Estimation and Confidence Intervals for Clock Offset in Networks with Bivariate Exponential Delays

Abstract

There is a large and increasing literature on statistical modeling-based estimation of the offset between two clocks. Recent work has focused on the construction of confidence intervals for offset. However, in most of this work it has been assumed that the network delays that occur during the synchronization process are independent. The network delays are often modeled as independent exponential random variables. Thus, we introduce the use of a bivariate exponential distribution to capture the anticipated correlation between the network delays and derive a maximum likelihood estimator and a confidence interval procedure for the offset parameter. We then illustrate how use of the independent model for network delays can lead to improper inference about the offset parameter.

Keywords:

• Bivariate exponential distributions
• Bootstrap calibration
• Clock offset
• Clock synchronization
• Maximum likelihood estimation

Mathematics Subject Classification:

• Primary 62
• Secondary 94

Acknowledgments

The authors would like to thank Dr. Barry C. Arnold for some helpful suggestions when proving Theorems 3.1 and 3.2.