A vehicle pulls out onto a single-lane highway that has a flow rate of 420 veh/hr (Poisson distributed). The driver of the vehicle does not look for oncoming traffic. Road conditions and vehicle speeds on the highway are such that it takes 1.7 seconds for an oncoming vehicle to stop once the brakes are applied. 

Which option below best represents the driver reaction times of oncoming vehicles so that the probability of an accident is 0.25? Assuming a negative exponential function of the headway.

It is predicted that the probability that the tunnel will experience at least 1 accident next week is 70%. Which options below best describes the average weekly accident rate of this tunnel (assuming a Poisson distribution)? 

Vehicles at a stop sign require 7 second headway to cross the main street that is located 300 meters downstream from a signalised intersection. 

If the average flow rate of the main street is 900 vehicle per hour, the minimum headway is 2 seconds and vehicle bunching with 60% free vehicles.

Which option below best describes the probability that vehicles at the stop sign can cross the main street safely?

At a specified point on a bicycle path, bicycles are assumed to arrive according to a Poisson probability distribution. Bicycles are counted in 15 second intervals for a period of 30 minutes. It is noted that no bicycles arrived in 15 of those 120 intervals.

Which options below best describes the number of these 120 intervals having exactly two bicycles arriving?

It is desirable to have the probability that a minor-stream vehicle at the stop sign can across the major road through the next gap in the mainstream is 50%. If the major stream volume is 450 vehicles per hour, which option below represents most accurately the time needed for the minor-stream vehicle to cross the main road safely? Assuming a negative exponential function of the headway.

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)?

Referring to the question 1 above, which option below best describes the total delay in vehicle-minutes (rounded up to the nearest one)?

Referring to question 1 above, which option below best describes the maximum queue length (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?