BMAP/M/∞队列的稳定性条件

Proceedings of the 11th International Conference on Queueing Theory and Network Applications Pub Date : 2016-12-13 DOI:10.1145/3016032.3016046

Moeko Yajima, Tuan Phung-Duc, H. Masuyama

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引用次数: 6

摘要

研究一类具有批量马尔可夫到达过程(BMAP)和服务时间指数分布的BMAP/M/∞队列。首先证明了BMAP/M/∞队列是稳定的当且仅当批大小分布的对数期望是有限的。利用这一结果，我们还给出了一类具有多类批处理马尔可夫到达过程和类相关指数服务时间的无限服务器队列的稳定性条件。

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The stability condition of BMAP/M/∞ queues

This paper considers a BMAP/M/∞ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/∞ queue is stable if and only if the expectation of the logarithm of the batch-size distribution is finite. Using this result, we also present the stability condition for an infinite-server queue with a multiclass batch Markovian arrival process and class-dependent exponential service times.

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Proceedings of the 11th International Conference on Queueing Theory and Network Applications

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