A practical methodology for defining histograms for predictions and scheduling

Current distributed parallel platforms can provide the resources required to execute a scientific application efficiently. However, when these platforms are shared by multiple users, the performance of the applications using the system may be impacted in dynamic and often unpredictable ways. Performance prediction becomes increasingly difficult due to this dynamic behavior. Even performance modeling techniques that are built specifically for distributed parallel systems often require parameterization by single (point) values. However, in shared environments, point values may provide an inaccurate representation of application behavior due to variations in resource performance. This paper address the use of practical histogram stochastic values to parameterize performance models. Whereas a point value provides a single value representation of a quantity, a stochastic value provides a set of possible values to represent a range of likely behavior. In previous work we investigated using either normal distributions or an upper and lower bound to represent stochastic data. In this work we examine using a combination of those methods, namely histograms, to represent this data. We define a practical approach to using histograms in a production setting, and then give experimental results for a set of applications under different load conditions. 1 Motivation Current distributed parallel platforms can provide the resources required to execute a scientific application efficiently. However, when these platforms are shared by multiple users, the performance of the applications using the system may be impacted in dynamic and often unpredictable ways. In order to obtain good performance, accurate performance prediction models for distributed parallel systems are needed. Most performance prediction models use parameters to describe system and application characteristics such as bandwidth, available CPU, message size, operation counts, etc. Model parameters are generally represented as a single likely value, which we refer to as a point value. For example, a point value for bandwidth might be 7 Mbits/second. In practice, point values are often a best guess, an estimate under ideal circumstances, or a value that is accurate only for a given timeframe. In some situations it may be more accurate to represent system and application characteristics as a range of possible values; for example, bandwidth might be reported as varying between 6 and 8 Mbits/second. We refer to such values as stochastic values. Whereas a point value gives a single value for a quantity, a stochastic value gives a set of values, possibly weighted by probabilities, to represent a range of likely behavior [TK93].