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The departure process of a single queue has been studied since the 1960s. Due to its inherent complexity, closed form solutions for the distribution of the departure process are nearly intractable. In this study, kernel type estimators of the density of interdeparture time in a GI/G/1 queue are studied. Uniform strong consistency of the estimators in a GI/G/1 queue and their rates of convergence are obtained. The stochastic processes are shown to satisfy the strong mixing condition with random instants of sampling. With the analysis presented, we provide a novel analytic tool for studying the departure process in a general queueing model.

This study developed a parallel algorithm to efficiently solve linear programming models. The proposed algorithm utilizes the Dantzig-Wolfe Decomposition Principle and can be easily implemented in a general distributed computing environment. The analytical performance of the well-known method, including the speedup upper bound and lower bound limits, was derived. Numerical experiments are also provided in order to verify the complexity of the proposed algorithm. The empirical results demonstrate that the speedup of this parallel algorithm approaches linearity, which means that it can take full advantage of the distributed computing power as the size of the problem increases.