دانلود رایگان مقاله تئوری مقدار افراطی برای بررسی بدترین حالت تاخیر در شبکه های بی سیم

Abstract

Wireless networks are more and more envisioned to be used as a support for critical safety applications. It is notably the case for large scale wireless networks such as vehicular networks, for which safety is one of the main motivations for their development. In this context, the system designer must be able to predict bounds on Quality of Service (QoS) parameters such as delay and delivery ratio. Nevertheless, obtaining strict bounds on such parameters is often difficult because of the unpredictability of the environment (electromagnetic interference, user mobility, etc). Even when the environment is well characterized, the derivation of the bound might be impractical because of the complexity of the models and techniques (the combinatorial explosion problem of model checking is an example) or the bound derived might not be tight (for example with Network Calculus). On the other hand, classic network performance evaluation techniques (stochastic modeling, discrete event simulation, experimentation, etc) usually focus on parameter averages and give very few insights on the extreme deviations from these averages which are of paramount importance for critical applications. In this paper, we propose to use the Extreme Value Theory (EVT) in order to investigate worst case delays in wireless networks. EVT is a statistical tool which allows to make predictions on extreme deviations from the average. These statistical predictions can be made based on data gathered from simulation or experimentation. We first briefly introduce the technique. Then we discuss its application to the study of delays in wireless networks and we illustrate our discussion with a case study: safety applications in vehicular networks.

6. Conclusion and future works

This paper aims at studying large delays in wireless networks using the EVT statistical method. We first discuss the application of EVT to the study of large delays in networks. We then apply the two techniques provided by EVT: BM and POT, to the study of inter-beacon delays in VANETs safety applications. We observe that in the BM case, it is the Frechet distribution family which fits best the distribution of maximum inter-beacon delays. This distribution could thus be used as a model of probabilistic worst case in this context. We also remark that EVT cannot be applied in the case the measured delays are not identically distributed (as for the first considered data set). We study the impact of the block size and the threshold value (resp. for BM and POT method) and observe that to chose too low values can lead to a too optimistic probabilistic worst case delay and thus to overestimate the safety of the system. We conclude that EVT is a powerful tool which allows to estimate large delays in networks. It can be used as a complementary tool to formal methods when they fail to provide results or as a way to double check their results with more realistic system models. EVT allows to deduce a model of the worst case delay based on data samples retrieve from simulation or experimentation. The sampling method is thus of uttermost importance: the sampled executions of the system must be representative of the whole set of its possible behaviors. If it is not the case, the EVT results might be biased. In the future, we plan to investigate the impact of the sampling methods on EVT results.