Mean value analysis for computer systems with variabilities in workload

When evaluating the performance of computer systems, often uncertainties or variabilities in service demands may be observed. Applying well known mean valve analysis (MVA) for single- or multiclass queueing network models of such systems is inappropriate and ineffective, because these models fail to represent variations within a class. This paper proposes to use histograms for characterizing model parameters that are associated with uncertainty or variability and presents an adaptation of the single class MVA algorithm, which traditionally accepts single (mean) values for service demands, so that one or more input parameters can be specified as a histogram. The adapted algorithm generates a histogram output for the performance measures, thus providing a more detailed information (e.g. percentile values) than the mean valves obtained from conventional MVA. The proposed technique is demonstrated on selected examples in different problem domains. It is shown, that the computational complexity is reasonable given that the number of parameters specified as histograms is not too high. Although the algorithm produces accurate results in many situations inaccuracies have been observed for certain systems. A technique called interval splitting that can be used for controlling such inaccuracies is described.