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首页> 外文期刊>International journal of stochastic analysis >A finite capacity queue with Markovian arrivals and two servers with group services
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A finite capacity queue with Markovian arrivals and two servers with group services

机译：具有Markovian到达和两个具有组服务的服务器的有限容量队列

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In this paper we consider a finite capacity queuing system in which arrivals are governed by a Markovian arrival process. The system is attended by two exponential servers, who offer services in groups of varying sizes. The service rates may depend on the number of customers in service. Using Markov theory, we study this finite capacity queuing model in detail by obtaining numerically stable expressions for (a) the steady-state queue length densities at arrivals and at arbitrary time points; (b) the Laplace-Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. The stationary waiting time distribution is shown to be of phase type when the interarrival times are of phase type. Efficient algorithmic procedures for computing the steady-state queue length densities and other system performance measures are discussed. A conjecture on the nature of the mean waiting time is proposed. Some illustrative numerical examples are presented.
机译：在本文中，我们考虑了一个有限容量排队系统，其中到达由Markovian到达过程控制。该系统由两个指数服务器参与，它们以不同大小的组提供服务。服务费率可能取决于服务客户的数量。使用马尔可夫理论，我们通过获得以下数值稳定表达式来详细研究此有限容量排队模型：（a）到达和任意时间点的稳态队列长度密度; （b）准入客户在到达点的固定等待时间分布的Laplace-Stieltjes变换。当到达间隔时间是相位类型时，静止等待时间分布显示为相位类型。讨论了用于计算稳态队列长度密度和其他系统性能指标的有效算法过程。提出了关于平均等待时间性质的猜想。给出了一些说明性的数值示例。

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