Error bounds for performance prediction in queuing networks

Abstract

Analytic models based on closed queuing networks (CQNS) are widely used for performance prediction in practical systems. In using such models, there is always a prediction error, that is, a difference between the predicted performance and the actual outcome. This prediction error is due both to modeling errors and estimation errors, the latter being the difference between the estimated values of the CQN parameters and the actual outcomes. This paper considers the second class of errors; in particular, it studies the effect of small estimation errors and provides bounds on prediction errors based on bounds on estimation errors. Estimation errors may be divided into two types: (1) the difference between the estimated value and the average value of the outcome, and (2) the deviation of the actual value from its average. The analysis first studies the sum of both types of errors, then the second type alone. The results are illustrated with three examples.