Bounding techniques for queuing network models used to analyze the performance of parallel and distributed computer systems accept single values as model inputs. Uncertainties or variabilities in service demands may exist in many types of systems. Using models with a single aggregate mean value for each parameter for such systems can lead to inaccurate or even incorrect results. This paper proposes to use histograms for characterizing model parameters that are associated with uncertainty and/or variability. The adaptation of the well-known asymptotic bounds as well as balanced job bounds for single class queuing networks to histogram parameters is presented in the paper.

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Parallel Computing
Department of Systems and Computer Engineering

Lüthi, J., Majumdar, S, Kotsis, G., & Haring, G. (1997). Performance bounds for distributed systems with workload variabilities and uncertainties. Parallel Computing, 22(13), 1789–1806.