Docstoc

defense

Document Sample
defense Powered By Docstoc
					The Impact of Long-Range-Dependent
Traffic on Network Performance

George Lin
Ph.D. Defense Presentation
Aug. 18, 2000
Outline

    Introduction
      – long-range-dependent traffic
      – motivation
      – overview and contributions
    Performance analysis with LRD input traffic
      – off-line performance analysis
                   finite buffer queueing analysis
                   reassembly and multiplexing queueing analysis
      – on-line sensitivity queueing analysis
      – summary
    Concluding remarks and future directions

Aug. 18, 2000                         George Lin - Defense Presentation   2
Introduction
Long-Range-Dependent Traffic

    Network traffic exhibits long-range-dependent (LRD)
     property
      –    LAN
      –    WAN
      –    Internet (WWW)
      –    VBR video
    Implication
      – autocorrelation function decays slower than exponential
      – bursty at a wide range of time scales




Aug. 18, 2000               George Lin - Defense Presentation     4
Long-Range-Dependent Traffic
                                          Ethernet trace                                        Poisson arrivals / i.i.d. packet sizes
                       1.5 104                                                                                    1.5 104




                                                                                                Bytes per sample
   Bytes per sample




                        1 104                                                                                         1 104

                         5000                                                                                         5000

                            0                                                                                            0
                                 0   50          100       150      200       250    300                                      0   50       100       150       200       250    300
                                      sample count (Sample interval = 0.01 sec.)                                                   sample count (Sample interval = 0.01 sec.)


                       1 105                                                                                          1 105




                                                                                                   Bytes per sample
 Bytes per sample




                       5 104                                                                                          5 104



                            0                                                                                            0
                                 0   50          100      150       200       250    300                                      0   50       100       150       200       250    300
                                      sample count (Sample interval = 0.1 sec.)                                                     sample count (Sample interval = 0.1 sec.)


                        4 106                                                                                         4 106
                                                                                                   Bytes per sample
    Bytes per sample




                        2 106                                                                                         2 106



                            0                                                                                            0
                                 0   50          100       150      200       250    300                                      0   50       100       150       200       250    300
                                          sample count (Sample interval = 10 sec.)                                                sample count (Sample interval = 10 sec.)



Aug. 18, 2000                                                               George Lin - Defense Presentation                                                                         5
Long-Range-Dependent Traffic

    LRD Traffic Models
      – Fractional Gaussian noise (FGN)
      – Fractional autoregressive integrated moving average (FARIMA)
      – Wavelet
        Heavy-tailed on/off sources
                   compelling physical evidence
                   file sizes and packet trains are heavy tailed
                   M/G/
                      –   video, FTP, TELNET; source behavior
                      –   model LRD traffic with G having a heavy tailed distribution
                      –   model SRD traffic with G having an exponential distribution




Aug. 18, 2000                               George Lin - Defense Presentation           6
Motivation

    It’s important to study the impact of LRD traffic
    Off-line performance analysis
      – existing methods
                   assume infinite buffer queues driven by LRD input traffic
                   study the asymptotic tail behavior of the buffer overflow probability
                      –   buffer overflow probability is the probability that the buffer occupancy exceeds a given threshold
                          value in the steady state

      – potential limitations of existing methods
                   asymptotic tail behavior often capture only the most slowly decreasing term of
                    the buffer overflow probability
                   apply to a limited range of parameter values
                   crucially rely on the infinite buffer assumption
                      –   derive the buffer overflow probability rather than the loss probability
                      –   loss probability is the fraction of lost work in the steady state



Aug. 18, 2000                                George Lin - Defense Presentation                                             7
Motivation

    On-line sensitivity queueing analysis
      – existing methods
                   determine performance sensitivities with respect to network parameters
                      –   determine how performance measures vary with the changes in network parameters
                   determine the performance sensitivities by observing a sample path
      – potential limitations of existing methods
                   only determine performance sensitivities with respect to continuous
                    parameters
                   crucially rely on the Markov structure of the systems




Aug. 18, 2000                              George Lin - Defense Presentation                               8
Overview and Contributions

