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' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 1 Accelerated Reliabilit y Analysis for Self-Healing SONET Net w orks z y Hakki C. Cank a y a and V. S. S. Nair y Computer Science and Engineering

slide-1
SLIDE 1 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 1 ' & $ % Accelerated Reliabilit y Analysis for Self-Healing SONET Net w
  • rks
Hakki C. Cank a y a z and V. S. S. Nair y y Computer Science and Engineering Departmen t Southern Metho dist Univ ersit y , Dallas, TX 75275, USA z Now at ALCA TEL Corp
  • rate
Researc h Cen ter Ric hardson, TX 75081, USA A CM SIGCOMM'98 Septem b er 4, 1998
slide-2
SLIDE 2 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 2 ' & $ % Accelerated Reliabilit y Analysis for Self-Healing SONET Net w
  • rks
Hakki C. Cank a y a z and V. S. S. Nair y y Computer Science and Engineering Departmen t Southern Metho dist Univ ersit y , Dallas, TX 75275, USA z Now at ALCA TEL Corp
  • rate
Researc h Cen ter Ric hardson, TX 75081, USA A CM SIGCOMM'98 Septem b er 1998
slide-3
SLIDE 3 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 3 ' & $ % Presen tation Outline
  • In
tro duction and
  • b
jectiv es
  • The
mo del
  • Analysis
  • f
run-time complexit y
  • Acceleration
tec hnique
  • Exp
erimen tal study and results
slide-4
SLIDE 4 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 4 ' & $ % Prelude
  • T
rends in T elecom: { f" T rac demandg 7 ! f" Sp eedg 7 ! f" Criticali t yg 7 ! f" Demand in reliabili t yg
  • Meet
the reliabili t y demand { F ault forecasting, F ault a v
  • idance,
F ault remo v al, F ault tolerance, etc.
  • Need
for reliabil i t y ev aluation and mo deling
  • Previous
w
  • rk
{ Prop
  • sed
mo del, SRMM/p { Prop
  • sed
set
  • f
metrics
slide-5
SLIDE 5 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 5 ' & $ % Ob jectiv es
  • Observ
e the run-time complexit y
  • f
the mo del
  • Analyze
the mo del to understand the cause
  • f
high complexit y
  • Study
the
  • ptions
to reduce complexit y
  • Ev
aluate the pros & cons
  • Accelerate
the analysis
  • Examine
the impro v emen t
slide-6
SLIDE 6 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 6 ' & $ % State Rew ard Mark
  • v
Mo del (SRMM/p)
  • Mark
  • v
Mo del { Probabilisti c b eha vior { Design details { Co v erage { System dep endencies
  • State-Rew
ard feature { P erformance as rew ard v alue
  • P
arametric feature { V arying p erformance { Multiple consecutiv e failures
slide-7
SLIDE 7 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 7 ' & $ % Reliabilit y/Av ailabilit y Ev aluation Pro cess

M(l,h,m)

F W Q

µ µ λ c. (1-c). θ θ Topology Related Data Restoration Related Data Event Related Data Availability Reliability

slide-8
SLIDE 8 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 8 ' & $ % Mo del P arameters
  • P
arameter l { Num b er
  • f
stages in the mo del { T rade-o b et w een complexit y and accuracy
  • P
arameter h { Threshold p erformance
  • P
arameter m { Num b er
  • f
dieren t p erformance lev els ab
  • v
e h { T rade-o b et w een complexit y and accuracy
slide-9
SLIDE 9 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 9 ' & $ % The Mo del with Multiple Stages

l F l

Stage

l µ F1

Stage2 Stage1 Stage 0

W0 Q1 W1 Q2 Q3 W2 W F2 c. (1-c). µ c. (1-c). µ θ θ θ θ e.λ (e-1). λ µ 2. λ (e-2).

slide-10
SLIDE 10 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 10 ' & $ % P erformance Mapping in to Tw
  • States

F W Failure Performance Spectrum in terms of demand satisfied h 1.0 Functioning System States

X ( ) = 8 < : W ; if
  • h;
F ; if
  • <
h.
slide-11
SLIDE 11 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 11 ' & $ % P erformance Mapping in to Multiple States

Full Performance Failure Performance Spectrum in terms of demand satisfied h 1.0 Functioning with Functioning with Partial Performance System States S K1 K2 Km F

~ X ( ) = 8 > > < > > : S; if
  • =
100%; K i ; if b i
  • <
b i1 i = 1; 2; :::; m; F ; if
  • <
h.
slide-12
SLIDE 12 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 12 ' & $ % The Mo del

