S i m p l e N e t w o r k P e r f o r m a n c e T o m o g r a p h y

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					                                            Simple Network

                    P   erf                 orma                 n    c        e T            omog                       ra     ph   y


                                                                 Nick Duffield


                            A   T   &   T    L   a   b   s - R   es       ea   r ch   ,   F   lo   r h   a   m   P   a   r k,   NJ




duffield@research.att.com
                                                                                                                                         1
                                          Network Performance Tomography


      B   a    s ic I         dea


                        Infer performance of interior links from end- to- end measu                   rements



      S       et up


                        M   esh    of intersecting   netw   ork path   s


                    M       easu   re end- to- end performance along       each   path   ( loss,   delay       )


                C           orrelate measu    rements to infer performance on common su                    b       path   s




duffield@research.att.com
                                                                                                                              2
                                                                 C   orrel ati ons                                                    and             Network Prob                           i ng


      P   a   cket - lev el co                                  r r ela        t io        n         b       y               des ig     n


                                    P   erform end- to- end measu                                                            rements u                sing     prob          e traffic


                                C       ou    ple prob         ing   on different netw                                                       ork path              s at th           e packet lev el



      M       ult ica                          s t - b   a   s ed t o     m        o   g       r a       p       h       y


                                    S       end prob         es dow     n mu                   lticast tree


                        P               acket performance identical on common path


                            O               ne- to- one map from link- performance to end- to- end performance


                        Inv ert map infer link performance


                    E                   x    ample:          infer    link loss rates from measu                                                                   re end- to- end loss rates


                R                       atnasamy              and M           cC       anne,                         M       IN   C    ( A    T   &   T   ,   IC    IR   ,   U   M    ass)




duffield@research.att.com
                                                                                                                                                                                                       3
                                                                                           W                                                            eaker C                                                                                                                                                   orrel ati ons                                                                                                                                                             and                                Network Prob                                 i ng


      U         nicast- b                                                     ased tomog                                                                                                                                                                     raph                                                           y


                        Emulate multicast probes: groups of closely spaced un                                                                                                                                                                                                                                                                                                                                                                                                                                                                                icast probes

                            •                 S                   t r i p                                              e               d                        a         c             r o             s s                          m                           u               l t i p                          l e                               d               e     s t i n                   a         t i o                    n           s



                        Performance within group on common links is correlated

                            •                 B       u                       t                    n           o                   t                    i d                    e         n            t i c                  a           l

                            •             N                           e               e        d                           a                       d        d                 i t i o                       n       a            l                       m                   o                d           e   l                 p               a                   r a           m         e       t e               r s                      t o             d          e       s c       r i b        e       c        o   r r e       l a       t i o    n   s



                        M   any                   - to- one map from link- performance to end- to- end performance


                    C       annot simply                                                                                                                                                     inv                        ert to perform inference:                                                                                                                                                                                                                                                    too many                                            link parameters



      Two approaches to u                                                                                                                                                                                                                        n                       i cast i n                                                                                           f           eren                                             ce


          1 .           I   f correlations strong within group:                                                                                                                                                                                                                                                                                                                                                                                            use multicast inference methods

                                              T               a                   i l o                    r                               s e                      l e             c         t i o                     n                    o                       f                p               r o               b               e                   s             t o                   e       n         h        a       n           c       e           c          o   r r e        l a   t i o            n

                                      V                   e                       r i f                            y                           c        o             r r e                            l a              t i o                                n                    s t r e                                           n                   g           t h                   t h               r o        u       g           h               d           i r e       c    t      m     e       a       s u      r e     m         e    n   t

                                  U                               I               N                    C                       P                       r o                    j e             c         t                   ( a                      s                   f                o           r            M                        I                   N         C           )



          2     .       C   ouple unknown parameters through q                                                                                                                                                                                                                                                                                                                                                                                                         ueueing model

                                              I   n                       c               i t e                                            P            r o                        j e            c             t            ( R                                 i c              e               )




duffield@research.att.com
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   4
                                    Tomography Without Strong Packet Correlations?


      Previous focus


               I           n    f   erri n         g        pack            et l oss,                                          d           el ay             ,       per l i n                     k


      S   im           p       l er q         uest ion


               Which are the badly performing links?


