Dynamische Verkehrs- und Preismodellierung für den Einsatz in Kommunikationssystemen

This thesis is devoted to investigations that are to be located at the interface between mathematical/theoretical modelling and the application of such models within really implemented platforms and tools. The main focus is directed towards the dynamic modelling of phenomena that are obviously time-dependent but nevertheless have been used to be modelled more or less statically up to now. In this context, we investigate especially two typical examples arising from the areas of traffic and tariff modelling in communication systems, resp. The first example concerns the dynamic modelling of empirically measured traffic presented in terms of Location Updates within a GSM network. After describing the (unfortunately failing) attempts to solve this "reference problem" with the help of classical autoregressive modelling approaches, the view is directed towards the TES (Trans-form-Expand-Sample) method. First, this model is introduced in its usual form. Then a generalization is proposed that turns out to be especially well-suited for modelling periodic traffic patterns with minimal expense. It is demonstrated how important characteristics of the empirical measurements (autocorrelation structure and marginal distribution as well as even the temporal run of the curve) can be modelled in a way that it is possible to use this approach within real-time GSM test environments. Furthermore it is demonstrated how the parametrization of the model may be automatized, before finally some directions of further research are indicated. Summarizing this part, a new approach for modelling periodic traffic has been proposed and evaluated which – under minimal complexity requirements – yields results that show an excellent matching between all practically relevant parameters of model and original measurement. The second part of the thesis deals with dynamic price models in the Internet. After summarizing the state of the art in this area, in a first approach a mathematical model is developped that allows to derive the relationship between resource usage and the charge to be paid for using it. The introduction of asymptotic approximations reduces the complexity of the solutions again in a way that it becomes possible for the first time to numerically calculate price functions for Internet specific scenarios with huge bandwidths and different traffic classes. Alternatively, Internet tariffs can also be derived by using auction based models. Therefore, CHiPS (Connection-Holder-is-Preferred-Scheme) is presented as a new auction mechanism for connections passing through a couple of Inter-net Service Providers. Using simulation results it is demonstrated that CHiPS is able to solve the problems connected with using auctions in multiprovider scenarios. Finally, it is shown how both approaches fit into current research projects, and again directions for further investigations are indicated. As a central result of this second part of the thesis it should be noted that we have successfully described and implemented a mathematical approach to approximate usage-dependent price functions for single resources whose complexity is independent of the resource capacity. Moreover it has been demonstrated how an auction mechanism that is well-known to be efficient for determining the price of single resources may be adapted to the special requirements of the Internet traffic without loosing its excellent properties

Dynamische Verkehrs- und Preismodellierung für den Einsatz in Kommunikationssystemen

This thesis is devoted to investigations that are to be located at the interface between mathematical/theoretical modelling and the application of such models within really implemented platforms and tools. The main focus is directed towards the dynamic modelling of phenomena that are obviously time-dependent but nevertheless have been used to be modelled more or less statically up to now. In this context, we investigate especially two typical examples arising from the areas of traffic and tariff modelling in communication systems, resp. The first example concerns the dynamic modelling of empirically measured traffic presented in terms of Location Updates within a GSM network. After describing the (unfortunately failing) attempts to solve this "reference problem" with the help of classical autoregressive modelling approaches, the view is directed towards the TES (Trans-form-Expand-Sample) method. First, this model is introduced in its usual form. Then a generalization is proposed that turns out to be especially well-suited for modelling periodic traffic patterns with minimal expense. It is demonstrated how important characteristics of the empirical measurements (autocorrelation structure and marginal distribution as well as even the temporal run of the curve) can be modelled in a way that it is possible to use this approach within real-time GSM test environments. Furthermore it is demonstrated how the parametrization of the model may be automatized, before finally some directions of further research are indicated. Summarizing this part, a new approach for modelling periodic traffic has been proposed and evaluated which – under minimal complexity requirements – yields results that show an excellent matching between all practically relevant parameters of model and original measurement. The second part of the thesis deals with dynamic price models in the Internet. After summarizing the state of the art in this area, in a first approach a mathematical model is developped that allows to derive the relationship between resource usage and the charge to be paid for using it. The introduction of asymptotic approximations reduces the complexity of the solutions again in a way that it becomes possible for the first time to numerically calculate price functions for Internet specific scenarios with huge bandwidths and different traffic classes. Alternatively, Internet tariffs can also be derived by using auction based models. Therefore, CHiPS (Connection-Holder-is-Preferred-Scheme) is presented as a new auction mechanism for connections passing through a couple of Inter-net Service Providers. Using simulation results it is demonstrated that CHiPS is able to solve the problems connected with using auctions in multiprovider scenarios. Finally, it is shown how both approaches fit into current research projects, and again directions for further investigations are indicated. As a central result of this second part of the thesis it should be noted that we have successfully described and implemented a mathematical approach to approximate usage-dependent price functions for single resources whose complexity is independent of the resource capacity. Moreover it has been demonstrated how an auction mechanism that is well-known to be efficient for determining the price of single resources may be adapted to the special requirements of the Internet traffic without loosing its excellent properties