Lecture23_2up

# Lecture23_2up - ECE-547 Introduction to Computer...

This preview shows pages 1–4. Sign up to view the full content.

1 Purdue University ECE ECE -547 547 Introduction to Computer Introduction to Computer Communication Networks Communication Networks Instructor: Instructor: Xiaojun Xiaojun Lin Lin Lecture Lecture 23 23 Purdue University Jackson Jackson ’s Theorem s Theorem 1 (1) m is i k i k k qq λλ λ = =+ ¾ Outline of proof: W.L.O.G., we assume one source and one destination. Hence:

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

View Full Document
2 Purdue University Jackson Jackson ’s Theorem s Theorem ¾ Example: . . . s s si q λ i 1 1( 2 ) m id ij j qq = + = −−− ¾ Similarly: ¾ Define: 1 12 1 1 ( ) { ,. .., } ( 1 ) { , ,..., , 1, ,..., } ( 1 1 ) { , ,. .., 1,. 1,. .. } m ii i i m ij i j m Pn n Pn n n n n n n n n −+ = −= −+ = + Purdue University Jackson Jackson ’s Theorem (Balance Equations) s Theorem (Balance Equations) ¾ State of the CTMC: (, , . . . , ) M nn n n = i i,j n 1 ,n 2 ,…,n m Two dimension One dimension m dimension: very cumbersome! } Rate arriving at n 11 1 Global balance equations: Rate leaving state n = Rate arriving into state n (n) ( 1 ) (1 ) is i i m id i i i pq p n qp n λμ μ == = ⎛⎞ + = ⎜⎟ ⎝⎠ + + ∑∑ (11 ) mm ji j i j ji n + + Rate leaving n (a) (b) (c) (3) when n i >= 1 for all i.
3 Purdue University

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 01/06/2010 for the course ECE 547 taught by Professor Xiaojunlin during the Spring '09 term at Purdue.

### Page1 / 8

Lecture23_2up - ECE-547 Introduction to Computer...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online