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Lecture12

# Lecture12 - ECE-547 Introduction to Computer Communication...

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Purdue University ECE ECE - - 547 547 Introduction to Computer Introduction to Computer Communication Networks Communication Networks Instructor: Instructor: Xiaojun Xiaojun Lin Lin Lecture 12 Lecture 12

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Purdue University State transition diagram State transition diagram ¾ State i: Represents i packets in the queueing system ¾ Arc from i to j : Rate at which transitions occur from i to j, conditioned on the current state being i ¾ We can determine P n in two ways: 0 1 2 n n+1 λλ λ λ λ μμ μ μ μ
Purdue University Global Balance Equations Global Balance Equations 1. Balancing the rates in and out (Global Balance Equations): λ P 0 = μ P 1 P 1 ( λ + μ ) = P 0 λ +P 2 μ P 1 λ = P 2 μ + (P 0 λ -P 1 μ ) Similarly: P n λ = P n+1 μ + (P n-1 λ n μ ) P n = P 0( ( λ / μ ) n P n = ρ n (1- ρ ), ρ <1 0 0

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Purdue University Local Balance Equations Local Balance Equations 2. Flux in = Flux out Draw a line that cuts the STD into half The rate from left to right must be equal to the rate from right to left P 0 λ =P 1 μ P n λ n+1 μ P n = ρ n (1- ρ ), ρ <1 ¾ Homework: Solve for the M/M/1/N queueing system from first principles.
Purdue University M/M/1/N M/M/1/N

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Lecture12 - ECE-547 Introduction to Computer Communication...

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