3. Vehicles begin to arrive to a parking lot at 7:00 AM at a rate of...

3. Vehicles begin to arrive to a parking lot at 7:00 AM at a rate of 2000 veh/hour, but the

demand reduces to 1000 veh/hour at 7:30 AM and continues at that rate. The ticketing booth

to enter the parking lot can only serve the vehicles at 1000 veh/hour until 7:15 AM, after

which the service rate increases to 2000 veh/hour. Assuming D/D/1 queuing, draw a

queuing diagram for this situation. Find: a) the time at which the queue clears, b) the total

delay, c) the longest queue length, and d) wait time of the 500th and 2000th vehicles to arrive

to the parking lot (assuming FIFO conditions)?

Solutions

Expert Solution

D/D/1 queu analysis is done for linear arrival and service rate . To analyse this problem we have taken 15 minute interval to tabulate arrival and service and cummulative queu . The plot shows two diffrent arrival rates as well as the two different service rates. One these two curves intersect each other the queu at that instant of time becomes 0. See the solution. Hope it will help you. Although if there will be any doubt than ask in comment section. Thank you.

Ally Wells answered 1 month ago

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