Centralized Wireless Data Networks: Performance Analysis

Transcription

1 Centralized Wireless Data Networks: Performance Analysis Sndhar Ram S ECE 559: Corse Presentations December 6, 2007

2 Centralized Wireless Data Networks Voice networks Inelastic traffic Drop packets Smaller data rates Data networks Elastic traffic Qee packets Larger data rates Aim: Obtain a convenient approximate characterization of the network performance in terms of network parameters

3 Network parameters and Performance metrics Network parameters Traffic No. of sers with packets Size of packets Physical channel (Fading, Bandwidth, Noise) Power sed in commnicating the packets Medim access scheme Performance Metrics Total time in commnicating a packet Denial of service Fairness Aim: Performance metric f(network parameters)

4 Model for Network Parameters Traffic model: Dynamic-ser model Users arrive according to a Poisson process of rate αλ Each ser has to commnicate αs bits, where S is a random variable Medim access scheme: Symmetric schemes If the same sers are in the qee for an arbitrarily long time the average capacity is the same and eqal to a deterministic constant ψ() for each ser. Mathematically: Z 1 t+t I j (τ; )dτ ψ() t T. I j (t; ) : Rate of j th at time t with total sers. Random process What determines the statistics of I j (t; )?

5 Example: TDMA in Simple Correlated-Block Fading Model Channel Fading for a ser in each slot (dration 1) is a constant. User j slot k is H j,k Channel across sers is independent H j,k follows the Glibert-Elliot Markov model 1/2 1/2 g g 0 1 1/2 If in state g i and a total of sers se power P(g i ) 1/2

6 Example: TDMA in Simple Correlated-Block Fading Model Medim access scheme is TDMA User 1 will commnicate only dring [k, k + 1 ] and will not commnicate in [k + 1, k + 1] => Brsty servicing For t [k, k + 1], 8 < W log 1 + H j,k 2 P(H j,k ) N I j (t; ) = 0 when t [k + j 1, k + j ]. : 0 otherwise Since H is random, so is I j (t; ). Using some simple argments ψ() = W h i log 1 + g 1 2 P(g 1) + log 1 + g 0 2 P(g 0)

7 Mathematical Problem Introdction Let π() be the stationary distribtion for the no. of sers in the system, U. Average Delay = E(U) Little s law αλ Block probability = Prob (U > U T ) PASTA property Fairness: Medim access scheme ensres this Problem: Determine π() as a fnction of distribtion of S, statistics of I (, t), and λ.

8 First Order Approximation Intitive Argments Users come very rarely αλ, α 0. Each ser has large file S α If we send α 0 fast enogh, each ser will see an average of ψ() on an average. Recall, bits/sec Z 1 t+t I j (τ; )dτ ψ() t T. This leads to the following simplification: Users arrive at rate λ (very small) Each ser has a random file size of size S that is large The capacity seen by each ser is non-random, non-time-varying ψ().

9 First Order Approximation The Example: S is exponentially distribted. λ λ 1 E(S) Ψ() E(S) Ψ(+1) π() is the stationary distribtion of this CTMC! π() 1 K (λe (S)) Π i=1 ψ(i). As the file size goes to and arrival rate to 0 approximation is correct Tre for general distribtions of S Convergence O(α)

10 Second Order Approximation: Intition Assme R T +t t I j (τ)dτ ψ() t 2 N (ψ, σ 2 ()) We can inclde a correction term π() 1 K (λe (S)) Π i=1 ψ(i) 1 2 ασ2 (). Accracy is o(α) Ths more the variance in the service the average service rate is going to be lower Intition: Assme I (t; ) = φ() + σ 2 () White noise CTMC with noisy rates

11 Network Layer Application Physical layer and MAC layer has been abstracted ot into π(). Network layer problem: Fix W, g 0 and g 1. D is delay. Fnction of. P is total power sed per slot by all sers i=1 P i. min P i E E (D(U))! UX P i < P i=1 ses dynamic programming

12 Introdction Thanks! Obtained a simple and sefl approximation for the network performance Discssed an example network layer application