In general, decision support is one of the main purposes of model-based analysis of systems. Response surface methodology (RSM) is an optimization technique that has been applied frequently in practice, but few automated variants are currently available. In this paper, we show how to combine RSM with numerical analysis methods to optimize continuous time Markov chain models. Among the many known numerical solution methods for large Markov chains, we consider a Gauss-Seidel solver with relaxation that relies on a hierarchical Kronecker representation as implemented in the APNN Toolbox. To effectively apply RSM for optimizing numerical models, we propose three strategies which are shown to reduce the required number of iterations of the numerical solver. With a set of experiments, we evaluate the proposed strategies with a model of a production line and apply them to optimize a class-based queuing system

The representation of general distributions or measured data by phase-type distributions is an important and nontrivial task in analytical modeling. Although a large number of different methods for fitting parameters of phase-type distributions to data traces exist, many approaches lack efficiency and numerical stability. In this paper, a novel approach is presented that fits a restricted class of phase-type distributions, namely, mixtures of Erlang distributions, to trace data. For the parameter fitting, an algorithm of the expectation maximization type is developed. This paper shows that these choices result in a very efficient and numerically stable approach which yields phase-type approximations for a wide range of data traces that are as good or better than approximations computed with other less efficient and less stable fitting methods. To illustrate the effectiveness of the proposed fitting algorithm, we present comparative results for our approach and two other methods using six benchmark traces and two real traffic traces as well as quantitative results from queuing analysis

In general, decision support is one of the main purposes of model-based analysis of systems. Response surface methodology (RSM) is an optimization technique that has been applied frequently in practice, but few automated variants are currently available. In this paper, we propose the combination of RSM with numerical analysis methods to solve continuous time Markov chain models of class-based queueing systems (CBQ). We consider first- and second-order models in RSM to identify an optimal parameter configuration for CBQ as part of the differentiated service architecture. Among the many known numerical solution methods for large Markov chains, we consider a Gauss-Seidel solver with relaxation that relies on a hierarchical Kronecker representation as implemented in the APNN Toolbox. To effectively apply the proposed optimization methodology we determine a suitable configuration of RSM and compare the results with previous results for optimizing CBQ.

The representation of general distributions or measured data by phase-type distributions is an important and non-trivial task in analytical modeling. Although a large number of different methods for fitting parameters of phase-type distributions to data traces exist, many approaches lack efficiency and numerical stability. In this paper, a novel approach is presented that fits a restricted class of phase-type distributions, namely mixtures of Erlang distributions, to trace data. For the parameter fitting an algorithm of the expectation maximization type is developed. The paper shows that these choices result in a very efficient and numerically stable approach which yields phase-type approximations for a wide range of data traces that are as good or better than approximations computed with other less efficient and less stable fitting methods. To illustrate the effectiveness of the proposed fitting algorithm, we present comparative results for our approach and two other methods using six benchmark traces and two real traffic traces.

Presents an efficient and accurate analytical model for the radio interface of the General Packet Radio Service (GPRS) in a GSM network. The model is utilized for investigating how many packet data channels should be allocated for GPRS under a given amount of traffic in order to guarantee appropriate quality of service. The presented model constitutes a continuous-time Markov chain. The Markov model represents the sharing of radio channels by circuit-switched GSM connections and packet-switched GPRS sessions under a dynamic channel allocation scheme. In contrast to previous work, the Markov model explicitly represents the mobility of users by taking into account arrivals of new GSM and GPRS users as well as handovers from neighboring cells. To validate the simplifications necessary for making the Markov model amenable to numerical solution, we provide a comparison of the results of the Markov model with a detailed simulator on the IP level.