      Padmanabhan e                                                   t .       al .              I       nf               o           c       o     m 2              0             0   3


               S               imple end- to- end loss measu                                                                                                          rements dow                                                    n sou                   rce tree

                               •    D    e   t e   r m      i n   e   d     f   r o       m           m        e       a           s       u       r e   d       T        C     P       r e       t r a        n   s   m   i s       s   i o   n         s   f   r o   m   w   e   b   s   e   r v   e   r


               N               o packet lev el correlation designed into measu                                                                                                                                                                                   rements


                   A           pply sev eral inference methods to end- to- end loss measu                                                                                                                                                                                                      rements


      C   an i de                       nt i f         y    badl y                    p       e       r f          o                   r mi ng                                l i nk          s        q   u       i t e         w         e       l l


               C               ertain performance models


               B               etter w                     hen bad links are rarer




duffield@research.att.com
                                                                                                                                                                                                                                                                                                             5
                                                                                                      Motivation and Summary


      H           o       w               c       an i nf       e    r e      nc     e       o    f       w       o    r s t     l i nk   s       w   o       r k    w       /   o   p    ac   k    e   t   c   o   r r e   l at i o   ns ?


          F   i r s t                         c    o   mp   o       ne       nt :        l i nk       p       e       r f   o   r manc        e           mo        de   l


                                  S       eparable performance:                                                             disj oin betw                      een “ good”                         and “ bad”               links


                              I           nv estigate conformance w                                                             ith separable performance model



      S       e       c               o       nd c      o   mp           o   ne     nt :         as s u               me        bad l i nk                s     ar e             r ar e


                                  E       asier to reliably identify w                                                           ith low                  false positiv e rate




duffield@research.att.com
                                                                                                                                                                                                                                              6
                                                                               Se        p     arab                    l e              L       ink              P     e   rf          ormanc                    e     Mode         l


      A       s s o              c    i at e       p           e        r f    o       r manc         e               me         t r i c             φ       w       i t h e           ac   h l i nk   ,     p       at h i
                                                                                                                                                         i



                            e. g.       parameter or q                                           u    antile of distribu                                                   tion of loss or delay


                        M            easu      rement interv al may be part of definition



      S   e     p               ar at e        p           o           s s i bl e            v al u           e   s    o     f      φ               i nt o           t w   o       di s j o     i nt       s u       bs e   t s :
                                                                                                                                                i



                            C    all these su                                  bsets “ good”                                     and “ bad”



      S   e     p               ar abl e               p           e     r f       o   r manc             e           mo         de         l       as s u           mp        t i o    n


                            A        path is bad if and only if contains at least one bad link


                    C            annot make a bad path ou                                                                         t of “ partially”                                         bad links




duffield@research.att.com
                                                                                                                                                                                                                                        7
                                                                                                                                                                                                                                                                                E                                                           x                                                           amp                                                                                                                                l e                                              s                                                                 of                                                                                                                    Se                                                                  p                               arab                                                                                                                         l e                                                   P                     e                  rf                          ormanc                                                               e


      E   x   ample 1                                                                                                                                  ( triv ial)


                   P   e           r f                                     o                           r m                                              a                       n                             c                           e                                         m                                                   e                                   t r i c                                                                                                   i s                                              p                       a                   c             k                       e                                t                                       l o                                   s                               s


               L           i n             k           s                                               e                       i t h                                                            e                             r                                           l o                                       s                           e                                                       n                    o                                        p                     a                     c                            k                           e               t s                                                    (                                   =                                         g                           o                               o           d                           ) ,                                         o                    r                            l o               s               e                                            a                   l l                     p     a                 c                   k      e       t s                         (               =          b         a        d    )


      E   x   ample 2                                                                                                                                  ( P                                                  admanabhan et.                                                                                                                                                                                                                                                                                                                                                                                                                al. ,                                                                                                     I                               nfocom 2                                                                                                                                                                0                               0                                3               )


                   S           o       u           r                           c                           e                                           t r e                                                              e                           :                             l i n                                                               k                               s                                            o                        f                                         t w                                                o                               t y                                p                               e                           s                         :

                                   •                       G                                   o                           o                       d                :                       l o                                   s s                                                               u                           n                       i f                                 o                            r m                                              l y                                                 d                            i s t r i b                                                                        u                               t e                                       d                                           i n                                     b           e                   t w                                         e                    e                n         0                                   a                   n                    d                       1 %

