Four vehicles are traveling on a 4-kilometer circular track. The four vehicles are traveling at constant speeds of 70 km/h, 63 km/hr, 75 km/hr, and 84 km/hr, respectively. Assume you are an observer standing at a point on the track for a period of 30 minutes and are recording the instantaneous speed of each vehicle as it crosses your point.

Which option below represents most accurately the time-mean speed for these vehicles during this observation period?

A single channel queue forms at the entrance to an off-street parking area. Arrivals are random, at an average rate of 12 vehicles per minute, and the time required for the service process of removing the time-card from the control box and driving past the boom gate is also random and averages 4 seconds per vehicle. To avoid spillback of the road, the entrance to the off-street parking area was designed to cater for a maximum of 10 vehicles (i.e. including both waiting and being served ). Which option below best represents the chance of spillback occurring?

Select the correct option in the following statements:

Vehicles at a stop sign require a 4-second headway to cross the main street. The traffic flow on the main street is 480 vehicles per hour. Assuming the headway follows a shifted negative exponential distribution with the minimum headway of 3 seconds. 

Which option below best describes the probability for those vehicles at the stop sign to cross the main street safely?

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)?