    Study the impact of LRD traffic
      – Finite buffer qeueing analysis
                   develop an off-line method which assumes a buffer with finite capacity and
                    are based on non-asymptotic method
                   determine the significance of finite buffer assumption and non-asymptotic
                    analysis
                      –   loss probability
                      –   we show that existing analysis assuming infinite buffer significantly underestimates the network
                          performance

      – Reassembly and multiplexing queueing analysis
                   develop off-line methods which are based on non-asymptotic analysis
                   determine practical impact of LRD traffic and non-asymptotic analysis
                      –   buffer overflow probability
                      –   frame loss probability
                      –   for reassembly queueing, we show that LRD traffic has no significant impact
                      –   for multiplexing queueing, we show that existing asymptotic analysis significantly
                          underestimates the impact of LRD traffic when the buffer size is small

Aug. 18, 2000                               George Lin - Defense Presentation                                                9
Overview and Contributions

    Study the impact of LRD traffic
      – On-line sensitivity queueing analysis
                   develop an on-line method which utilizes the proportional relationship
                   determine performance sensitivity with respect to discrete parameters for a
                    queueing system with LRD traffic
                      –   loss probability
                      –   mean queue length
                      –   mean delay
                      –   we show our method is useful for systems which are not amenable to existing on-line methods




Aug. 18, 2000                              George Lin - Defense Presentation                                            10
Performance Analysis with LRD
Input Traffic

Off-Line Performance analysis
   Finite buffer queueing analysis
   Reassembly and multiplexing queueing analysis
On-line sensitivity queueing analysis
Summary
Finite Buffer Queueing Analysis

    Goal: Investigate the significance of the finite buffer
     assumption
      – analyze the performance of a network multiplexer with finite
        buffer capacity
                   network multiplexers are fundamental building block for sharing network
                    resources such as bandwidth and buffer space
      – obtain loss probability based on non-asymptotic method
                   rather than buffer overflow probability
                   determine the implication of using buffer overflow probability as the
                    performance measure (or to approximate loss probability)
      – determine the impact of LRD traffic




Aug. 18, 2000                          George Lin - Defense Presentation                      12
 Queueing Model

                                                    General fluid input process
                                                       – include a large class of LRD
                                                         and SRD processes
                                                                    M/G/
                                                                    Gaussian process
                                                       – the instantaneous input rate Lu
                                                                    Lu takes on integer values
                                                                    P[Lu=k], E[Lu]            t

                                                                    total work flow in [0,t],  L u du.
             if (0 < X u  B)
                                                                                                 0

                                                    Buffer with finite capacity B
     
dX u L u  c or ( X u ,  0, L u  c)              Single server with constant
    
                                 

                                                     output rate c
 du          or ( X u  B, L u  c)
                                 

      0
                   otherwise                       buffer occupancy Xu


 Aug. 18, 2000               George Lin - Defense Presentation                                             13
Loss Probability
          ~
     Let X t denote the stationary buffer occupancy in the steady state,
     ~
     X t  lim X s
                s
          ~
     Let L t denote the stationary input rate in the steady state,
     ~
     L t  lim L s
                s

                                amount of lost work in [0,s]
     Loss Probability  lim
                        s amount of arriving work in [0,s]

                           E[ work lost rate]
                      
                        E[work arriving rate]
                           1
                       ~  ( k  c) P[ X t  B, L t  k ]
                                             ~       ~
                        E [ L t ] k c


Aug. 18, 2000                George Lin - Defense Presentation             14
Loss Probability
     The joint probability in the loss probability is given as follows.
                                      
                                                 
            P[ X t  B, L t  k ]    (c  n)
               ~        ~                                    ~            ~
                                                   P[Ws  w, L t  s  n, L t  k ]ds           ,
                                    0 n0
                                                w                                    w B  cs
                           t
                            ~
            where Ws      L u du.
                          t s


     Proposition If the following condition holds:
     i) the input process in the steady state is stationary and ergodic, and
     ii) the average input rate is less than the constant output rate,
     then buffer full probability is given as follows.
                                                             
                                                       
                                                                 
            Buffer Full Probability = P[ X t  B]    (c  n)
                                         ~                                   ~
                                                                   P[Ws  w, L t  s  n]ds            ,
                                                    0 n0
                                                                w                          w  B  cs
                            t
                                 ~
            where Ws       L udu.
                          t s