S0 S1 S2 K1.1 K1.2 K1.m K2.1 K2.2 K2.m F1 F2

Stage 0 Stage1 Stage2

F l K .m K .2 K .1 S l l l l

Stage l

QS1 QS2 QK2.2 QK2.m QS3 QK3.1 QK3.2 QK3.m QK2.1 θ λ e. µ µ µ µ

slide-13
SLIDE 13 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 13 ' & $ % Run-Time Complexit y
  • Steady-state
Beha vior { Balance equations { Linear equation system
  • T
ransien t Beha vior { Kolmogoro v equations { Dieren tial equation system
  • Adaptiv
e Runge-Kutta metho d
  • Rate
  • f
c hange
  • Iteration
in terv al
slide-14
SLIDE 14 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 14 ' & $ % What Driv es the Complexit y
  • Num
b er
  • f
states in the mo del { Mo del parameters: l and m
  • Time
span
  • f
the transien t b eha vior
  • Num
b er
  • f
iterations { T ransition rates
slide-15
SLIDE 15 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 15 ' & $ % Eect
  • f
Discrepancy in T ransition Rates
  • Num
b er
  • f
iterations

2 4 6 −3 −2 −1 1 2 3 2 3 4 5 6 7 8 9 10 11 12 log(rest. rate/repair rate) log(number of iterations) log(rest. rate/failure rate)

  • Time
to in tegrate

2 4 6 −3 −2 −1 1 2 3 −2 2 4 6 8 10 12 log(rest. rate/failure rate) log(rest. rate/repair rate) log(time to integrate)

  • Determines
the transien t b eha vior
slide-16
SLIDE 16 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 16 ' & $ % Eect
  • f
Mo del P arameters
  • s(l
; m) = m(2l
  • 1)
+ 3l + 4

5 10 15 20 5 10 15 20 200 400 600 800 1000 parameter: m parameter: l number of states in the model

slide-17
SLIDE 17 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 17 ' & $ % Options to Accelerate the Run-Time
  • Beha
vioral decomp
  • sition
{ Near-complete decomp
  • sition
  • Imp
  • rtance
sampling { Needs go
  • d
heuristics
  • State
Aggregation { F using states
slide-18
SLIDE 18 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 18 ' & $ % State Aggregation
  • In
ter-arriv al time for b
  • th
failure and restoration are exp
  • nen
tiall y distributed
  • Aggregation
  • f
w
  • rking
and restoration states

W Q

µ λ Θ Θ Θ . k1 . k2 . kn

C

µ α α α . k1 . k2 . kn

  • =
  • +
slide-19
SLIDE 19 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 19 ' & $ % The Reduced Mo del

F l K .m K .2 K .1 S l l l l

Stage l

S0 S1 S2 K1.1 K1.2 K1.m K2.1 K2.2 K2.m F1 F2

Stage 0 Stage1 Stage2

µ µ µ µ + λ e. θ

slide-20
SLIDE 20 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 20 ' & $ % Reduction in T ransition Rate Ratio F unctions to quan tify the eect
  • f
transition rates
  • F
  • r
the
  • riginal
mo del: g (; ; ) = max(j log
  • j;
j log
  • j;
j log
  • j)
  • F
  • r
the reduced mo del: g (; ; ) = j log
  • +
  • j

1 2 3 4 5 −3 −2 −1 1 2 3 2 4 6 8 log(rest. rate/failure rate) log(rest. rate/repair rate) g 1 2 3 4 5 −3 −2 −1 1 2 3 2 4 6 8 log(rest. rate/failure rate) log(rest. rate/repair rate) g’

slide-21
SLIDE 21 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 21 ' & $ % Reduction in Num b er
  • f
States F unctions to quan tify the eect
  • f
mo del parameters
  • F
  • r
the
  • riginal
mo del: s(m; l ) = m(2l
  • 1)
+ 3l + 4
  • F
  • r
the reduced mo del: s (m; l ) = ml + 3l + 1

5 10 15 20 5 10 15 20 200 400 600 800 1000 number of states in the original model m l 5 10 15 20 5 10 15 20 200 400 600 800 1000 number of states in the reduced model m l

slide-22
SLIDE 22 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 22 ' & $ % Net w
  • rks
Used in the Exp erimen tal Study
  • New
Jersey Net w
  • rk

1 2 3 4 5 6 7 8 9 10 11 53(20) 48(26) 47(17) 53(20) 74(22) 71(43) 55(16) 52(0) 16(6) 81(23) 41(10) 16(7) 71(33) 68(15) 50(24) 48(26) 57(26) 64(30) 65(29) 59(15) 34(8) 51(27) 78(29)

