论文标题
最短的3个Queue投票系统 - 服务最长的政策
A 3-Queue Polling System with Join the Shortest -- Serve the Longest Policy
论文作者
论文摘要
1987年，J.W。科恩分析了所谓的最长队列（SLQ）排队系统，其中一台服务器参加了两个非对称$ m/g/1 $ -type队列，从而行使了非抢先优先转换策略。科恩（Cohen）在1998年进一步分析了一个非对称的2 Queue Markovian系统，新来的客户遵循加入最短的队列（JSQ）学科。当前的论文通过研究合并的JSQ-SLQ模型，并将分析范围扩大到非对称的3 Queue系统，从而概括并扩展了Cohen的作品，在该系统中，到达客户遵循JSQ策略，单个服务器行使了先发制人的优先级SLQ SLQ纪律。该系统指出的多维概率分布函数是在应用基础过程状态空间的非规定表示时得出的。该分析结合了概率生成函数和矩阵几何方法。结果表明，联合JSQ-SLQ操作策略实现了平衡队列大小之间的目标。当计算与平均队列大小之间差异相关的GINI指数时，强调了这一点：系数的值接近零。提出了广泛的数值结果。
In 1987, J.W. Cohen analyzed the so-called Serve the Longest Queue (SLQ) queueing system, where a single server attends two non-symmetric $M/G/1$-type queues, exercising a non-preemptive priority switching policy. Cohen further analyzed in 1998 a non-symmetric 2-queue Markovian system, where newly arriving customers follow the Join the Shortest Queue (JSQ) discipline. The current paper generalizes and extends Cohen's works by studying a combined JSQ-SLQ model, and by broadening the scope of analysis to a non-symmetric 3-queue system, where arriving customers follow the JSQ strategy and a single server exercises the preemptive priority SLQ discipline. The system states' multi-dimensional probability distribution function is derived while applying a non-conventional representation of the underlying process's state-space. The analysis combines both Probability Generating Functions and Matrix Geometric methodologies. It is shown that the joint JSQ-SLQ operating policy achieves extremely well the goal of balancing between queue sizes. This is emphasized when calculating the Gini Index associated with the differences between mean queue sizes: the value of the coefficient is close to zero. Extensive numerical results are presented.
