Bounkhel Messaoud, Tadj Lotfi, Hedjar Ramdane
Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia.
Department of Industrial Engineering, Alfaisal University, Riyadh 12714, Saudi Arabia.
Entropy (Basel). 2020 Sep 3;22(9):979. doi: 10.3390/e22090979.
In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level , the server serves customers one a time when the queue length is less than , and in batches of fixed size when the queue length is greater than or equal to . The server is subject to failure when serving either a single or a batch of customers. Service rates, failure rates, and repair rates, depend on whether the server is serving a single customer or a batch of customers. While the analytical method provides the initial probability vector, we use the entropy principle to obtain both the initial probability vector (for comparison) and the tail probability vector. The comparison shows the results obtained analytically and approximately are in good agreement, especially when the first two moments are used in the entropy approach.
本文考虑了一个通用的马尔可夫排队系统。给定一个固定的阈值水平，当队列长度小于该阈值时，服务器一次为一个客户提供服务；当队列长度大于或等于该阈值时，服务器以固定大小的批次为客户提供服务。服务器在为单个客户或一批客户提供服务时可能会发生故障。服务率、故障率和修复率取决于服务器是在为单个客户还是一批客户提供服务。虽然解析方法提供了初始概率向量，但我们使用熵原理来获得初始概率向量（用于比较）和尾概率向量。比较结果表明，解析得到的结果与近似结果吻合良好，特别是当熵方法中使用前两个矩时。
