An amusement park has 5 major attractions: The Cork Screw, The Caramel Carousel, The Cranium, The...

Question

An amusement park has 5 major attractions: The Cork Screw, The Caramel Carousel, The Cranium, The Wave Swinger, and the Sky Flyer.

David · Accepted Answer

Problem 4
An amusement park has 5 major attractions: The Cork Screw, The Caramel Carousel, The Cranium, The 
Wave Swinger, and the Sky Flyer. List below are the probabilities at which a person moves between 
rides. For example, if a person is currently riding the Cork Screw they will ride the Cranium next with .19 
probability.
1. The amusement park is expecting on average 2,000 customers per day. Assuming each customer rides 
10 rides in a given day, what is the volume for each of the rides (how many people will ride each ride?) 
Ans:
Total no. of rides will be 2000*10=20000 
Since, this is quite high, we can assume a steady state distribution and then we can get the volume for 
each of the rides by multiplying 20000 with the corresponding probability. 
To find a steady state distribution for a Markov System with transition matrix P, we solve the system of 
equations given by
∑
(          )  (          ) 
 
We can also compute higher powers of   until the rows become identical; which would be our desired 
vector. Using matrix power we compute P^16 (this can be very easily computed, given the fact that 16 is 
a power of two) and get that all the rows are equal to  
(0.225148,

An amusement park has 5 major attractions: The Cork Screw, The Caramel Carousel, The Cranium, The Wave Swinger, and the Sky Flyer.

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