Performance of the modified clock skew estimator and its upper bound for the IEEE 1588v2 (PTP) case under packet loss and fractional Gaussian noise environment

Abstract

Precision Time Protocol (PTP) is a time protocol based on the Master and Slave exchanging messages with time stamps. In practical PTP systems, we have packet loss, a phenomenon where some of the PTP messages get lost in the Network. Packet loss may reduce the performance of the clock skew estimator from the mean square error (MSE) perspective. Recently, the same authors presented simulation results that show the clock skew performance of the three clock skew estimators (the two-way delay (TWD) clock skew estimator and the one-way delay (OWD) clock skew estimator for the Forward and Reverse paths) under the packet loss case in the fractional Gaussian noise (fGn) environment with Hurst exponent parameter (H) in the range of 0.5 ≤ H < 1, where indeed the clock skew performance was degraded compared to the non-packet loss case. Please note that for 0.5 < H < 1, the corresponding fGn is of long-range dependency (LRD). This paper proposes an algorithm that estimates the missing timestamps in the packet loss and fGn (0.5 ≤ H < 1) case. We use those estimates to generate three modified clock skew estimators (the two-way delay (TWD) modified clock skew estimator and the one-way delay (OWD) modified clock skew estimator for the Forward and Reverse paths) applicable to the packet loss, non-packet loss, and fGn (0.5 ≤ H < 1) case based on the same authors’ previously developed clock skew estimators. Those modified clock skew estimators led, based on simulation results, to an improved clock skew performance in the packet loss and fGn (0.5 ≤ H < 1) case compared with the authors’ previously developed clock skew estimators and those known from the literature (the ML-like (MLLE) and Kalman clock skew estimators). With the MSE expression, the system designer can know how many Sync periods are needed for the clock skew synchronization task to reach the system’s requirements from the MSE perspective. But no MSE expression exists in the literature for the packet loss case. In this paper, we derive closed-form approximated expressions for the MSE upper bounds related to the modified TWD and OWD clock skew estimators valid for the packet loss and fGn (0.5 ≤ H < 1) cases.

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

“…In this work, we derive new upper limits for the MSE applicable for the gfGn model where packets may also get lost, with the a parameter in the range of 0 < a ≤ 1. The results of the simulations will demonstrate that the revised MSE upper bounds are in close proximity to the suggested clock skew estimator's performances from [9]. It should be pointed out that up to today, we have in the literature only reference [9] dealing with the packet loss situation, although the packet loss situation is a significant problem in the system design.…”

“…The results of the simulations will demonstrate that the revised MSE upper bounds are in close proximity to the suggested clock skew estimator's performances from [9]. It should be pointed out that up to today, we have in the literature only reference [9] dealing with the packet loss situation, although the packet loss situation is a significant problem in the system design. Without having on hand in advance any indication of the clock synchronization acquisition time that reaches a required MSE level, the whole system can not safely be released into the tracking stage.…”

“…The lost time stamps may decrease the clock skew or offset estimator's performance. Recently, the same authors presented in [9] an algorithm for estimating the missing packets and derived the upper limits for the MSE valid for the three revised clock skew estimators proposed in [9]. The MSE upper limits help to estimate the entire amount of packets required by the system (from the perspective of the MSE).…”

“…Obviously, this is a waste of time if you can approximately have this data in advance without having to carry out any simulation. With the help of the upper limits of the MSE expressions derived in [9] for the fGn case, we can calculate approximately the clock synchronization acquisition time for each required MSE level. But, as already mentioned before, those MSE expressions were derived only for the fGn scenario.…”

“…Thus, having upper limits for the MSE supporting the gfGn model is mandatory. It is important to emphasize that the clock skew estimators presented in [9] are up-to-date, applicable for the gfGn model, for asymmetric H values in the paths, for asymmetric variances in the PDVs, for asymmetric fixed delays, and are robust against the packet loss phenomena. Those estimators are based on the derived estimators from [10] and [11] where [10] is also based on [11].…”