Lecture11 - 1 ECE & CSE ECE-CSE 861: Introduction to...

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Unformatted text preview: 1 ECE & CSE ECE-CSE 861: Introduction to Computer Communication Networks Ness B. Shroff ECE & CSE Lecture 11 ECE & CSE Birth-death Models iii. M-server example: M/M/m system > = = = m n m m n n n n ; ,... 2 , 1 ; μ μ μ λ λ Poisson( λ ) Exp( μ ) 1 2 m . . ECE & CSE Birth-death process State transition diagram for the m-server example: 1 2 m m+1 λ λ λ λ μ 2 μ 3 μ m μ Better to solve by writing balance equations. Try it for Homework. ECE & CSE Example B-D systems iv. Discouraged Arrivals Packet arrivals depend on the queue length Exponential inter-arrival time Exponential service time Rudimentary Flow Control (arrivals depend on state of the queue) λ n μ = + = μ μ λ λ n n n 1 Birth-Death Parameters 2 ECE & CSE Discouraged Arrivals The corresponding STD: 1 2 n n+1 λ /1 λ /2 λ /3 λ /n μ μ μ μ 1 1 + = + n n P P n μ λ ECE & CSE Discouraged Arrivals Therefore, ∑ ∑ ∞ = − − = ⇒ = = ∴ = − = ⇒...
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This note was uploaded on 03/05/2011 for the course ECE 861 taught by Professor Shroff during the Winter '11 term at Ohio State.

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Lecture11 - 1 ECE & CSE ECE-CSE 861: Introduction to...

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