Authors: Johannes Luethi and Guenter Haring

  Title: Mean Value Analysis for Queueing Network Models
	 with Intervals as Input Parameters

     In: Performance Evaluation (North Holland, Elsevier Science), 
         Vol.32, No.3, pp.185-215, April 1998.

Abstract:

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
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.

Keywords: Queueing systems; Analytic modeling; Mean value analysis;
          Workload uncertainties; Parameter intervals