As the summer heats up, everyone loves going to the California Dreamin\' Water P
ID: 390869 • Letter: A
Question
As the summer heats up, everyone loves going to the California Dreamin' Water Park primarily because of their most popular ride, a series of water slides called Grizzly Mountain. When the park opens each day at 10 am, guests enter the park and rush over to Grizzly Mountain at a constant rate of 11 per minute until 4 p.m. From 4 pm. until the park closes at 10 p.m. guests arrive at Grizzly Mountain at a constant rate of 5 per minute. The line gets long quickly at Grizzly Mountain so the park built a canopy over the line area that accommodates up to 440 guests waiting in line. Once the line exceeds 440 people, the remaining guests are left to wait in the sun and jump around on the hot sidewalk. The ride operators at Grizzly Mountain send guests down the slides at a constant rate of 460 per hour. Grizzly Mountain begins each day with completely empty lines. What is the maximum number of guests jumping around on the hot sidewalk outside of the Grizzly Mountain canopy on any given day at Califomia Dreamin' Water Park?Explanation / Answer
This is a D/D/1 queueing model.
The arrival rate (lambda) is 11*60 = 660 guests per hour
The service rate (mu) is 460 guests per hour
Since lambda > mu, there will be formation of infinite queue till 4 PM. The queue will be the longest at 4 PM.
From 10 AM to 4 PM is 6 hours window during which every hour, there has been an addition of 660-460 = 200 guests in the queue.
In 6 hours the length of the total queue will be 6*200 = 1200 guests in the queue. Now 440 guests will be able to stay under the canopy this means the number of guests that will be jumping around on the hot sidewalk is 1200-440 = 760
The maximum number of guest jumping around on hot sidewalk outside of canopy on any given day is 760
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