- Problem 1 At A Parking Lot Vehicles Arrive According To A Poisson Process And Are Processed Parking Fee Collected At 1 (21.67 KiB) Viewed 74 times
- Problem 1 At A Parking Lot Vehicles Arrive According To A Poisson Process And Are Processed Parking Fee Collected At 2 (18.29 KiB) Viewed 74 times
- Problem 1 At A Parking Lot Vehicles Arrive According To A Poisson Process And Are Processed Parking Fee Collected At 3 (63.18 KiB) Viewed 74 times
- Problem 1 At A Parking Lot Vehicles Arrive According To A Poisson Process And Are Processed Parking Fee Collected At 4 (20.81 KiB) Viewed 74 times
Consider the parking lot and conditions described in Problem #2. If the rate at which vehicles are processed became exponentially distributed (instead of deterministic) with a mean processing rate of 5 veh/min, what would be the average length of queue, the average time spent in the system, and the average waiting time in the queue?
Vehicles arrive at a single toll booth beginning at 8:00 A.M. They arrive and depart according to a uniform deterministic distribution. However, the toll booth does not open until 8:10 A.M. The average arrival rate is 8 veh/min and the average departure rate is 10 veh/min. Assuming D/D/1 queuing, when does the initial queue clear and what are the total delay, the average delay per vehicle, longest queue length (in vehicle), and the wait time of the 100th vehicle to arrive (Assuming FIFO)? 100- 90- 80- 70- 60- 50- 40- 30- 20– 10- 0 1 10 1 40 1 50 0 1 60 1 70 1 80 1 90 O 20 1 100 30
Problem #3 Vehicles arrive at a toll bridge at a rate of 420 veh/h (the time between arrivals is exponentially distributed). Two toll booths are open, and each can process arrival (collect tolls) at a mean rate of 12 seconds per vehicles (the processing time is also exponentially distributed). What is total time spent in the system by all vehicles in a 1-hour period?