Refer to Question 5 above, which option below best describes the time it takes for the queue to clear?

Four vehicles are traveling on a 4-kilometer circular track. The four vehicles are traveling at constant speeds of 75 km/h, 71 km/hr, 66 km/hr, and 77 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 (rounded to the nearest two decimal places)?

A single channel queue forms at the entrance to an off-street parking area. Arrivals are random, at an average rate of 10.7 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 2 seconds per vehicle. 

In order to accommodate the queuing vehicles in 90% of cases, which option below best represents the storage space in front of the boom barrier? Assuming M/M/1 queueing model.

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?

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

Referring to the question 1 above, which option below best describes the total delay in vehicle-minutes?

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 600 vehicle per hour, the minimum headway is 2.5 seconds and vehicle bunching with 67% free vehicles.

What is the probability that a headway will be greater than 7 seconds?

If the weekly accident rate at a critical intersection is 1.6, what is the probability that the intersection will experience at least 2 accidents next week (assuming a Poisson distribution)?

Round your answers to the nearest 2 decimal points in percentage. Note: Only include the numerical value (e.g. If your answer is 51.36%, fill in 51.36 as your answer).

Minor stream vehicles at a stop-sign intersection need a 8-second headway in the major stream to cross the road. 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 72%. What is the volume of the major stream?

Round your answers to the nearest 2 decimal points in veh/h. Note: Only include the numerical value (e.g. 51.36)

Which option below best describes the headways on a single lane

(oneway) road with no overtaking: