Chapter3-helmy-F09-1

Chapter3-helmy-F09-1 - Mode Analysis ling Mathe atical Mode...

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Transport Layer 3-1 Modeling & Analysis Mathematical Modeling: probability theory queuing theory application to network models Simulation: topology models traffic models dynamic models/failure models protocol models

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Transport Layer 3-2 Simulation tools VINT (Virtual InterNet Testbed): catarina.usc.edu/vint [USC/ISI, UCB,LBL,Xerox] network simulator (NS), network animator (NAM) library of protocols: TCP variants multicast/unicast routing routing in ad-hoc networks real-time protocols (RTP) …. Other channel/protocol models & test-suites extensible framework (Tcl/tk & C++) Check the ‘Simulator’ link thru the class website
Transport Layer 3-3 OPNET: commercial simulator strength in wireless channel modeling GlomoSim (QualNet): UCLA, parsec simulator Research resources: ACM & IEEE journals and conferences SIGCOMM, INFOCOM, Transactions on Networking (TON), MobiCom IEEE Computer, Spectrum, ACM Communications magazine www.acm.org, www.ieee.org

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Transport Layer 3-4 Modeling using queuing theory - Let: - N be the number of sources - M be the capacity of the multiplexed channel - R be the source data rate - α be the mean fraction of time each source is active, where 0< α≤ 1
Transport Layer 3-5

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Transport Layer 3-6 - if N.R=M then input capacity = capacity of multiplexed link => TDM - if N.R>M but α .N.R<M then this may be modeled by a queuing system to analyze its performance
Transport Layer 3-7 Queuing system for single server

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Transport Layer 3-8 λ is the arrival rate Tw is the waiting time The number of waiting items w= λ .Tw Ts is the service time ρ is the utilization ‘fraction of the time the server is busy’, ρ = λ .Ts The queuing time Tq=Tw+Ts The number of queued items (i.e. the queue occupancy) q=w+ ρ = λ .Tq
Transport Layer 3-9 λ = α .N.R, Ts=1/M ρ = λ .Ts= α .N.R.Ts= α .N.R/M Assume: - random arrival process (Poisson arrival process) - constant service time (packet lengths are constant) - no drops (the buffer is large enough to hold all traffic, basically infinite) - no priorities, FIFO queue

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Transport Layer 3-10 Inputs/Outputs of Queuing Theory Given: - arrival rate - service time - queuing discipline Output: - wait time, and queuing delay - waiting items, and queued items
Transport Layer 3-11 Queue Naming: X/Y/Z where X is the distribution of arrivals, Y is the distribution of the service time, Z is the number of servers G: general distribution M: negative exponential distribution (random arrival, poisson process, exponential inter-arrival time) D: deterministic arrivals (or fixed service time)

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Transport Layer 3-12
Transport Layer 3-13 M/D/1: Tq=Ts(2- ρ )/[2.(1- ρ )], q= λ .Tq= ρ + ρ 2 /[2.(1- ρ )]

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Transport Layer 3-14
Transport Layer 3-15

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Transport Layer 3-16
Transport Layer 3-17 As ρ increases, so do buffer requirements and delay The buffer size ‘q’ only depends on ρ

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Transport Layer 3-18 Queuing Example If N=10, R=100, α =0.4, M=500 Or N=100, M=5000 ρ = α .N.R/M=0.8, q=2.4 -
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This document was uploaded on 05/27/2011.

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Chapter3-helmy-F09-1 - Mode Analysis ling Mathe atical Mode...

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