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Lecture15_2up

# Lecture15_2up - ECE-547 Introduction to Computer...

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1 Purdue University ECE ECE -547 547 Introduction to Computer Introduction to Computer Communication Networks Communication Networks Instructor: Instructor: Xiaojun Xiaojun Lin Lin Lecture 15 Lecture 15 Purdue University Example Example Example: Calculate γ ( throughput ), E[N], and E[T] in an M/M/1 and M/M/1/N queueing systems. ¾ Solution: ρ μ λ = = = = = = < = = = = 1 1 ) ( ) ( , 1 ) 1 ( ) 1 ( ) ( 1 ), 1 ( 1 1 1 1 N E T E Now n n nP N E P n n n n n n n n

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2 Purdue University Example Example ¾ Example (cont): ¾ γ↑ means E[T] (bad). Want to operate below the “knee” of the curve. 0.2 0.4 0.6 1.0 delay normalized t E T E ] [ 1 ] [ μ = ρ 1 1 delay Purdue University Example Example ¾ Finite Buffer (M/M/1/N) P L ρ→ 1 ), 1 ( 1 ) 1 ( 1 << = + N N N N L for P 1 1 1 1 + N
3 Purdue University Example Example ¾ Also, λ Maximize γ such that P L < ε 1 , E[T]< ε 2 1 1 + = N N μ γ Purdue University Two servers versus one server? Two servers versus one server? ± Example: Compare the M/M/1 with service rate 2 μ and an M/M/2 system with each servers having rate μ .

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Lecture15_2up - ECE-547 Introduction to Computer...

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