Two-Dimensional Exponential Smoothing for Storage Response Time
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for estimating response time and I/O size in data storage devices are computationally expensive and limited, particularly when dealing with constantly changing conditions and large I/O sizes that span multiple disk zones, as they require frequent recalculations and can only operate on single parameters.
Innovation Solution
A two-dimensional exponential smoothing method that initializes and updates average response time and I/O size estimates using a configurable step size, allowing for continuous estimation of the slope and y-intercept of the linear relationship between response time and I/O size, even in the absence of prior knowledge, by weighting recent measurements more heavily.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If linear regression is used to estimate y-intercept and slope from a data set, then measurement precision is improved, but device complexity and computational cost increase because the entire data set must be re-run each time a new measurement arrives
Solution Approach 1:
The patent segments the estimation problem into two separate one-dimensional estimation problems. Instead of estimating both slope and intercept simultaneously from the linear relationship y=ax+b, the invention estimates the intercept b first, then estimates the slope a separately using the already-estimated intercept. This segmentation transforms a computationally intensive two-parameter problem into two simpler one-parameter problems that can be solved sequentially with less computational overhead.
Solution Approach 2:
The patent applies preliminary action by first estimating the y-intercept b before estimating the slope a. By establishing the intercept estimate first, the subsequent slope estimation can proceed with reduced computational requirements. This preliminary estimation of one parameter simplifies the overall computational process, avoiding the need to re-run complete regression analysis when new measurements arrive.
2Productivity
If traditional exponential smoothing is used to estimate a single parameter, then productivity is improved through efficient single-parameter estimation, but adaptability deteriorates because it cannot operate on multiple parameters simultaneously
Solution Approach 1:
The patent extends the one-dimensional exponential smoothing approach to handle two-dimensional estimation problems. By applying exponential smoothing sequentially in two dimensions - first for the intercept parameter, then for the slope parameter - the invention maintains the computational efficiency of single-parameter smoothing while achieving multi-parameter estimation capability. This dimensional extension allows the system to estimate both slope and intercept efficiently without requiring complex multi-parameter algorithms.
Data Source
AI summary
A method of estimating the average response time and average I/O size that can be used as an alternative for or addition to existing response time and I/O estimation techniques. One method involves initializing values for an average response time and an average I/O size, and initializing an angle. Measurements of the I/O size and response times are received. The technique involves adjusting the average I/O size using the current value of the average I/O size and the received I/O size measurement. The average response time is adjusted using the current value for the average response time and the received response time measurement. The angle value is adjusted using the adjusted average I/O size, the current angle value and the I/O size and time measurements. The slope and y-intercept of a line, formed by plotting the average I/O size verses response time, can then be reported.