Utilization analysis of area based push services

Area based services enable the provisioning of various useful applications for users of smart and transportable wireless mobile clients in defined geographical areas. Special events are generated if clients change their spatial relations to an area, being used for the triggering of certain push services. One of the fundamental questions for the provider of an area based service is the expected number of event occurrences. This type of information is essential for a proper dimensioning of the system, i.e. the corresponding access network resources like bandwidth and processing capabilities. This paper presents an analytical investigation of the problem. We determine the probabilities for mobile clients to enter or leave an area between two consecutive position changes, assuming uniformly distributed user positions and movement directions. Different area sizes and shapes (circular, rectangular and hexagonal) are investigated. Additionally, we evaluate the cases of failed detections, occurring when some clients cross the area in between two successive position updates, and provide some numerical results for different client velocity distributions. The mathematical results have been validated by simulations. [PUBLICATION ABSTRACT]