ANALYSIS OF THE WAITING TIME IN M^<[X]>/G/1 QUEUES WITH GATED RANDOM ORDER OF SERVICE

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  • ランダム順処理規則に従うゲート式M^<[X]>/G/1 システムの待ち時間の解析
  • ランダム ジュンショリ キソク ニ シタガウ ゲートシキ M X G 1 シス

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Relatively few models of M^<[x]>/G/1 queues, an important extension of M/G/1 queues that permit batch arrivals of messages, have been studied in the literature. In this paper, we consider M^<[x]>/G/1 queues with gated random order of service, for both cases in which the server does not take vacations and in which it does when the queue is empty. For a vacationless model, we use the method of delay cycles analysis to derive the Laplace-Stieltjes transform (LST) of the distribution function (DF) for the message waiting time, and obtain its mean and second moment. For a system with multiple server vacations, we investigate service cycles for a similar analysis. Numerical values for the waiting time are plotted for various settings of parameters, with discussion on its characteristics.

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