Paola Bermolen

Quality of service parameters and link operating point estimation based on effective bandwidths

This work addresses the estimation and calculation of the operating point of a networks link in a digital traffic network. The notion of operating point comes from effective bandwidth (EB) theory. The results shown are valid for a wide range of traffic types. We show that, given a good EB estimator, the operating point, i.e. the values of time and space parameters in which the EB is related with the asymptotic overflow probability, can also be accurately estimated. This means that the operating point (and other parameters) inherits the statistical properties of the EB estimation. This affirmation is not an obvious one, because operating point parameters are related with the EB through an implicit function involving extremal conditions computations. Imposing some regularity conditions, a consistent estimator and confidence regions for the operating point and Quality of Service parameters are developed. These conditions are very general, and they are met by commonly used estimators as the averaging estimator presented in [C. Courcoubetis, R. Weber, Buffer overflow asymptotics for a switch handling many traffic sources, J. Appl. Probability 33 (1996)] or the Markov Fluid model estimator presented in [J. Pechiar, G. Perera, M. Simon, Effective bandwidth estimation and testing for Markov sources, Perform. Eval. 48 (2002) 157-175]. Using a software package developed by our group that estimates the EB and other relevant parameters from traffic traces, simulation results are compared with the analytical results, showing very good fitting.

End-to-end quality of service-based admission control using the fictitious network analysis

The performance analysis of a network link is a well-studied problem. However, the most interesting issue for a service provider is to evaluate the end-to-end quality of service (QoS). The evaluation of the end-to-end QoS (e.g. loss probability or delay) depends on the traffic statistic which is constantly modified as the traffic traverse the network, making its analysis a very difficult problem. In this work we use a simplified framework known as fictitious network analysis that allows us to estimate on-line the end-to-end loss ratio from input traffic traces statistics. We prove that the defined estimator is consistent and that a Central Limit Theorem is verified. Based on these estimations an admission control mechanism can be implemented. More precisely, we propose a simply method to estimate the control admission region, i.e. which are the flows that can be accepted in the network that verifies that its end-to-end loss ratio is smaller than a given threshold. While decisions based on the fictitious network analysis are safe, it may lead to network resources under-utilization (it generally overestimates the QoS parameters). In this work we establish sufficient conditions to assure that results obtained by means of the fictitious network coincide with real ones (there is no overestimation). We present first the conditions in the one-link case and extend them to the multilink case, necessary to evaluate the end-to-end loss ratio. When different results are obtained we define a method to find a bound for the overestimation. We also present numerical examples to compare the performance obtained in the real and the fictitious network, validating our main results.

Estimating the Transmission Probability in Wireless Networks with Configuration Models

We propose a new methodology to estimate the probability of successful transmissions for random access scheduling in wireless networks, in particular those using Carrier Sense Multiple Access (CSMA). Instead of focusing on spatial configurations of users, we model the interference between users as a random graph. Using configuration models for random graphs, we show how the properties of the medium access mechanism are captured by some deterministic differential equations when the size of the graph gets large. Performance indicators such as the probability of connection of a given node can then be efficiently computed from these equations. We also perform simulations to illustrate the results on different types of random graphs. Even on spatial structures, these estimates get very accurate as soon as the variance of the interference is not negligible.

Estimating the medium access probability in large cognitive radio networks

Abstract During the last decade we have seen an explosive development of wireless technologies. Consequently the demand for electromagnetic spectrum has been growing dramatically resulting in the spectrum scarcity problem. In spite of this, spectrum utilization measurements have shown that licensed bands are vastly underutilized while unlicensed bands are too crowded. In this context, Cognitive Radio Network emerges as an auspicious paradigm in order to solve those problems. The main question that motivates this work is: what are the possibilities offered by cognitive radio to improve the effectiveness of spectrum utilization? With this in mind, we propose a methodology, based on configuration models for random graphs, to estimate the medium access probability of secondary users. We perform simulations to illustrate the accuracy of our results and we also make a performance comparison between our estimation and one obtained by a stochastic geometry approach.

Scaling Limits and Generic Bounds for Exploration Processes

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.

A Stochastic Geometry Analysis of Multichannel Cognitive Radio Networks

With the explosive development of wireless technologies, the demand of electromagnetic spectrum has been growing dramatically. Therefore, looking for more available spectrum, regulators have already begun to study secondary assignments in licensed bands. In this paper we present a probabilistic model based on a stochastic geometry approach to analyze cognitive radio networks. We focus on those scenarios where more than one band is available, a natural situation in this kind of networks. Quiet surprisingly, and to the best of our knowledge, such scenario has not been deeply explored yet in the literature. In particular we focus our study in the two main performance metrics: medium access probability and coverage probability. We evaluate our proposal through simulations and we present the analytical results of a particular case.