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首页> 外文期刊>International journal of stochastic analysis >Analysis of Queue-Length Dependent Vacations and P-Limited Service in BMAP/G/1/NSystems: Stationary Distributions and Optimal Control
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Analysis of Queue-Length Dependent Vacations and P-Limited Service in BMAP/G/1/NSystems: Stationary Distributions and Optimal Control

机译：BMAP / G / 1 / NSystems中队列长度相关的休假和P限制服务的分析：平稳分布和最优控制

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摘要

We consider a finite-buffer single server queueing system with queue-length dependent vacations where arrivals occur according to a batch Markovian arrival process (BMAP). The service discipline is P-limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit ofLcustomers has been served. Depending on the number of customers present in the system, the server will monitor his vacation times. Queue-length distributions at various epochs such as before, arrival, arbitrary and after, departure have been obtained. Several other service disciplines like Bernoulli scheduling, nonexhaustive service, and E-limited service can be treated as special cases of the P-limited service. Finally, the total expected cost function per unit time is considered to determine locally optimal valuesN*ofNor a maximum limitL^*ofL^as the number of customers served during a service period at a minimum cost.
机译：我们考虑一个具有依赖于队列长度的休假的有限缓冲区单服务器排队系统，其中根据批处理马尔可夫到达过程（BMAP）发生到达。服务准则是P限制服务，也称为E限制，具有限制变化（ELV），其中服务器将服务到服务器，直到清空系统或已满足Lcustomers的随机选择限制为止。根据系统中存在的客户数量，服务器将监视其休假时间。已经获得了各个时期的队列长度分布，例如之前，到达，任意和之后，离开。其他一些服务学科，例如伯努利调度，非穷举服务和限价服务，可以视为限价服务的特殊情况。最后，考虑每单位时间的总预期成本函数，以确定局部最优值N * ofN或最大极限L ^ * ofL ^作为在服务期内以最小成本服务的客户数量。

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