Average TimeSync with bounded random time-delay is almost divergent

This paper studies Average TimeSync (ATS) - a time synchronization protocol for wireless sensor networks. In the ideal delay-free condition, the ATS protocol is proved convergent. However, any time synchronization algorithm used in practice is inevitably accompanied by the existence of time delays. This paper studies if the ATS protocol could keep convergent with a bounded steady error under bounded random time-delays. It is proved that in the circumstance of bounded adjustment for clock parameters known as drift and offset, ATS with bounded random time-delay is almost divergent.