                                   •                               B                       a                           d                       :                        l o                                 s s                                                   u                     n                               i f                                     o                           r m                                                  l y                                                d                             i s t r i b                                                                        u                    t e                                                 d                                     b                               e                           t w                         e               e                       n                           5                     %                     a                   n                   d                                        1 0                     %


                   Separable if depth of (logical) tree ≤                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       5


      Example 3 (Delay spike measurements: Zhang et. al., IMC 2001)


                   E       n       d- to- en                                                                                                                                                                d m                                                                             eas                                                                                     u                                    rem                                                                                    en                                                 ts                                        ex                                                       hibit delay                                                                                                                                                                                                                                s                pik                               es

                                   •                       P                           e                               r i o                                            d                   s                                     o                           f                                         g                           r e                                         a                                       t l y                                                     e                         l e                            v a                                     t e                       d                                        d                           e                           l a                               y

                                   •                       “ B                                                     a               d                    ” :                                                 i f                                           m                                 a                           x                                               d                                   e                l a                                  y                             e                     n                    c                       o                   u             n               t e                                              r e                                       d                                               b                       y                       s t r e                                                             a                    m                          o           f                       p                           a                    c           k           e               t s                         ≥                ( h           i g             h           )          t h             r e           s h       o   l d


                   R           eq              u                               irem                                                                                             en                                                        ts                                                                        for (approx                                                                                                                                                                                                                                                            im                                     ately                                                                                                                                 ) s                                     eparable perform                                                                                                                                                                                                                                                                             an              ce

                                   •                       A                                           s s u                                                    m                                       e                                 s p                                       i k                                             e                       s                                                       d            u                e                                     t o                                                            d                       e           l a                   y                s                                           o                           n                                 o                               n                   e                   o                   r                       m                           o                        r e                        l i n                                   k                s

                                   •                                   H                               i g                             h                                    c                       h                 a                           n                        c                                e                                       f                       o                                   r                            p                        r o                                   b                      e                                   s t r e                                                        a                           m                                                 t o                                                             e               n           c                   o               u                   n                   t e                               r s                       d                       e                       l a                      y                           s p               i k                   e              o   n               b       a              d             l i n           k

                                   •                           S                                   m                           a                       l l                              c                         h                           a                       n                         c                           e                                       f                           o                        r                            p                       a                         c                 k                        e                   t                        t o                                       e                               n                           c                     o                           u                       n                   t e                         r                           d               e                       l a                   y             s p                                     i k                          e                           o               n             m                 u                   l t i p              l e                       l i n        k         s


                   Satis                                                                   fied reas                                                                                                                                                                                                                    on                                                      ably                                                                                                                clos                                                                               ely                                                                    in                                                data for realis                                                                                                                                                                                                                                                                         tic probe s                                                                                                                     et

                                   •                                               ~                           a                           f                e                       w                                                 m                                   i n                                   u                           t e                                                     s                                    a                u               d                                 i o                                            t r a                                         n                   s f                                      e                           r




duffield@research.att.com
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                             Separability an                                                                                             d                       C               o                rrelatio                                    n    s


      Separability eq                                                                          u         iv .                 to                ex                  ac            t c           o       rrelatio                             n               o           f                    m            u       ltic           as t lo                  s s       m    o       d   el


          C       o       m            pare:


                                  S     eparab                          le: any path thro                                                                                     ugh a b                          ad          link is b                                                     ad


                                  Multic                      ast: pac                                   ket lo                                st o                  n any end                                   - to          - end                                     path if                                         lo       st o        n a c              o       mmo          n link


      C       o       n               s eq           u    en       c         e


                                  Mo         d           el: link i is ind                                                    epend                                  ently b                             ad          w         ith pro                                       b               ab                ility              α    i



                                  Measure frequencies                                                                                                   γ             o       f end                     - t o        - end                       b       ad                          ness o                              v er m               ul t ip            l e int erv al s
                                                                                                                                                                i



                              I        nfer {                    α}                 fro              m               {       γ}        b            y               usual                   m           ul t icast                           inference al g                                                                        o       rit h       m         ( e. g       .       MI   N   C   )
                                                                         i                                                    i



      Limitation


                                  S     t il l           need                      t o         co            o           rd           inat e m                                    easurem                                ent s t em                                                      p         o       ral l y

                                        •        M        u    l t i p       l e         a   l i g       n       e       d        m        e    a       s       u    r e      m     e   n           t    i n   t e       r v   a   l s               f   o           r               a       l l       p       a   t h    s   .


