Pablo Research Group UIUC Markov Model Prediction of Markov Model Prediction of I/O Requests for Scientific I/O Requests for Scientific Applications Applications James Oly and Daniel A. Reed James Oly and Daniel A. Reed Pablo Research Group Pablo Research Group Department of Computer Department of Computer Science Science University of Illinois University of Illinois {jamesoly,reed}@cs.uiuc.edu {jamesoly,reed}@cs.uiuc.edu 1
Pablo Research Group UIUC Outline = Markov Models for I/O Markov Models for I/O = = Description of Scientific Application Traces Description of Scientific Application Traces = = Trace Trace- -driven Simulations driven Simulations = – Prediction accuracy results Prediction accuracy results – – Cache simulation results Cache simulation results – = Experimental Results Experimental Results = = Summary Summary = 2
Pablo Research Group UIUC Introduction = I/O continues to be a bottleneck in scientific I/O continues to be a bottleneck in scientific = computing computing = Knowledge of the I/O request pattern can be Knowledge of the I/O request pattern can be = crucial to improving performance crucial to improving performance = Exact descriptions of request patterns: Exact descriptions of request patterns: = – May require expensive, multilevel May require expensive, multilevel – instrumentation to capture complex patterns instrumentation to capture complex patterns – May vary due to data dependence or user May vary due to data dependence or user – interaction interaction 3
Pablo Research Group UIUC Markov Models for I/O = Probabilistic models can help Probabilistic models can help = = Markov property: the probability of encountering a Markov property: the probability of encountering a = future state depends solely on the current state future state depends solely on the current state – Little history Little history - -> compact model > compact model – = Each file block is represented by a state in the Each file block is represented by a state in the = model model 4
Pablo Research Group UIUC Example Model 5
Pablo Research Group UIUC Prediction Algorithms = Greedy Greedy = – Always chooses the most likely transition from Always chooses the most likely transition from – last chosen state last chosen state = Path Path- -based based = – Depth Depth- -limited search for most likely path limited search for most likely path – = Amortized Amortized = – Finds most likely state for 1, 2, 3... transitions Finds most likely state for 1, 2, 3... transitions – from current state from current state – Generated using state occupancy vectors and Generated using state occupancy vectors and – Kolmogorov equation: π π (t+1) = (t+1) = π π (t) P (t) P Kolmogorov equation: 6
Pablo Research Group UIUC Application Traces = Cactus Cactus = – Modular environment for numerical relativity Modular environment for numerical relativity – – Small reads (<16 bytes), 65% sequential Small reads (<16 bytes), 65% sequential – = Dyna3D Dyna3D = – Explicit finite Explicit finite- -element code analyzing transient element code analyzing transient – dynamic response of 3D solids and structures dynamic response of 3D solids and structures – 2MB worth of one byte reads, 100% sequential 2MB worth of one byte reads, 100% sequential – 7
Pablo Research Group UIUC Application Traces = CONTINUUM CONTINUUM = – Unstructured mesh continuum mechanics code Unstructured mesh continuum mechanics code – – Widely varying request size, 43% sequential Widely varying request size, 43% sequential – 8
Pablo Research Group UIUC Application Traces = Hartree Hartree- -Fock Fock = – Calculates interactions among atomic nuclei and Calculates interactions among atomic nuclei and – electrons in reaction paths, storing numerical electrons in reaction paths, storing numerical quadrature data for subsequent reuse quadrature data for subsequent reuse – 80KB reads, 100% sequential; read six times 80KB reads, 100% sequential; read six times – = SAR SAR = – Produces surface images from aircraft Produces surface images from aircraft- - or or – satellite- -mounted radar data mounted radar data satellite – 370KB to 2MB requests, 67% sequential 370KB to 2MB requests, 67% sequential – 9
Pablo Research Group UIUC Application Traces = HYDRO HYDRO = – Block Block- -structured mesh hydrodynamics code structured mesh hydrodynamics code – – Widely varying request size, 67% sequential Widely varying request size, 67% sequential – 10
Pablo Research Group UIUC Prediction Accuracy = Judges how accurately the model represents the Judges how accurately the model represents the = original pattern original pattern = A prediction of length L is created before each A prediction of length L is created before each = block request block request = The prediction is compared to the next L blocks The prediction is compared to the next L blocks = actually requested actually requested = The percentages of correctly predicted blocks are The percentages of correctly predicted blocks are = averaged to form the overall accuracy rating averaged to form the overall accuracy rating 11
Pablo Research Group UIUC Prediction Accuracy = Block size and prediction length Block size and prediction length = 12
Pablo Research Group UIUC Prediction Accuracy = Prediction algorithm Prediction algorithm = – Most cases showed little difference between the – Most cases showed little difference between the algorithms, with amortized usually performing slightly algorithms, with amortized usually performing slightly better better – Amortized performed far better for Hartree – Amortized performed far better for Hartree- -Fock Fock 13
Pablo Research Group UIUC Cache Simulation = LRU replacement LRU replacement = = Prefetched blocks inserted at LRU end of the Prefetched blocks inserted at LRU end of the = replacement queue replacement queue = Block sizes ranging from 1 KB to 64 KB Block sizes ranging from 1 KB to 64 KB = = Prediction horizon ranging from 1 to 10 Prediction horizon ranging from 1 to 10 = blocks blocks = Compared hit ratios with N Compared hit ratios with N- -block readahead block readahead = policy policy 14
Pablo Research Group UIUC Cache Simulation = All strategies yield relatively high hit ratios All strategies yield relatively high hit ratios = = Markov model predictions usually have Markov model predictions usually have = slightly higher hit rates, especially for N>1 slightly higher hit rates, especially for N>1 15
Pablo Research Group UIUC Experimental Results = Cactus Cactus = – 50x50x50 grid, 2000 iterations 50x50x50 grid, 2000 iterations – – 2 millions block reads over 2 GB file 2 millions block reads over 2 GB file – = Synthetic Hartree Synthetic Hartree- -Fock Fock = – Synthetic application that mimics Hartree Synthetic application that mimics Hartree- -Fock Fock – – Sequential 80 KB reads to a 2.64 MB file, repeated Sequential 80 KB reads to a 2.64 MB file, repeated – six times six times – ~1 ms compute time between requests ~1 ms compute time between requests – 16
Pablo Research Group UIUC Experimental Results = Applications modified for PPFS 2, our user Applications modified for PPFS 2, our user- -level level = parallel filesystem parallel filesystem = Prediction policies compared Prediction policies compared = – No prefetching No prefetching – – N N- -block readahead block readahead – – Markov model (greedy prediction) Markov model (greedy prediction) – 17
Pablo Research Group UIUC Experimental Results (Cactus) = Execution time decreased by up to 10% compared to Execution time decreased by up to 10% compared to = not prefetching not prefetching = N N- -block readahead was not effective block readahead was not effective = 18
Pablo Research Group UIUC Experimental Results (H-F) = Sequential pattern is ideal for N Sequential pattern is ideal for N- -block readahead block readahead = = Markov model prediction matches its performance Markov model prediction matches its performance = 19
Pablo Research Group UIUC Summary = Markov models can accurately represent the Markov models can accurately represent the = access patterns of scientific applications access patterns of scientific applications – Usually have minimal loss of accuracy over a wide Usually have minimal loss of accuracy over a wide – range of block sizes range of block sizes – More sophisticated prediction policies can reduce More sophisticated prediction policies can reduce – error error = Markov models for prefetching Markov models for prefetching = – Can noticeably reduce the execution time of a Can noticeably reduce the execution time of a – scientific application scientific application – Low overhead Low overhead – 20
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