Referring to question 1 above, which option below best describes the maximum queue length (rounded up to the nearest one)?

A new computer system is put in place at a toll booth. The system comes online at 8.00 am (with no vehicle in the queue) and vehicles arrive at a rate of λ(t)=15-0.5t (with λ(t) in veh/min and t in min). Due to a computer systems failure, cars are not serviced until 8:15 am. Between 8:15 and 8:30 they are serviced at 5 vehicles per minute. After 8:30 am they are serviced at 10 vehicles per minute. Assuming D/D/1 queueing model. 

Which option below best describes the time it takes for the queue to disappear (rounded up to the nearest one)?

Regarding speed, flow, and density relationships, which statement below is TRUE?

The fundamental diagram for a road section can be modelled using a triangular flow-density relationship, having a capacity (maximum flow) of 2000 vehicles per hour (veh/h), a free-flow speed of 80 kilometres per hour (km/h), and a jam density of 125 vehicles per kilometre (veh/km). 

In the peak hour, the congested traffic condition is observed with a speed of 43km/h. Which option below best describes the density during this peak hour?

A section of an arterial road has been found to have a speed-density relationship that was modelled using the following form:

where v is the space-mean speed in kilometres per hour (km/h), and k is the density in vehicles per kilometres (veh/km).

The relationship was found to have the best fit to the data by using the following coefficients:

a = 3.5

k_m = 138 veh/km

Which option below best presents the critical density (ie the density at which the capacity is obtained) of the above arterial road?

A linear regression fit to real traffic data speed (v) and density (k) data has the following relationship: v= 110 –0.5*k, where v is measured in kilometres per hour (km/h) and k is measured in vehicles per kilometre (veh/km). Which option below best describes the maximum flow of this fundamental diagram, measured in vehicles per hour (veh/h)?

Regarding speed, flow, density relationships, which statement below is TRUE?