                                  D     esirab                         l e t o                 infer fro                                                    m             m       easurem                                ent s o                             v er sing                                                   l e int erv al




duffield@research.att.com
                                                                                                                                                                                                                                                                                                                                                                                                       9
                                                                                                                                                                                                                                                                                                             Identification of Rare Bad Links


                               S           up           p                 o                               se b                                                                   ad                                             l ink                                           s are rare:


                                                                i n                           t e                                     r s                  e                 c                   t i n                              g                       b               a                d                               p           a         t h               s                       m           o               s           t         l i k                     e               l y                          h               a               v           e        c       o           m         m           o       n    b    a     d       l i n       k


                               E       x        am                                            p                           l e:


                                                                L         i n                                     k                       s               i n                    d                e                     p               e               n               d           e                n                   t l y                       b           a           d                       w                   i t h                          p               r o                      b            a               b                   i l i t y                            p           ≈         0

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             P       r o   b       e   S   o   u   r       c   e
                               S           up           p                 o                               se p                                                               at h                                                   s ( 1 2                                                                      )                   and                                     ( 1 3                                   )                   b          o               t h                              b                    ad


                                                                C             o                       n                   d                   i t i o                                        n              a               l                   p           r o                          b                   a                   b           i l i t y                                       t h             a               t               l i n                  k                1                       i s                          b                   a       d

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               1
                                                                                                                                                                                                                                            p
                                                                                                                                                                                                                                                                                                                                                                                                                                             2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     ≈1 −p
                                                                                                                                                                                                                                                                        (p                                           + (1 − p)p                                                                                                                             )                                                                                                                                                                                                            2                                             3




                                                            O                             v                   e                       r w                            h                   e                l m                               i n                 g                       l i k                            e               l y             f               o       r                   l i n                       k            t o                            b               e                    b               a               d


                               I       nference:                                                                                                                                                  id                                ent ify                                                                                                  l ink                                       1               as b                                           ad


                           S               t eng                                                          t h                                         :


                                                                l o                       w                                       f               a                l s               e                          p               o                   s       i t i v                                      e                           r a            t e


                               W                eak                                               ness:                                                                                          co                                         v erag                                                                               e


                                                                S                 u                       p                   p               o                s         e                                l i n                             k                       1           g                o                   o               d         ,             l i n                   k           s               2                   , 3        ,               b                a       d               :                d                   o           n           ’t       d           e           t e       c       t       t h       i s   c       a   s       e           .




d   u   f   f   ie   l d           @        r   e   s                 e               a           r                   c               h       . a                  t t . c                            o             m
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   10
                                                                                S               m                   al l est C                                                onsistent F                           ail u          re S                       et ( S                      C           F       S        )        A   l g   orith       m


                           Data: single snapshot of end- to- end per for m                                                                                                                                        anc   e on sou                     r c   e tr ee

                                                e       a           c       h               p       a         t h    is        g       o   o       d    o   r   b     a   d


                           Deter m                                          ine sm                                   allest set of link                                               s c   onsistent w       ith ob            ser v ed b                 adness

                                                Those nearest to root



                                                                                                                                                       1                                                                                                                                                          1
                                                                                                                                                                                                  good
                                                                                                                                                                                                  bad
                                                                                                                                                                                            ?     undetermined
                                                                                                                                           1                                                                                                                                                              1
                                            1                                                                                                                                                                                                                1
                                                                                                                                                                                      1   ?                                                                                                                                               1
                                                                                                                                                                                                  b                                                                                                                                               b
                                                                                                                    ?
                                                                                                                                       a                            1                         0                                                                                                       a                     1                 0
                                                                                                                                                                                          ?           ?

