Networking Theory and Fundamentals - Lecture 4 & 5 doc

... lim i i tt Tt pPNti t →∞ →∞ === 4& amp; 5- 1 8 PASTA Theorem: Intuitive Proof  t a and t r : randomly selected arrival and observation times, respectively  The arrival processes prior to t a and t r respectively ... ρρ ρ ρ − − ∞−∞− − ====    =⇒ = + + = +    −    ∑∑∑∑ 4& amp; 5 -4 1 Moment Generating Function 1. De ¯nition: for an y t 2 IR: M X (t)=E[e tX ]= 8...

Ngày tải lên: 22/07/2014, 18:22

... i iij iii ii qnm r n r n rr n n ≠ =γ+µ >+µ > =γ+µ + ⋅ > =γ+µ > ∑∑∑ ∑ ∑∑∑ ∑∑ ** 0 (,) 1{0} 1{0} iii ii ii mn i i i i qnm n r n ≠ =γ+µ >=λ+µ > ∑∑∑ ∑∑ 8-1 5 Kleinrock Independence Assumption 1. ... times and service times  Exponentially distributed service times Network model: Jackson network “Product-Form” stationary distribution 1 TCOM 50 1: Networking Theory &am...

Ngày tải lên: 22/07/2014, 18:22

... MST, and F extended by arc e and node j is a fragment. A E C D F B G 4 4 3 1 6 7 2 3 4 e 'e F 6 Spanning Tree Algorithm 1. Select arbitrary node n∈N, and initialize: G' = (N ', A' ... D E  D E = 4 + D G  D G = 3 + D B = 3  D D = 2 + D G  D C = 1 + D D  D F = 6 + D B = 6  AB = A-E-G-B B A C D E F G 3 4 2 7 3 6 4 1 4 34 Complexity o...

Ngày tải lên: 22/07/2014, 18:22

... G(M ,5) based on the iterative algorithm using these values 12 34 51 53 1 3 51 3 1 , 2 rr λ=λ λ=λ =⇒λ=λ λ=λ+λ=λ 121 34 3 1 55 1 1 /2 , / 2 /2 /4/ , with / ρ=ρ=λ µρ=ρ=λ µ=ρ ρ=λ λ=λ λ=ρ ρ ρ≡λµ 12 34 5 1, ... denote the set of all such states 1 µ 2 λ 3 µ 4 µ 5 µ 1 λ 2 µ 4 λ 3 λ 5 λ 51 r 53 r M 1 ,1, , K ijji j ri K = λ= λ = ∑ 1 0 and | | K ii i nnnM = ≥≡= ∑ 8-1 4 Marg...

Ngày tải lên: 22/07/2014, 18:22

... j →∞ = == = = 6-1 0 Continuous-Time Markov Chains  {X(t): - < t <∞} irreducible aperiodic Markov chain with transition rates q ij , i≠j  Unique stationary distribution (p i > 0) if and only ... π / jj jjji ij ii i pqj ν ν ν ≠ =≡= ∑ ∑ 1 TCOM 50 1: Networking Theory & Fundamentals Lecture 6 February 19, 2003 Prof. Yannis A. Korilis 6-1 7 Kolmogorov’s Criteri...

Ngày tải lên: 22/07/2014, 18:22

... 0 P   =    () 111 π , , 0.310, 0. 3 45 , 0. 3 45 333 p ppp  − ==  −−−  0.310 0. 3 45 0. 3 45 lim 0.310 0. 3 45 0. 3 45 ( 150 ) 0.310 0. 3 45 0. 3 45 n n Pn →∞   =≈    3-3 4 M/M/1 Queue  Arrival process: ... wet} π 3 p Ppp p − == − 1 TCOM 50 1: Networking Theory & Fundamentals Lecture 3 January 29, 2003 Prof. Yannis A. Korilis 3 -4 Discrete-T...

Ngày tải lên: 22/07/2014, 18:22

... property {|}{} P XxtXt PXx>+ > = > () { , }{ } {|} {} {} {} xt x t PX x tX t PX x t PX x t X t PX t PX t e ePXx e µ µ µ −+ − − >+ > >+ >+ > = = >> ===> 2-1 0 Probability Fundamentals  ... … and packets that arrive at a network switch {} , 0,1,2, ! k PX k e k k λ λ − == = 1 TCOM 50 1: Networking Theory & Fundamentals Lecture 2 January 22,...

Ngày tải lên: 22/07/2014, 18:22

... value a+b. Two cases, 0<a+b< 1and 1<a+b<2 are shown. K 2K 3K 4K 0ψ<ψa + bψ<ψ1 K 2K 3K 4K 0 0 A(t) D(t) N(t) t t 0ψ<ψa + bψ<ψ2 K 2K 3K 4K K 2K 3K 4K 5K 5K 0 0 N(t) A(t) D(t) t t What ... probability, P{X>r+ s | X>r} = P{X>r+ s,X>r} P{X>r} = P{X>r+ s} P{X>r} = G(r + s) G(r) , 17 Class Notes Santosh S. Venkatesh c  1997 TCOM 50 1: Networking Theor...

Ngày tải lên: 22/07/2014, 18:22

... ] 2 E REX=λ P-K Formula: 2 [] [ ] [] 12(1) E REX EW λ == −ρ − ρ 1 TCOM 50 1: Networking Theory & Fundamentals Lectures 9 & 10 M/G/1 Queue Prof. Yannis A. Korilis 1 0-1 2 Distribution ... over 1 b ¡ a e tb ¡ e ta t(b ¡ a) a+b 2 (b ¡ a) 2 12 ( a; b ) a<x<b Expo nential ¸e ¡ ¸x ¸ ¸ ¡ t 1 ¸ 1 ¸ ¸ x ¸ 0 Normal 1 p 2¼¾ e ¡ (x ¡ ¹) 2 =2¾ 2 e ¹t+(¾t) 2 =2 ¹¾ 2 ( ¹; ¾...

Ngày tải lên: 22/07/2014, 18:22

... Bearings, Theory and Applications36 -0 .1 -0 . 05 0 0. 05 0.1 -5 -2 .5 0 2 .5 5 0 .4 0.6 0.8 1 1.2 i x [A] i y = 0 A, y = 0 mm x [mm]a) h x [p.u.] -0 .1 -0 . 05 0 0. 05 0.1 -5 -2 .5 0 2 .5 5 0 .4 0.6 0.8 1 1.2 i x ... 100.8 N/A – non-optimized AMB -0 .1 -0 . 05 0 0. 05 0.1 -5 -2 .5 0 2 .5 5 0 .4 0.6 0.8 1 1.2 i x [A] i y = 0 A,...

Ngày tải lên: 20/06/2014, 06:20