1. Vehicles begin to arrive at a parking lot at 6:00 A.M. at a rate of eight per minute. Due to an accident on the access highway, no vehicles arrive from 6:20 to 6:30 A.M. From 6:30 A.M. on, vehicles arrive at a rate of two per minute. The parking-lot attendant processes incoming vehicles (collects parking fees) at a rate of four per minute throughout the day. Assuming D/D/1 queuing, determine total vehicle delay.
2. Vehicles begin to arrive at a toll booth at eight vehicles per minute from 9 A.M. to 10 A.M. The booth opens at 9:10 A.M. and services at a rate of 10 vehicles per minute until 9:40 A.M. From 9:40 A.M. until 10 A.M. the service rate is six vehicles per minute. Assuming D/D/1 queuing, what is the total vehicle delay from 9 A.M. to 10 A.M. assuming D/D/1 queuing?
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3. The arrival rate at a parking lot is 6 veh/min. Vehicles start arriving at 6:00 P.M., and when the queue reaches 36 vehicles, service begins. If company policy is that total vehicle delay should be equal to 500 veh-min, what is the departure rate? (Assume D/D/1 queuing and a constant service rate.)
4. At 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of λ(t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of μ(t) = 2.1 + 0.3t [λ(t) and μ(t) are in vehicles per minute and t is in minutes after 8:00 A.M.]. Assuming D/D/1 queuing, what is the maximum queue length, and what would the total delay be from 8:00 A.M. until the queue clears?