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首页> 外文期刊>Performance Evaluation >Overland flow as a queueing process: The B/D/1 queue with an arbitrary service time
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Overland flow as a queueing process: The B/D/1 queue with an arbitrary service time

机译：陆上流动作为排队过程：具有任意服务时间的B / D / 1队列

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摘要

We study the single server B/D/1 FIFO queue with Bernoulli inter-arrival times t (t is an element of 10, 11) and arbitrary deterministic service times (s < 1). This queue is introduced in hydrology to model overland flow generation during a rainfall event on a sloping flat soil surface with infiltration rate distributed randomly in space. The service time, the inter-arrival time and the waiting time stand respectively for the rainfall rate, the infiltration rate and the overland flow-rate. The main performance measure of interest in hydrology is the mean overland flow-rate. Its variation with the rainfall rate is of primary importance for peak-flow forecasting. For this purpose the queue must be solved for any real value of s. Two solutions, one exact and one approximate, are presented. The exact one is developed for rational values of s. The queue is transformed into a discrete time queue with a slot equal to 1/q, where q is the denominator of the irreducible fraction s = p/q (p and q integers). The waiting time and the queue'length distributions are derived, and for each value of p and q there is a characteristic equation to solve inside the unit disk. The approximate, and simpler, solution is an extrapolation of the special case where s is a unit fraction (s = 1/q) to an arbitrary value of s. Simulations show that this extrapolation seems to be acceptable only for the mean and standard deviation of the waiting time. (C) 2016 Elsevier B.V. All rights reserved.
机译：我们研究具有伯努利到达时间t（t是10、11的元素）和任意确定性服务时间（s <1）的单服务器B / D / 1 FIFO队列。该队列被引入水文学中，以模拟在降雨事件期间在坡度平坦的土壤表面上的陆上水流的产生，入渗率在空间中随机分布。服务时间，到达间隔时间和等待时间分别代表降雨率，入渗率和陆上流速。在水文学中感兴趣的主要性能指标是平均陆上流速。其随降雨率的变化对于峰值流量预报至关重要。为此，必须针对s的任何实际值解决队列。提出了两种解决方案，一种是精确的，一种是近似的。为s的有理值开发了一个精确的值。该队列被转换为一个时隙等于1 / q的离散时间队列，其中q是不可约分数s = p / q（p和q整数）的分母。得出等待时间和队列长度分布，并且对于p和q的每个值，都有一个特征方程式要在单位圆盘内部求解。近似且更简单的解决方案是特殊情况的外推，其中s是单位分数（s = 1 / q）到s的任意值。仿真表明，这种推断似乎仅对于等待时间的平均值和标准偏差是可以接受的。 （C）2016 Elsevier B.V.保留所有权利。

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