Study of Probabilistic Worst Case Inter-Beacon Delays Under Realistic Vehicular Mobility Conditions

Road safety applications are one of the main incentives to deploy vehicular networks. These applications rely on periodic message exchange among vehicles (known as beaconing). The beacon messages contain information about the environment which is used to perceive dangerous situations and alert the drivers. The inter-beacon delay is the time between two consecutive beacons received from a car. It is an essential parameter because, if this delay exceeds the application requirement, the application cannot accurately predict dangerous situations and alert the drivers on time. The worst case inter-beacon delay has thus to be bounded according to the application requirements. Unfortunately, a tight and strict bound is in fact very difficult to obtain for a real network because of the randomness of the collisions among beacons coming from: the unpredictable mobility patterns, random interferences, randomness of the MAC layer backoff, etc. In this paper, we propose to provide a probabilistic worst-case of the inter-beacon delay under realistic mobility using Extreme Value Theory (EVT). EVT provides statistical tools which allow to make predictions on extreme deviations from the average of a parameter. These statistical predictions can be made based on data gathered from simulation or experimentation. We first introduce the EVT technique. Then we discuss its application to the study of inter-beacon delays. Finally, we apply EVT on the results of extensive vehicular network simulation using a realistic mobility trace: the Cologne trace.