Highway Engineering

If it is assumed that the intersection is at a saturated level of flow, the queue
length will vary gradually over any given interval of time. The average queue
length can thus be estimated as the product of the actual flow,q, and the average
vehicle delay,d.To this value, an estimate accounting for cyclical fluctuations
caused by short-term variations in flow during the red and green periods must
be added. These can range from zero to qr, therefore an average value ofqr/2
is taken.
Combining these two terms, an expression for the saturated case is:

(5.39)

where

Ns=queue length at the commencement of the green period (assuming the
approach is saturated)
d =average delay per vehicle on the approach (see previous section).

At a minimum, in this case,dwill equal r/2, therefore the equation for the sat-
urated case reduces to that for the unsaturated case, i.e.Ns =qr. Since this is the
minimum value ofNs, Equation 5.39 can be adjusted as:

Ns=qd +1/2 qror qr,whichever is greater.

Nqd qrs=+ 12

The Design of Highway Intersections 145

Example 5.8 – Calculation of average queue length at the approach to a

signalised junction

Taking the figures from the previous example, calculate the average queue

length at the approach.

Solution

c=100 s

q=0.278 veh/s

r=35 s

d=22 s

Therefore, taking the saturated case:

Nqd qrqrs or

or 0.278

say 11 or 9.73 say 10

vehicles

=+

=¥()+¥()()¥

= () ( )

=

12

0 278 22 1 2 0 278 35 35

10 98

11

..

.