Aug. 18, 2000                             George Lin - Defense Presentation                                15
Loss Probability
    High level proof for the Proposition:
          By extending Benes analysis, we show that
                                   
                                                
                P[ X t  x ]  1    (c  n)
                   ~                                        ~            ~
                                                  P[Ws  w, L t  s  n, X t  s {0, B}]ds
                                   0 n 
                                               w                                           w  x  cs
                                   
                                                
                             1    ( c  n)
                                                            ~
                                                  P[Ws  w, L t  s  n]ds
                                  0 n
                                               w                          w x  cs
                                  
                                                           ~               ~
                                   ( c  n)    P[Ws  w, L t  s  n,0  X t  s  B]ds
                                  0 n
                                               w                                          w x  cs


                                   
                   ~                                      ~
                P[ X t  B]  1    (c  n)    P[Ws  w, L t  s  n]ds
                                  0 n
                                              w                          w x  cs

                                                    
                   ~                 ~                                  ~
                P[ X t  B]  1  P[ X t  B]    (c  n)    P[Ws  w, L t  s  n]ds
                                                0 n
                                                            w                          w x  cs



Aug. 18, 2000                       George Lin - Defense Presentation                                    16
Finite Buffer Queueing Analysis
Example

                                 ~
                                 L t is characterized by a M / G /  process

                                                    M/P/ , H1=0.55,
                                                    M/P/ , H3=0.9,
                                                    M/M/
                                                     ~
                                    ~           ( E[ L t ]) k  E [ Lt ]
                                                                    ~
                                 P[ L t  k ]               e
                                                     k!
                                                  ~
                                 System load = E[ L t ] / c

                                 c = 1.55 Mbps




Aug. 18, 2000   George Lin - Defense Presentation                          17
Finite Buffer Queueing Analysis
Results
      M/P/ , H1=0.55
                                                    This figure compares loss probability
      System load = 0.77, 0.58, 0.38                 with buffer overflow probability
                                                       – buffer overflow probability is the
                                                         probability that buffer occupancy
                                                         exceeds a given threshold value,
                                                         where the threshold value equals to
                                                         the buffer capacity of the
                                                         corresponding finite buffer system
                                                       – simulation results agree with our
                                                         analysis.
                                                       – buffer overflow probability
                                                         significantly overestimate the loss
                                                         probability



Aug. 18, 2000                 George Lin - Defense Presentation                        18
Finite Buffer Queueing Analysis
Results

                                       This figure shows the impact of
                                        LRD traffic when buffer size is
                                        small
                                          – LRD traffic has significant
                                            impact on network performance
                                            even when the buffer size is
                                            small




Aug. 18, 2000   George Lin - Defense Presentation                      19
Summary of Finite Buffer Queueing
Analysis

    Investigate the significance of finite buffer assumption
      – Buffer overflow probability (existing analysis) significantly
        overestimates the loss probability, and designing networks using
        buffer overflow probability as the performance measure will cause
        inefficient network utilization
      – Existing analysis underestimate the impact of LRD traffic when
        the buffer capacity is small




Aug. 18, 2000              George Lin - Defense Presentation            20
Performance Analysis with LRD
Input Traffic

Off-Line Performance analysis
   Finite buffer queueing analysis
   Reassembly and multiplexing queueing analysis
On-line sensitivity queueing analysis
Summary
Reassembly and Multiplexing
Queueing Analysis

    Goal: study the buffer requirements of reassembly and
     multiplexing operations in networks and determine
     practical impact of LRD traffic based on non-asymptotic
     mehod
      – intermediate network elements
                   routers
                   connectionless servers
      – interworking units
                   network gateways
                   application gateways (e.g., transcoders)




Aug. 18, 2000                          George Lin - Defense Presentation   22
IP over ATM

                                       Exit Router

                Packets                                              ATM
                                                                    Switch




      Higher                                                                 Higher
      Layer                                                                  Layer
        IP                                    IP                               IP
       AAL                                 AAL                               AAL
       ATM                ATM              ATM                      ATM      ATM
       PHY                PHY              PHY                      PHY      PHY


Aug. 18, 2000                   George Lin - Defense Presentation                     23
       Queueing Model