  • US
Net w
  • rk

6 7 8 16 19 20 21 24 2 3 4 1 5 9 10 11 12 13 14 15 17 18 22 25 23 26 27 28 1 4 6 3 5 1 5 3 5 5 4 5 5 6 6 4 4 4 2 3 1 7 8 1 6 3 5 1 1 7 5 4 3 4 1 7 6 2 4 1 6 7 6 4 8 2

slide-23
SLIDE 23 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 23 ' & $ % Mo dels Used: M(3,0.5,4)
  • Original
Mo del
  • 30
State

Stage 0 Stage1 Stage2

θ λ e. µ µ µ µ

1 2 3 4 5 6 7 8 9 10 14 15 16 17 18 19 20 25 26 27 28 29 30 13 12 11 23 24 22 21

Stage3

  • Reduced
Mo del
  • 19
State

Stage 0 Stage1 Stage2

θ λ e. µ µ µ µ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Stage3

slide-24
SLIDE 24 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 24 ' & $ % Iterations for the Original & Reduced Mo dels
  • New
Jersey Net w
  • rk
Sim ulated Num b er
  • f
steps analysis Original Reduced p erio d (hr) (30 State) (19 State) 1 1295 18 2 2586 19 3 3878 22 4 5168 24 5 6460 25 6 7752 26 7 9043 27 8 10335 28 9 11626 29 10 12917 32 20 25831 72 50 77485 183 100 129141 368
  • US
Net w
  • rk
Sim ulated Num b er
  • f
steps analysis Original Reduced p erio d (hr) (30 State) (19 State) 1 821 18 2 1636 21 3 2452 25 4 3267 27 5 4082 29 6 4897 31 7 5714 32 8 6530 33 9 7346 34 10 8162 34 20 16320 63 50 40791 152 100 68014 301
slide-25
SLIDE 25 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 25 ' & $ % Run-Time for the Original & Reduced Mo dels
  • New
Jersey Net w
  • rk
Sim ulated Run-Time (hr:min:sec) analysis Original Reduced p erio d (hr) (30 State) (19 State) 1 00:03:49 00:00:00.23 2 00:08:56 00:00:00.21 3 00:15:27 00:00:00.24 4 00:23:10 00:00:00.26 5 00:32:25 00:00:00.28 6 00:51:64 00:00:00.29 7 00:57:11 00:00:00.30 8 01:16:21 00:00:00.58 9 01:26:40 00:00:00.45 10 01:58:19 00:00:00.70 20 02:48:32 00:00:04 50 06:25:11 00:00:08 100 46:38:46 00:00:19
  • US
Net w
  • rk
Sim ulated Run-Time (hr:min:sec) analysis Original Reduced p erio d (hr) (30 State) (19 State) 1 00:00:42 00:00:00.21 2 00:01:42 00:00:00.23 3 00:03:05 00:00:00.28 4 00:04:51 00:00:00.30 5 00:07:13 00:00:00.32 6 00:09:35 00:00:00.35 7 00:12:30 00:00:00.52 8 00:16:25 00:00:00.61 9 00:20:27 00:00:00.71 10 00:24:11 00:00:00.57 20 00:38:03 00:00:03 50 01:42:23 00:00:07 100 12:15:22 00:00:17
slide-26
SLIDE 26 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 26 ' & $ % Reliabilit y
  • f
the Exp erimen tal Net w
  • rks
  • New
Jersey Net w
  • rk

Original Model (30_state) Reduced Model (19_state) 10 20 30 40 50 60 70 80 90 100 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 time (hour) Reliability(t)

  • US
Net w
  • rk

Original Model (30_state) Reduced Model (19_state) 2 4 6 8 10 12 0.4 0.5 0.6 0.7 0.8 0.9 1 time (hour) Reliability(t)

slide-27
SLIDE 27 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 27 ' & $ % Av ailabilit y
  • f
the Exp erimen tal Net w
  • rks
Av ailabilit y Exp erimen tal Net w
  • rks
Original Mo del Reduced Mo del (30 State) (19 State) \New Jersey" net w
  • rk
0.999833389 953 0.9998334109 15 \US" net w
  • rk
0.98434267 72 0.984346150
slide-28
SLIDE 28 Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 28 ' & $ % Conclusion
  • Ma
jor run-time reduction { Order
  • f
thousands
  • Minor
accuracy lost { Order
  • f
10 6
  • Non
div ergen t transien t b eha vior
  • Complemen
tary use
  • f
b
  • th
mo dels