A DFO technique to calibrate queueing models

A crucial step in the modeling of a system is to determine the values of the parameters to use in the model. In this paper we assume that we have a set of measurements collected from an operational system, and that an appropriate model of the system (e.g., based on queueing theory) has been developed. Not infrequently proper values for certain parameters of this model may be difficult to estimate from available data (because the corresponding parameters have unclear physical meaning or because they cannot be directly obtained from available measurements, etc.). Hence, we need a technique to determine the missing parameter values, i.e., to calibrate the model.As an alternative to unscalable “brute force” technique, we propose to view model calibration as a non-linear optimization problem with constraints. The resulting method is conceptually simple and easy to implement. Our contribution is twofold. First, we propose improved definitions of the “objective function” to quantify the “distance” between performance indices produced by the model and the values obtained from measurements. Second, we develop a customized derivative-free optimization (DFO) technique whose original feature is the ability to allow temporary constraint violations. This technique allows us to solve this optimization problem accurately, thereby providing the “right” parameter values. We illustrate our method using two simple real-life case studies.