                                 Frame
ON/OFF Work Batches              Reassembly                          Aggregated LRD Input Process
Sources E[A]                     Queue                                 – ON/OFF Sources
      R         Aggreg.
   1            LRD                  X1        Frame                   – Work-Batches; frames (MTU), cells
                                               Multiplexing
         R             Input         +         Queue                   – M/G/; , E[A],
   2                   Process       X2
                                                                       – LRD, SRD
             MTU         
         R                           +
  Nt                                 XNt                             Frame Reassembly Queue
                                                                       – accumulate and reassemble
                                                                       – infinite buffer with a given threshold value

             ON/OFF Source                                           Frame Multiplexing Queue
                Work-Batch (A)
                                                                       – re-segment and transmit
                ON                         OFF
                State R               0 State                          – infinite buffer with a given threshold value

              Cell T3        Frame (MTU)
                                      T2              T1

       Aug. 18, 2000                          George Lin - Defense Presentation                             24
Differences in Queueing Models

    Finite buffer queueing analysis                Reassembly and multiplexing
      – assume general fluid input                   queueing anaylsis
        process, and use M/G/ as an                   – assume M/G/ process with
        example                                          the notion of frame (because
      – multiplexing queue with finite                   we obtain frame loss
        buffer capacity                                  probability)
                                                       – reassembly queue with infinite
                                                         buffer
                                                       – multiplexing queue with
                                                         infinite buffer




Aug. 18, 2000                George Lin - Defense Presentation                        25
Analysis of the Both Queues

    Performance measures
      – buffer overflow probability
                  the probability that buffer occupancy exceeds a certain threshold value
                in an infinite buffer system
                 provides an upper bound to loss probability of the corresponding
                finite buffer system

      – frame loss probability
                  the ratio between the number of lost frames and the number of
                total frames in the steady state
                  a frame with cells arriving when the buffer occupancy exceeds
                the threshold value is lost




Aug. 18, 2000                         George Lin - Defense Presentation                      26
Frame Reassembly Queue Results:
Impact of LRD Traffic

                                               • This figure indicates that
                                               LRD traffic and Markov
                                               traffic yield similar queueing
                                               behavior




Aug. 18, 2000   George Lin - Defense Presentation                         27
Frame Multiplexing Queue Results:
Impact of LRD Traffic

                                                • The Figure indicates that
                                                LRD traffic and Markov
                                                traffic yield similar behavior
                                                when the buffer size is small,
                                                but yield diverse behavior
                                                when the buffer size is large.




Aug. 18, 2000   George Lin - Defense Presentation                         28
Summary of the Reassembly and
Multiplexing Queueing Analysis

    Frame reassembly operation
      – LRD does NOT have a significant impact
                   finite MTU size reduces the negative effects of LRD
      – MTU size has a significant impact
    Frame multiplexing operation
      – LRD has a significant impact
                   especially when target loss probability is small
      – MTU size is not a factor




Aug. 18, 2000                           George Lin - Defense Presentation   29
Performance Analysis with LRD
Input Traffic

Off-Line Performance analysis
   Finite buffer queueing analysis
   Reassembly and multiplexing queueing analysis
On-line sensitivity queueing analysis
Summary
On-Line Sensitivity Queueing Analysis

    Goal: develop a new on-line performance sensitivity
     estimation method for systems with discrete parameters
     and LRD traffic
      – examine in real-time how performance measures would vary with
        the changes in system parameters
                   example application: simulate the system with a given set of parameters, then
                    obtain the entire performance measure vs. system parameter(s) curve with the
                    simulation data
      – discrete parameters + LRD traffic raise difficulties
                   exiting methods rely on the partial or complete knowledge of the Markov
                    structure of the system




Aug. 18, 2000                          George Lin - Defense Presentation                        31
Overview of Our Method

Proportional Relationship Method                 Obtain the steady state probabilities
                                                  of the nominal system from the
                                                  observed sample path
                                                 Obtain the performance measure of
                                                  the nominal system
                                                 Obtain the steady state probabilities
                                                  of the perturbed system by utilizing
                                                  the proportional relationship
                                                 Obtain the performance measure of
                                                  the perturbed system
                                                 Calculate the differences between
                                                  the performance measures of the
                                                  two systems

Aug. 18, 2000             George Lin - Defense Presentation                      32
Queueing Model

