At one of the entrances to the car parking area at the proposed new Mill project at Albion, a single line of vehicles approach a manually operated entry gate, where payment will be required to gain entry. The process of stopping at the payment point, offering payment, receiving change if necessary and departing the payment point is estimated to average 15 seconds per vehicle. Vehicles are expected to arrive randomly at an average rate of 174 vehicles per hour. Appropriate design of the entry arrangements requires knowledge of the queue storage,vehicles waiting and delay.
1) what is the proportion of vehicles that will have to wait in a queue before entering the payment point?
2)What is the average total delay,including time spent in the payment process, to vehicles entering the parking area at this gate?
3) what is the probability of there being more than 4 vehicles in the system?