{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lect0212 - IEOR 4106 Introduction to Operations Research...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
IEOR 4106: Introduction to Operations Research: Stochastic Models Spring 2009, Professor Whitt Reversibility 1. Four Problems (1) The Knight Errant (The Random Knight) A knight is placed alone on one of the corner squares of a chessboard (having 8 × 8 = 64 squares). What is the expected total number of moves required for the knight to first return to its initial position, if we assume that the knight moves randomly, taking each of its legal moves in each step with equal probability? (2) A Big Closed Maze for Markov Mouse Suppose that the closed maze for Markov mouse is enlarged to be 10 × 20 instead of 3 × 3; i.e., it now has 10 × 20 = 400 rooms instead of 3 × 3 = 9 rooms, but still arranged in a rectangular fashion, with doors connecting neighboring rooms. Now there are 10 rows of rooms, with 20 rooms in each row. There are doors connecting neighboring rooms on each row. And there are doors connecting neighboring rooms on each column. Suppose that, just as before, the mouse moves randomly according to a Markov chain, moving to one of the available neighboring rooms on each move, with each of the available alternatives chosen with equal probability.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern