# HW9 - IE 336 Apr 4 2011 Handout#10 Due Apr 15 2011 Homework...

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

IE 336 Handout #10 Apr. 4, 2011 Due Apr. 15, 2011 Homework Set #9 1. Let p 12 ( t ) = 7 11 (1 - e - 11 t ) be the transition probability function from state 1 to state 2 in a continuous Markov random process. (Time t is measured in minutes.) (a) Find the steady-state probabilities. (b) Determine the transition diagram and the transition rate matrix. (c) At some point the process is in state 1. How likely is that 5 minutes later the process is still in state 1. (d) If the process spent last 15 minutes in state 2 how likely is that within the following 7 minutes a transition to state 1 will occur? 2. Let Λ = r + 2 0 0 3 q 0 0 - 7 - r 3 p 0 0 q 0 0 2 2 2 p - 8 t 2 t 2 1 2 s be the transition rate matrix of a continuous time Markov process. (a) Compute p , q , r , s , and t . Determine the transition diagram. (b) If the process is initially in state 5 determine the expected length of time before it reaches either state 1 or state 3.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/19/2012 for the course IE 230 taught by Professor Xangi during the Spring '08 term at Purdue.

### Page1 / 2

HW9 - IE 336 Apr 4 2011 Handout#10 Due Apr 15 2011 Homework...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online