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A Preliminary Attempt ECEn 670 Semester Project Wei Dang Jacob Frogget Poisson Processes and Maximum Likelihood Estimator for Cache Replacement

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Outline Motivation Cache replacement algorithms Poisson processes in webserver-based cache Poisson processes in microprocessor-based cache Maximum Likelihood estimator Predicting procedures Simulation and evaluation Results compared to LRU Future work

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Motivation Memory-processor speed gap is getting larger

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One of the Solutions Memory hierarchy L1/L2/L3 closer to chip, less latency, but smaller size Cache replacement Cache is fast but limited in size conflict Good replacement policies needed on contention

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Cache Replacement Algorithms Cache conflict in a 4-way associative cache Set index

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Common Cache Replacement Algorithms Random Least Recently Used (LRU, most widely used) Least Frequently Used FIFO

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Poisson Processes for webserver cache Arrival time of queries to a webserver can be modeled as a Poisson Process Interpretation: the probability of having k queries up to some point of time Assumption Arrivals of queries are independent of each other Not always true but valid for most cases

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Poisson Processes for microprocessor cache Independence assumption invalid References to cache are highly correlated (especially to data cache) Temporal locality Spatial locality

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Poisson Processes for microprocessor cache cont. One Poisson process for each block within a set Set index An example set from a 4-way associative cache

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Poisson Processes for microprocessor cache cont. Correlation between these four random processes Set index Local counters to each block One global counter n for each set

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Maximum Likelihood Estimator The estimate is the arithmetic mean of

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Predicting Procedures Initially each block has Given a previous calculated for block, the estimated is calculated as: Probabilities for replacement is then Replace block with lowest probability Choose randomly on equal probabilities

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Simulation and Evaluation Simulator: MyDLX cache simulator from EE628 Metrics: miss rate for Instruction-cache and Data-Cache Various associativities Five benchmarks Compared to LRU

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Results

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Results not encouraging Sometimes 0% miss rate for both algorithms (might be due the inherent characteristics of benchmarks) Statistical approach worse than LRU for most cases Getting worse for higher associativity (more blocks to predict)

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Analysis of deficiencies of our model Independence model may be inaccurate (even accesses to the same block within a set may not be independent) Local counter is reset to 0 on eviction (history eliminated)

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Future work and challenges More accurate model with more correlation parameters for each Poisson process Implementation complexity (hardware expensive; LRU is already expensive at high associativity) May be implemented as a software cache as a supplement to hardware cache.

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The End Thank you! Questions?

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