A lower bound for vehicles' trajectory duration

In Palm Calculus, the Palm intensity of a particular transition is the model's expected number of transitions per time unit when considered at stationary regime. Considering transitions as the event of vehicles reaching a waypoint in MANETs' Mobility Models, the Inverse Palm Intensity(IPI) is defined as the mean interval between two waypoints, or the expected time spent by vehicles to reach a predefined target. We propose in this paper to study this Palm intensity because such information might be very useful in MANET for example to efficiently adjust the refreshing intervals of ad hoc routing and topology control protocols. We obtain in this paper a lower bound for the IPI situated roughly at 7 seconds averaged on the Random-Waypoint mobility model (RWM) and the City Section mobility model (CityM), both considered at steady state. Therefore, by setting a refreshing period to this time interval, it is possible to improve the global performance of topology control and routing protocols, since control overhead is reduced.