        1                                                   0                                                       ?
                                                                                                                                       0                ?
                                                                                                                                                                                                                                 1                             0                                      0
                                                                                                                                                                                  0                       0                                                                                                                         0                     0
                                                                                        0                                                                            0                                                                                             0                                                        0
                           Measured data                                                                                                                                                                                                A        f     ter usi n     g   S   C        F           S

                                G   ood                     p           aths hav                                          e al l               g       ood          l i nk    s                               A    ttri b   u    te c       om         m   on l oss to c         om           m       on c        au       se




d   u   f   f   ie   l d    @       r   e   s       e           a       r           c   h               . a    t t . c     o       m
                                                                                                                                                                                                                                                                                                                                                              11
                                                                                 SCFS Performance


                         Model: link i independently bad with probability p
                                                                                                                                     i



                         Model am                    enable to direc             t analys is


                         P       erf       orm   anc          e Meas u   res


                                       False positive rate


                                       C   overag        e (    =   proportion   of   b   ad   lin   k   s id   en   tif   ied   )




d   u   f   f   i el d       @    researc    h. att. c   om
                                                                                                                                         12
                                                                                               SCFS Fal s            e Pos i t i v e R           at e


                             C       alc       u   late u    n    if   orm   b   ou    n   d   s of   f    alse positive rate




                                                                                                                                                                        
                                                                                                                                                                                
                                           As function of 1 -                    maximum probability of link badness:                            α   =   1   -   max       p


                                           D       epends on topolog                  y only th       roug    h   ( minimum)   branc   h   ing   ratio r




                             Decreases rapidly as branching ratio increases


                         C           an be applied to su                         btrees w                 ith larger r,   α



d   u   f   f   i el d           @    researc        h. att. c   om
                                                                                                                                                                                   13
                                                        SCFS False Positive Rate (2)


      Computations on selection of 1000 node trees,


           R   andom   branching ratios betw                               een 2                    and 1 0




                            p =                     P   rob( link   bad)      F               alse P                            ositiv e R                          ate


                                5       %                                             0       . 0       2           %         - 0         . 0           8       %


                            1 0             %                                     0           . 0   9           %             - 0         . 2       4       %


                            2       0           %                                         0   . 4           %           - 0         . 9         %




duffield@research.att.com
                                                                                                                                                                          14
                SCFS Cover ag          e:   D   ep   en   d   en   c   e on     B   r an   c   h   in   g   Ratio


      Cov erag    e relativ ely   insensitiv e to b       ranch        ing   ratio




duffield@research.att.com
                                                                                                                    15
                    SCFS Cover ag               e:       D    ep   en   d       en   c   e on       T    r ee D   ep   th


      Cov erag     e decreases w         ith   depth


           C   ov erage ≈   p /   T   ree Depth:     w       hen p =        P   rob( L   ink   B   ad)   ≈   0




duffield@research.att.com
                                                                                                                            16
                        SCFS Cover ag          e:        Con   stan   t Path   Failu   r e Rate


      T   rees w    ill not b   e arb   itrarily     deep for constant link      b   adness


            O   therw   ise all paths becom        e u   nreliable



      O   pposite:      scale p to k     eep path         failure rate constant


            C   ov erage insensitiv e to depth in this scaling




duffield@research.att.com
                                                                                                  17
                                                           Com      p    ar ison   s


      S   CF       S    Computationally         v ery    simple


      Comparison


               w       ith three ref   erence m    ethods in P          adm   anabhan et.       al.


               com       pared w   ith pu   blished resu    lts,    not reim     plem       entation



      F   alse positiv e rate:


               seem       s at least as good in all cases



      Cov erag            e:


               nearly as good if            badness rare,     ( less than 1 0      %    )


               noticeably w        orse than sim        ple ref    erence m      ethods if       less rare




duffield@research.att.com
                                                                                                             18
                                                                                     Su    m   m   ar y


      T       omog                    raph     y       and Correlations


                    M               any ex     isting m        ethods depend on intricate probing m                      ethods


                T               o arrange f                 or pack   et lev el correlations in probes



      S       eparab                    le P           erformance M           odel


                    E           nables ex               ploitation of     correlations and probe stream                   s;   less intricate


                        A           pplicable to m             odel in literatu      re,   observ ed netw        ork    perf   orm   ance



      I       nference from one time measurements


                    S           m    allest consistent f               ailu   re set algorithm


                            V   ery low            f   alse positiv e rate to identif              y bad link   s,   especially if    rare



      M       odels v ery                              amenab     le to analy        sis


          F   urth                   er w    ork        :   need simulation/         ex    perimental ev aluation




duffield@research.att.com
                                                                                                                                                19

				
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