Modeling & Simulation, SYCS 410 Quiz #2

Professor: Dr. Kathleen M. Kaplan, Dept. of Systems & Computer Science

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This quiz was a "group quiz" where teams worked on a different problem then presented the answers and their methods.

  1. What is the equilibrium (stationary) state probability?
     1/41/41/2
    Q = 01/21/2
     010
    Answer: This is not steady. See that state 1 only goes to itself - no other state goes to state 1! It is reducible.
  2. What is the equilibrium (stationary) state probability?
     01/54/5
    Q = 1/302/3
     1/21/20
    Answer:
    π = [(10/33) (9/33) (14/33)]
  3. What is the equilibrium (stationary) state probability?
     010
    Q = 1/201/2
     1/32/30
    Answer:
    π = [(4/13) (6/13) (3/13)]
  4. What is the equilibrium (stationary) state probability?
     1/201/2
    Q = 04/51/5
     2/31/61/6
    Answer:
    π = [(8/19) (5/19) (6/19)]
  5. What is the equilibrium (stationary) state probability?
     010
    Q = 1/41/41/2
     100
    Answer:
    π = [(1/3) (4/9) (2/9)]