(a) A section of road has a free flow speed of 55km/h and a jam density of 367 vehicles per kilometre. Assuming under a linear speed-density relationship, calculate the density at maximum flow, the maximum flow rate and the speed at maximum flow.
(b) A roadway has an average hourly traffic volume of 360 veh/h. Assuming that the arrival of vehicles is Poisson distributed, estimate the probabilities of having 0, 1, 2, 3, 4 and 5 or more vehicles arriving over a 20 second time interval. Determine the probability that the gap between successive vehicles will be less than 8 seconds.
(c) Consider the following traffic situation for an intersection. Minor road vehicles at a STOP sign need a 6 seconds gap from the major road traffic to cross the road. If the major road traffic volume is 450 veh/h, estimate the percentage of vehicles from the minor road that could make a successful crossing without being delayed. If the minor road vehicles have a follow-up time of 2 seconds, determine the maximum number of minor road vehicles that could cross the major road during one hour.