Extreme value theory for the study of probabilistic worst case delays in wireless networks

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.