Networking Theory and Fundamentals - Lecture 2 potx

... … and packets that arrive at a network switch {} , 0,1 ,2, ! k PX k e k k λ λ − == = 1 TCOM 501: Networking Theory & Fundamentals Lecture 2 January 22 , 20 03 Prof. Yannis A. Korilis 2- 8 Queue ... →∞ === ∑ .EN ET λ = [()] lim t Et t α λ →∞ = 2- 1 5 Poisson Distribution (cont.)  Mean and Variance Proof: [] , Var()EX X λ λ = = 000 0 22 2 000 2 00 0 22 2 [] {...

Ngày tải lên: 22/07/2014, 18:22

... in 2 and M-n in 1  Normalization constant  Utilization factor and throughput of node 1: 2 µ 2 λ 11 122 21 11 2 21 , . Choose solution: and pp pλ= λ+λ λ= λ λ=µ λ= µ 21 12 2 1, p µ ρ= ρ= µ 12 2 11 ( ... 1,) k Gmk Gmk Gm k=−+ρ−  Example: 2 3 2 (1, 2) (1,1) (0, 2) 1 1 2 (1,3) (1 ,2) (0,3) 2 2 4 (2, 2) (2, 1) (1 ,2) 1 2 3 GG G GG G GG G = +ρ = + = = +ρ =+= = +...

Ngày tải lên: 22/07/2014, 18:22

... care of customer i. Let N  i and N i denote the steady- state average, instantaneous number of customers seen by servers i  and i, 12 TCOM 501: Networking Theory and Fundamentals University of ... 1) λ k k! = λ 2 ∞  k =2 λ k 2 (k − 2) ! = λ 2 e λ . It follows readily that if X is Poisson with parameter λ, then E(X)= ∞  k=0 ke −λ λ k k! = λ, and, likewise, E(X 2 )= ∞...

Ngày tải lên: 22/07/2014, 18:22

... If i and j are nodes in N and (i, j) is an arc in A, the arc is said to be incident on i and j  Walk: sequence of nodes (n 1 , n 2 , …, n k ), where (n 1 , n 2 ), (n 2 , n 3 ), …, (n k-1 , ... 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 of Floyd-Warshall  N iterations steps One for each pos...

Ngày tải lên: 22/07/2014, 18:22

... times and service times  Exponentially distributed service times Network model: Jackson network “Product-Form” stationary distribution 1 TCOM 501: Networking Theory & Fundamentals Lecture ... +µδ + δ λδ + − ⋅µδ + δ 7 -2 Topics  Open Jackson Networks  Network Flows  State-Dependent Service Rates  Networks of Transmission Lines  Kleinrock’s Assumption 8-1 2 Non-Poiss...

Ngày tải lên: 22/07/2014, 18:22

... tedious 2 λ 2 µ 2 λ 2 µ 2 λ 2 µ 1 λ 1 µ 2 λ 2 µ 2 λ 2 µ 2 λ 2 µ 1 λ 1 µ 1 λ 1 µ 1 λ 1 µ 2 λ 2 µ 2 λ 2 µ 2 λ 2 µ 02 12 1 λ 1 µ 01 11 21 1 λ 1 λ 1 µ 1 µ 00 10 20 30 1 λ 1 λ 1 µ 1 µ 03 13 22 31 12 1 2 {( ... Q2 up to t. Thus N 1 (t) and N 2 (t) independent:  Letting t→∞, the joint stationary distribution 1 11 1 1 1 ( ) (1 ) , 0,1, n pn n ρρ =...

Ngày tải lên: 22/07/2014, 18:22

... ) (1)! n th t T t P ntt f te n λ λ δδ λδ − − += = − 4& 5 -2 6 M/M/1 Queue with State-Dependent Rates 0 1 n+1n2 0 λ 1 µ n λ 1n µ + 1 λ 2 µ 1n λ − n µ  Interarrival times: independent, exponential, ... lim i i tt Tt pPNti t →∞ →∞ === 4& 5-1 8 PASTA Theorem: Intuitive Proof  t a and t r : randomly selected arrival and observation times, respectively  The arrival processes p...

Ngày tải lên: 22/07/2014, 18:22

... π 3 p Ppp p − == − 1 TCOM 501: Networking Theory & Fundamentals Lecture 3 January 29 , 20 03 Prof. Yannis A. Korilis 3-4 Discrete-Time Markov Chain  Discrete-time stochastic process {X n : n = 0,1 ,2, …}  Takes ... ∑ λµλµ λ λλ − = − == 11N T ρ λ ρ ===−= and 1 2 WNTW ρ λµµ −− 1 Q 3-1 3 Example: Finite Markov Chain p 1 001 01 10 P pp pp   =−  −   0 2 1 1...

Ngày tải lên: 22/07/2014, 18:22

... Electronics, Electrical Drives, Automation and Motion, Italy, 1109 - 1113 ISBN: 97 8-1 - 424 4-1 66 3-9 . Halbaoui, K.; Boukhetala, D. and Boudjema, F. (20 09a). Speed Control of Induction Motor Drives ... 1986. [25 ] Leah Edelstein-Keshet., Mathematical models in Biology, McGraw Hill, 1988. pp. 23 4 -2 36. [26 ] Hofbauer, J., and Sigmund, K., “Growth Rates and E...

Ngày tải lên: 20/06/2014, 04:20

... M. et al. (20 04). OWL Web Ontology Language Guide, http://www.w3.org/TR /20 0 4- /REC-owl-guide -2 0 04 021 0/OWL Web Ontology Language Guide, http://www.w3.org/TR /20 04/REC-owl-guide -2 0 04 021 0 Sommerville, ... M. et al. (20 04). OWL Web Ontology Language Guide, http://www.w3.org/TR /20 0 4- /REC-owl-guide -2 0 04 021 0/OWL Web Ontology Language Guide, http://www.w3.org/TR /20...

Ngày tải lên: 21/06/2014, 18:20