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applied approximate arrival assume average system batch Borel set bounded bucket method computational consider constraints convex Corollary cost Coxian distribution defined denote distribution dom(R dynamic programs equations exists exponentially distributed extreme points fair copy feasible fluid flow model given integer iteration Japan Vol Jiro Kondo Journal knapsack problem labels Laplace transform Lemma linear manuscript Markov Markov decision processes Masao Mathematical matrix node number of customers number of jobs obtained Operations Research Society optimal policy optimal solution optimal stopping paper parameter penalty functions period piecewise polymatroid probability Proof quaternary tree queueing system random respectively Restart satisfies sequence server shortest path Simulation Society of Japan solving stable set stationary stationary policy step submodular Table Theorem tion Tokyo tool module total number variable vector Voronoi diagram