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CUSUM statistical monitoring of M/M/1 queues and extensions

机译：CUSUM对M / M / 1队列和扩展的统计监视

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摘要

Many manufacturing and production systems are modeled as queuing systems mainly to investigate the performance metrics such as queue lengths and waiting times. It is observed that since such metrics are often highly stochastic it is difficult to monitor the same using existing methods. In this paper, it is proposed to develop cumulative sum (CUSUM) chart schemes to efficiently monitor the performance of such typical performance metrics of queuing systems. In this regard M/M/1 queues are used to design the required CUSUM chart schemes. The performances of the proposed CUSUM statistical monitoring schemes are compared with those of several alternative methods. It has been demonstrated through extensive numerical studies that the performance of the proposed CUSUM is superior as it responds faster to many shift patterns. Possible extensions of the proposed CUSUM charts to more general queues, such as M/G/1, G/G/1, or M/M/c queues are also discussed. The application of the proposed approach is demonstrated using several case studies. (33 refs.)
机译：许多制造和生产系统都被建模为排队系统，主要用于研究性能指标，例如队列长度和等待时间。可以观察到，由于此类度量通常是高度随机的，因此很难使用现有方法来监视它们。在本文中，建议开发累积总和（CUSUM）图表方案，以有效地监视这种排队系统的典型性能指标的性能。在这方面，M / M / 1队列用于设计所需的CUSUM图表方案。拟议的CUSUM统计监视方案的性能与几种替代方法的性能进行了比较。通过大量的数值研究表明，所提出的CUSUM的性能优越，因为它对许多换档模式的响应速度更快。还讨论了将建议的CUSUM图表扩展到更通用的队列（例如M / G / 1，G / G / 1或M / M / c队列）的可能性。通过几个案例研究证明了所提出方法的应用。 （33参考）

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