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A queuing system with a finite number of input flows controlled by a fixed-time cyclic algorithm is considered. The input flows are formed in a random external environment with finite number of states. The environment is synchronized with the server. In each environment state the input flows are Poisson flows of groups with intensities and size distributions depending on the state. A mathematical model is constructed as a multivariate denumerable Markov chain, necessary and sufficient conditions for the existence of a stationary distributions are found. Martingale sequences are introduced. Using these one can study the mean emptying time for a particular queue.

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Unloading Time Martingale Relations in a Cyclic Queueing System in Random Environment

  • 会议论文

  • 发表日期：

    2025年

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  • Andrei V. Zorine

摘要

A queuing system with a finite number of input flows controlled by a fixed-time cyclic algorithm is considered. The input flows are formed in a random external environment with finite number of states. The environment is synchronized with the server. In each environment state the input flows are Poisson flows of groups with intensities and size distributions depending on the state. A mathematical model is constructed as a multivariate denumerable Markov chain, necessary and sufficient conditions for the existence of a stationary distributions are found. Martingale sequences are introduced. Using these one can study the mean emptying time for a particular queue.