we will discuss the definition of speed in

more detail in Section 8.5.), andnrepresents the total number of cars. There is a relationship

among the traffic parameters — namely, the flow of traffic, density, and the average speed —

according to

(8.7)

whereq,k, and were defined earlier by Equations (8.4) through (8.6).

The relationship among flow, density, and average speed is shown in Figures 8.6 and

8.7. Figure 8.6 shows that when the average speed of moving cars is high, the value of den-

sity is near zero, implying that there are not that many cars on that stretch of highway. As you

may expect, as the value of density increases (the number of vehicles per kilometer), the aver-

age speed of vehicles decreases and will eventually reach a zero value, meaning bumper-to-

bumper traffic. Figure 8.7 shows the relationship between the average speed of vehicles and

the flow of traffic. For bumper-to-bumper traffic, with no cars moving, the flow of traffic

stops, and thusqhas a value of zero. This is the beginning of the congested region shown in

u

qku

u

1

n

(^) a
n
i 1
ui
1 u 2
k
1000 n
d
Average speed (
u
)
Density (k)
Average speed (
u
)
Flow (q)
Uncongested flow
Congested flow
■Figure 8.6 The relationship between speed and density. ■Figure 8.7 The relationship between speed and flow.
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