' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er - PowerPoint PPT Presentation

' $ 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 Departmen t Southern Metho dist Univ ersit y , Dallas, TX 75275, USA z ALCA TEL Corp orate Researc h Cen ter Now at Ric hardson, TX 75081, USA A CM SIGCOMM'98 Septem b er 4, 1998 & %

' $ 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 orks z y Hakki C. Cank a y a and V. S. S. Nair y Computer Science and Engineering Departmen t Southern Metho dist Univ ersit y , Dallas, TX 75275, USA z ALCA TEL Corp orate Researc h Cen ter Now at Ric hardson, TX 75081, USA A CM SIGCOMM'98 Septem b er 1998 & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 3 Presen tation Outline � In tro duction and ob jectiv es � The mo del � Analysis of run-time complexit y � Acceleration tec hnique � Exp erimen tal study and results & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 4 Prelude � T rends in T elecom: f" T ra�c demand g 7� ! f" Sp eed g 7� ! f" Criticali t y g 7� ! { f" Demand in reliabili t y g � Meet the reliabili t y demand F ault forecasting, F ault a v oidance, F ault remo v al, F ault { tolerance, etc. � Need for reliabil i t y ev aluation and mo deling � Previous w ork Prop osed mo del, SRMM/p { Prop osed set of metrics { & %

' $ 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 of the mo del � Analyze the mo del to understand the cause of high complexit y � Study the options to reduce complexit y � Ev aluate the pros & cons � Accelerate the analysis � Examine the impro v emen t & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 6 State Rew ard Mark o v Mo del (SRMM/p) � Mark o 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 & % {

' $ 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) Topology Related Data λ Reliability W Q µ c. θ Event Related Data F µ (1-c). θ Availability Restoration Related Data & %

' $ 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 of 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 of di�eren t p erformance lev els ab o v e h { T rade-o� b et w een complexit y and accuracy { & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 9 The Mo del with Multiple Stages µ 2. µ e. λ c. (e-1). λ c. (e-2). θ θ λ W0 Q1 W1 Q2 W2 Q3 W l (1-c). θ (1-c). θ µ µ F1 F2 F l Stage 0 Stage1 Stage2 Stage l & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 10 P erformance Mapping in to Tw o States 1.0 W Functioning h F Failure 0 Performance Spectrum System States in terms of demand satisfied 8 if � h ; W ; � < ( � ) = X if h . F ; � < : & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 11 P erformance Mapping in to Multiple States Functioning 1.0 S with Full Performance K1 Functioning K2 with Partial Performance Km h F Failure 0 Performance Spectrum System States in terms of demand satisfied 8 if = 100%; S; � > > < ~ ( � ) = X if � = 1 ; 2 ; m ; K ; b � < b i :::; i � 1 i i > & > % if h . F ; � < :

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 12 The Mo del µ e. λ θ S0 QS1 S1 QS2 S2 QS3 S l µ K1.1 QK2.1 K2.1 QK3.1 K .1 l µ K1.2 QK2.2 K2.2 QK3.2 K .2 l µ K1.m QK2.m K2.m QK3.m K .m l F1 F2 F l Stage 0 Stage1 Stage2 Stage l & %

' $ 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 { Di�eren tial equation system { � Adaptiv e Runge-Kutta metho d � Rate of c hange � Iteration in terv al & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 14 What Driv es the Complexit y � Num b er of states in the mo del Mo del parameters: and l m { � Time span of the transien t b eha vior � Num b er of iterations T ransition rates { & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 15 E�ect of Discrepancy in T ransition Rates � Num b er of iterations � Time to in tegrate 12 11 12 10 10 log(number of iterations) 9 log(time to integrate) 8 8 6 7 4 6 5 2 4 0 6 3 6 −2 2 3 4 4 3 2 2 1 1 2 0 2 0 −1 −1 −2 0 −3 −2 log(rest. rate/failure rate) 0 −3 log(rest. rate/repair rate) log(rest. rate/failure rate) log(rest. rate/repair rate) � Determines the transien t b eha vior & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 16 E�ect of Mo del P arameters � s ( l m ) = m (2 l � 1) + 3 l + 4 ; 1000 number of states in the model 800 600 400 200 20 0 15 0 5 10 10 5 15 0 20 parameter: l parameter: m & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 17 Options to Accelerate the Run-Time � Beha vioral decomp osition Near-complete decomp osition { � Imp ortance sampling Needs go o d heuristics { � State Aggregation F using states { & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 18 State Aggregation � In ter-arriv al time for b oth failure and restoration are exp onen tiall y distributed � Aggregation of w orking and restoration states . k1 µ λ Θ µ α . k1 W Q C . k2 Θ α . k2 Θ . kn . kn α = � + � � & %

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 19 The Reduced Mo del µ e. λ + θ S0 S1 S2 S l µ K1.1 K2.1 K .1 l µ K1.2 K2.2 K .2 l µ K1.m K2.m K .m l F1 F2 F l Stage 0 Stage1 Stage2 Stage l & %

' $ 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 e�ect of transition rates � F or the original mo del: � � � (� ; � ) = max ( j log j ; j log j ; j log j ) g �; � � � � F or the reduced mo del: � + � 0 (� ; � ) = j log j g �; � 8 8 6 6 4 4 g’ g 2 2 5 5 0 4 0 4 3 3 3 3 2 2 & % 1 1 2 2 0 0 −1 1 −1 1 −2 −2 0 0 −3 −3 log(rest. rate/failure rate) log(rest. rate/failure rate) log(rest. rate/repair rate) log(rest. rate/repair rate)

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 21 Reduction in Num b er of States F unctions to quan tify the e�ect of mo del parameters � F or the original mo del: s ( m; ) = m (2 l � 1) + 3 l + 4 l � F or the reduced mo del: 0 ( m; ) = + 3 l + 1 s l ml 1000 1000 number of states in the reduced model number of states in the original model 800 800 600 600 400 400 200 200 20 20 0 0 15 15 0 0 5 10 5 10 10 10 5 5 15 15 m m & % 0 0 20 20 l l

' $ Hakki Candan Cank a y a A CM SIGCOMM'98/Septem b er 1998 22 Net w orks Used in the Exp erimen tal Study � New Jersey Net w ork � US Net w ork 2 74(22) 6 18 1 53(20) 1 17 6 5 2 7 6 71(43) 1 55(16) 5 3 4 13 6 3 1 19 4 4 4 6 4 4 5 1 52(0) 16 20 16(7) 3 14 53(20) 48(26) 5 8 5 2 4 4 7 6 1 7 71(33) 2 16(6) 6 7 5 47(17) 4 3 15 24 7 2 41(10) 68(15) 21 6 81(23) 5 9 1 1 7 8 12 48(26) 23 8 6 8 3 59(15) 22 4 57(26) 1 5 50(24) 10 4 11 64(30) 51(27) 3 27 26 5 65(29) 3 9 10 5 25 1 78(29) 34(8) 28 11 & %