                                                                            Controlled stream
                                                                              – customers arrive in batches
                                                                              – batch size is probabilistically determined
                                                                                by the queue length
                                                                            Uncontrolled stream
                                                                              – customer arrive in batches
                                                                              – batch size is governed by an underlying
                                                                                Markov chain
a (j ,N ,c)  P[ An1 ,c)  k |Yn( N )  j ]
    i
      k
                  (N      i           i                                                   infinite or finite number of states
                                                                                          structure of the Markov chain is unknown
ai(,N,k,u )  P[ An1 ,u )  k , Pn1  j| Pn  i ]
    j
        i         (N          i
                                                                            Buffer and single server
 P[ A      ( N i ,u )
            n 1          k | Pn 1  j ] P[ Pn 1  j| Pn  i ]             –    nominal system with capacity N1
                                                                              –    perturbed system with capacity N0
Yn(Ni )  min((Yn( Ni )  1)   An 1i ) , N i )
    1
                                   (N



Zn 1i )  ((Yn( Ni )  1)   An 1i )  N i ) 
 (N                             (N



Aug. 18, 2000                                          George Lin - Defense Presentation                                         33
Example 1
Markov Uncontrolled Stream


                                        Nominal buffer capacity, N1=50
                                        Perturbed buffer capacity, N0=40




Aug. 18, 2000   George Lin - Defense Presentation                    34
Example 2
LRD Uncontrolled Stream


                                        Nominal buffer capacity, N1=200
                                        Perturbed buffer capacity, N0=150




Aug. 18, 2000   George Lin - Defense Presentation                    35
Summary of
On-Line Sensitivity Queueing Analysis

    Develop the proportional relationship for on-line
     sensitivity queueing analysis
      – apply the proportional relationship method and perform sensitivity
        analysis of the feedback controlled queueing system with respect
        to buffer capacity
      – we show the proportional relationship method successfully
        perform sensitivity analysis with respect to discrete parameters for
        a system with LRD traffic
      – we show that our method is comparable with simulation methods




Aug. 18, 2000               George Lin - Defense Presentation              36
Performance Analysis with LRD
Input Traffic

Off-Line Performance analysis
   Finite buffer queueing analysis
   Reassembly and multiplexing queueing analysis
On-line sensitivity queueing analysis
Summary
Summary

    Performance analysis with LRD traffic
      – Finite buffer queueing analysis
                   loss probability
                   we show that existing analysis assuming infinite buffer significantly
                    underestimates the network performance
                   Existing analysis underestimate the impact of LRD traffic when the buffer
                    capacity is small
      – Reassembly and multiplexing queueing analysis
                   buffer overflow probability and frame loss probability
                   we show that LRD has no impact on reassembly operations
                   we show that existing asymptotic analysis significantly underestimates the
                    impact of LRD traffic when the buffer size is small




Aug. 18, 2000                          George Lin - Defense Presentation                         38
Summary

    Performance analysis with LRD traffic
      – On-line sensitivity queueing analysis
                   utilize proportional relationship
                   determine performance sensitivity with respect to discrete parameters for a
                    queueing system with LRD traffic
                      –   loss probability
                      –   mean queue length
                      –   mean delay
                      –   we show our method is useful for systems which are not amenable to existing on-line methods




Aug. 18, 2000                              George Lin - Defense Presentation                                            39
Concluding Remarks
and
Future Directions
Concluding Remarks

    Contributions


        Provide new methods for performance analysis and
        performance optimization with LRD traffic




Aug. 18, 2000           George Lin - Defense Presentation   41
Future Directions

    Off-line performance analysis extension
      – application to designing static network components or configuring
        quasi-static network parameters
      – Finite buffer multiplexing queueing analysis extension
                   Obtain asymptotic loss probability in close form
                   apply to admission control based on a priori characterizations

    On-line sensitivity analysis extension
      – application to configuring dynamic network parameters
                   apply the proportional relationship method to more realistic models
                   apply the proportional relationship method to dynamic buffer allocation
                   apply to admission control based on measurement data
      – improve estimation efficiency for LRD traffic


Aug. 18, 2000                          George Lin - Defense Presentation                      42

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:21
posted:12/19/2011
language:English
pages:42