Task $1$: Calculation of Traffic Flow Parameters

For a road section between chainages $200$m and $600$m$,$ the following space$-$time diagram $($see Figure $1)$ is produced for a time period between $20$ seconds and $80$ seconds.

Figure $1$: Space$-$Time diagramUsing the space$-$time diagram, perform the following sub$-$tasks:

i$.$ Compute and compare the hourly traffic volumes at chainages $300m$ and $500m.$

Comment on your results.

ii$.$ Compute the average headway of vehicles at chainage $300m$ using two methods: $($a$)$ use

of the space$-$time diagram $($i$.$e$.,$ calculate the headway from the diagram$),$ and $($b$)$ use of

the mathematical expressions of Traffic flow theory $($i$.$e$.,$ calculate the headway by

computing another parameter from the diagram, such as flow, density, spacing etc.$).$

Compare and comment on the two headway values $($i$.$e$.,$ why they are equal or different$).$

iii. If the average length of vehicles observed at this section is $5\mathrm{.}3m,$ compute the average

gap between all vehicles observed at the $40$ second mark. Briefly discuss if you can

compute any other traffic flow parameters using the computed value of average gap.

iv$.$ At the $40$ seconds mark, compute the average speed and average density of all vehicles

observed at the road section.

v$.$ Assuming that the capacity of the road section is $2700ve\frac{h}{h}r$ and that the first vehicle

in the traffic stream is travelling at free flow speed, determine the jam density of the

road section. State any assumptions you may make to compute the jam density value.