Performance of the Modified MSE Upper Bounds Under Packet Loss and the gfGn Surroundings for the PTP Scenario

A time synchronization system utilized by computer networks is the PTP. The packet loss phenomenon may cause degradation in the clock skew or offset estimators’ performances from the mean square error (MSE) point of view. Recently, the same authors provided an algorithm for estimating the missing time stamps and MSE upper bounds for the modified clock skew estimators (the two-way delay (TWD) clock skew estimator and the one-way delay (OWD) clock skew estimators for the Forward and Reverse paths). Those MSE upper bounds help to estimate the entire amount of packets required by the system (from the perspective of the MSE) in the event of packet loss. The recently discovered upper bounds for the MSE are applicable to the fractional Gaussian noise (fGn) setting with a Hurst exponent parameter (H) between half and one. However, practical PTP systems may also be characterized as generalized fractional Gaussian noise (gfGn), with the a parameter in the range of 0 < a ≤ 1. The three revised clock skew estimators are tested in this study under the gfGn environment and packet loss scenario, and new MSE upper limits are provided for this case. The newly derived upper limits for the MSE applicable for the gfGn scenario are very useful, as will demonstrated by simulation results.