Mean value analysis for queueing network models with intervals as input parameters

Mean value analysis (MVA) is a well-known solution technique for separable closed queueing networks used in performance modeling of computer and communication systems. In many cases, like for sensitivity analysis or with inaccurate model input parameters, intervals are more appropriate as model inputs than single values. This paper presents a version of the MVA algorithm for separable closed queueing networks with one customer class consisting of load-independent queueing centers as well as delay devices, which accepts both single values and intervals as input parameters in an arbitrary combination. Monotonicity of the model outputs with respect to all input parameters is proved and these monotonicity properties are used to construct a low cost interval-version of the MVA algorithm providing exact output intervals as results. Thus, dependency problems commonly arising with the interval evaluation of arithmetic expressions are avoided without significant increase in computation costs. Additionally, asymptotic results for the performance measure intervals obtained through interval-based analysis and corresponding bottleneck analysis are presented.