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 nonlinear 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

Modeling of a slotted mac protocol for manets

Abstract — Global positioning systems like GPS or GALLILEO will soon provide a very good timing accuracy, making possible the synchronization of nodes in a mobile ad hoc network (MANET). With this assumption, TDMA based MAC protocols can provide a very good utilization of the shared radio resources. This paper presents an analytical model for the performance evaluation of slotted MAC protocols with reservation for MANETs. A fully connected network is assumed and nodes generate a ON/OFF exponential traffic. The analysis is based on the study of a discrete time Markov chain. The methodology is applied to a recently proposed protocol, called CROMA [6], but can also be applied, with suitable modifications to any slotted protocol with reservation. I

An Efficient Analytical Model for the Dimensioning of WiMAX Networks

This paper tackles the challenging task of developing a simple and accurate analytical model for performance evaluation of WiMAX networks. The need for accurate and fast-computing tools is of primary importance to face complex and exhaustive dimensioning issues for this promising access technology. In this paper, we present a generic Markovian model developed for three usual scheduling policies (slot sharing fairness, throughput fairness and opportunistic scheduling) that provides closed-form expressions for all the required performance parameters at a click speed. This model is compared in depth with realistic simulations that show its accuracy and robustness regarding the different modeling assumptions. Finally, the speed of our analytical tool allows us to carry on dimensioning studies that require several thousands of evaluations, which would not be tractable with any simulation tool.</p

Performance Evaluation and Dimensioning of WiMAX

International audienceThis chapter tackles the challenging task of performance evaluation and dimensioning of WiMAX networks. It provides a simple analytical model which is able to take into account the effects of elastic traffic, radio channel variations and scheduling policy. Compared to packet-level simulation based evaluations, our model instantaneously delivers the dimension- ing parameters necessary for the deployment of a WiMAX network. Compared to existing analytical solutions, we derive closed-form expressions for all performance metrics. We com- pare the results obtained through analytical model with those of simulations. We show that our analytical model is not only accurate but also robust with respect to the modeling as- sumptions. Finally, the quick results produced through our analytical tool allows to carry out dimensioning analyses that otherwise require several thousands of evaluations, which would not be tractable with any simulation tool.</p