The roller coaster at Treasure Island Amusement Park consists of 15 cars, each o

Question

The roller coaster at Treasure Island Amusement Park consists of 15 cars, each of which can carry three passengers. Each run takes 1.5 minutes and the time to load and unload passengers takes 3.5 minutes.

(a) What is the maximum capacity of the system in number of passengers per hour?

(b) The system manager would like to determine how much time people are spending waiting for a ride. There are 150 people waiting in the queue on average. If the arrival rate to the roller coaster is 400/hr, what is the average time a person spends in the queue?

(c) What is the expected number of customers waiting for or riding the roller coaster?

Explanation / Answer

(a) Maximum capacity of the system = Number of cars * Capacity of each car * 60 minutes per hour / (run time + time to load and unload)

= 15*3*60/(1.5+3.5)

= 540 passengers per hour

(b) Given that average length of waiting line, Lq = 150

Arrival rate, = 400/hr

Using Little's law, Lq = Wq.

So, Average time a person spends in queue, Wq = Lq/

= 150/400

= 0.375 hours or 22.5 minutes (=0.375*60)

(c) It is given that at any point, there are 150 people waiting in the queue on average. In addition to that, there are 45 people (=15 cars * 3 passengers per car) riding the roller coaster.

So, expected number of customers waiting for or riding the roller coaster = 150+45 = 195

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