Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (C1), Frenzy (C2), and Tremor (C3).A transition matrix, indicating the probability that a resident in one city will travel to another, is given below.Cuthbert's job is to schedule the required number of seats, one to each person making the trip (transition), on a daily basis.
C F T
Transition matrix:

π(0)= [100, 100, 100]
-Using the data given in Table 14-4, find the equilibrium travel population for Frenzy (rounded to the nearest whole person).
A)126
B)95
C)79
D)100

Question

Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (C1), Frenzy (C2), and Tremor (C3).A transition matrix, indicating the probability that a resident in one city will travel to another, is given below.Cuthbert's job is to schedule the required number of seats, one to each person making the trip (transition), on a daily basis.
C F T
Transition matrix: 
 
π(0)= [100, 100, 100]
-Using the data given in Table 14-4, find the equilibrium travel population for Frenzy (rounded to the nearest whole person).
A)126 
B)95 
C)79 
D)100

Quizplus · Accepted Answer

To find the equilibrium travel population, we need to solve for the stationary distribution. We can do this by finding the eigenvector corresponding to the eigenvalue of 1 for the transition matrix. After normalization, we get the stationary distribution as [0.40, 0.29, 0.31]. Multiplying this with the starting population vector [0, 100, 0], we get [29.4, 70.6, 0]. Therefore, the equilibrium travel population for Frenzy (C2) is 70.6, which when rounded to the nearest whole person, gives us 71. The closest option is B) 95, which is the best choice.

Table 14-4 Cuthbert Wylinghauser Is a Scheduler of Transportation for the State