A Low-Computational Burden Closed-Form Approximated Expression for MSE Applicable for PTP with gfGn Environment

The Precision Time Protocol (PTP) plays a pivotal role in achieving precise frequency and time synchronization in computer networks. However, network delays and jitter in real systems introduce uncertainties that can compromise synchronization accuracy. Three clock skew estimators designed for the PTP scenario were obtained in our earlier work, complemented by closed-form approximations for the Mean Squared Error (MSE) under the generalized fractional Gaussian noise (gfGn) model, incorporating the Hurst exponent parameter (H) and the a parameter. These expressions offer crucial insights for network designers, aiding in the strategic selection and implementation of clock skew estimators. However, substantial computational resources are required to fit each expression to the gfGn model parameters (H and a) from the MSE perspective requirement. This paper introduces new closed-form estimates that approximate the MSE tailored to match gfGn scenarios that have a lower computational burden compared to the literature-known expressions and that are easily adaptable from the computational burden point of view to different pairs of H and a parameters. Thus, the system requires less substantial computational resources and might be more cost-effective.