We introduce a new estimator of the uncertainty of a jackknife estimate of standard error: the jack-knife-after-jackknife (JAJ). Using Monte Carlo simulation, we assess the accuracy of the JAJ in a variety of settings defined by statistic of interest, data distribution, and sample size. For comparison, we also assess the accuracy of the jackknife-after-bootstrap (JAB) estimate of the uncertainty of a bootstrap standard error. We conclude that the JAJ provides a useful new supplement to Tukey's jackknife, and the combination of jackknife and JAJ provides a useful alternative to the combination of bootstrap and JAB.

We introduce a new estimator of the uncertainty of a jackknife estimate of standard error: the jack-knife-after-jackknife (JAJ). Using Monte Carlo simulation, we assess the accuracy of the JAJ in a variety of settings defined by statistic of interest, data distribution, and sample size. For comparison, we also assess the accuracy of the jackknife-after-bootstrap (JAB) estimate of the uncertainty of a bootstrap standard error. We conclude that the JAJ provides a useful new supplement to Tukey's jackknife, and the combination of jackknife and JAJ provides a useful alternative to the combination of bootstrap and JAB.

In this study, we propose a mathematical model based on the graph theory for the wavelength assignment problem arising in the design of SDH (Synchronous Digital Hierarchy) over WDM (Wavelength Division Multiplexing) ring networks. We propose a branch- and -price algorithm to solve the suggested models effectively within reasonable time in realistic SDH over WDM ring networks. By exploiting the structure of ring networks, we developed a polynomial time algorithm for efficient column generation and a branching rule that conserves the structure of column generation. In a computer simulation study, the suggested approach can find the optimal solutions within reasonable time and show better performance than the existing heuristics.

This paper develops channel reallocation methodologies for survival transmission networks, Any failure on a high-speed telecommunication network needs to be restored rapidly and a channel real-location methodology has an important role for the fast restoration. This paper considers the channel reallocation problems under a line restoration with distributed control, where the line restoration restores the failed channels by rerouting the channels along the two alternative routes. The objective is to determine the optimal number of rerouting channels on the alternative rerouting paths of a given transmission network, where the optimality criteria are the first, the last and the mean restoration times. For each criterion, the problem is formulated as a mixed integer programming and the optimal channel reallocation algorithm is suggested based upon the characterization of the optimal solution.