Reliability Analysis in HPC clusters

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3 Algorithm for calculatig the time betwee failure for a system of k odes Figure 2 ime betwee failures obtaied from failure logs by removig dowtimes, ad calculatig the differece betwee times., 1 where... = U s 2 1 k2 2 k ode2....odek aretheset of failuretimeso ode1,... U = { = { BF = { s s 1 2 k = {, k i+ 1 k1,..., k i= 1 = { s, s s }, i = 1,2,3... m i k2, hetimebetwee failure(bf) of thek odessystemis: i k3,...},...},...} measthestart timeof secodfailureo odek For a systemof k ode,thefailuretimeset F is 21 = 11 U 12, 22, s s,... s } 2, 3 m Figure 3. ime betwee failures of a system of k odes 5. Compariso Results We calculate the reliability of k odes by aalyzig the time betwee failures of the system comprisig the k odes. he time betwee failures is calculated usig the algorithm give i sectio 4. Differet failure distributio for expoetial, weibull ad logormal are the compared with empirical failure distributio. We assume that parallel programs are usually allocated to 2 processors. We show the time to failure distributios for k = 4, 64, 128 ad 256. We compare the goodess of fit whe odes are selected radomly, ad whe odes are selected i order i able 1. Kolmogorov- Smirov (K-S) goodess of fit test is used to compare the distributios. he K-S goodess of fit test gives the maximum distace betwee the empirical ad theoretical distributio. A p-value equal or less tha 0.05 idicates that the distributio does ot fit the data. able 2 shows the goodess of fit for two cases, whe odes are selected radomly, ad whe odes are selected accordig to ode umber. I both cases of our experimet, weibull is observed to be a better model for reliability of a system of k odes as compared to expoetial ad logormal fit. Distributio Expoetial Weibull CDF F( t) = 1 e λ -e failure rate λt m ( t / c) F( t) = 1 e c - characteristic life, m- shape parameter Distributio Log Normal CDF t l 50 F ( t) = Φ σ σ - shape parameter 50 - medial life at 50% failure poit

4 K = 8 Nodes K = 16 Nodes K = 32 Nodes K = 64 Nodes K = 128 Nodes K = 256 Nodes Figure 4. Compariso of empirical ad Weibull CDFs whe k=4, 64,128 ad 256 odes are selected.

6 [ 6] Lawrece Livermore Natioal Laboratory race Logs: url: [ 7] R. K. Sahoo, A. J. Olier, I. Rish, M. Gupta, J. E. Moreira, S. Ma, R. Vilalta, ad A. Sivasubramaiam. Critical evet predictio for proactive maagemet i large-scale computer clusters. I Proceedigs of the ACM SIGKDD, Itl. Cof. o Kowledge Discovery Data Miig, pages , August [ 8] Schroeder, B. ad Gibso, G. A A largescale study of failures i high-performace computig systems. I Proceedigs of the iteratioal Coferece o Depedable Systems ad Networks, Jue [ 9] op 500 Super Computig Sites List, July 2006, : url: [ 10] Y. Liu ad C. B. Leagsuksu. "Reliabilityaware Checkpoit/Restart Scheme: A Performability rade-off". Submitted to IEEE Cluster Computig (Cluster), Bosto, MA, USA, September [ 11] Yiglug Liag, Yayog Zhag, Aad Sivasubramaiam, Morris Jette, Ramedra Sahoo, "BlueGee/L Failure Aalysis ad Predictio Models," ds, pp , Iteratioal Coferece o Depedable Systems ad Networks (DSN'06), 2006.

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