Interval Matrices for the Bottleneck Analysis of Queueing Network Models with Histogram-Based Parameters

Bottleneck analysis using queueing network models is an important technique for the performance analysis and capacity planning of computer and communication systems. Conventional single class as well as multiclass queueing network models use single mean values as input parameters. However, uncertainties and variabilities in service demands may exist in many models. This paper proposes to use extended histograms for characterizing model parameters that are associated with workload uncertainty and/or variability. Because with histogram-based parameters, system bottlenecks need not be unique, methods are presented which produce interval-based bottleneck identification matrices. Additionally, interval matrices for the approximation of potential effects of service demand modifications are presented. With the proposed interval matrix approach, associated input parameter variabilities and uncertainties are also represented in the model output. Thus, model uncertainties are not hidden but an overview of the potential model behavior is provided to the analyst.