Group service system with three queues and load balancing

IF 0.3 Q4 MATHEMATICS, APPLIED Discrete Mathematics and Applications Pub Date : 2022-08-01 DOI:10.1515/dma-2022-0019
M. P. Savelov
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引用次数: 0

Abstract

Abstract A group service system for three queues is considered. At each time t = 1, 2, . . ., with some probability, a customer enters the system, selects randomly two queues, and goes to the shorter one. At each moment such that there is at least one customer in each queue, each queue performs instantly the service of one customer. By means of Lyapunov functions, a criterion for the ergodicity of the Markov chain corresponding to this queuing system is established. The limiting joint distribution of queue lengths is found, and the connection with the problem of balanced allocations of particles into cells is described. In the corresponding problem of balanced allocation of particles, the limiting distribution of the range is found, i. e. the difference between the maximal and minimal numbers of particles in cells.
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三队列、负载均衡的群服务系统
摘要考虑了一个具有三个队列的群服务系统。在每个时间t=1、2、…、。,在一定概率下,客户进入系统,随机选择两个队列,然后转到较短的队列。在每个队列中至少有一个客户的时刻,每个队列都会立即执行一位客户的服务。利用李雅普诺夫函数,建立了与该排队系统对应的马尔可夫链遍历性的判据。发现了队列长度的极限联合分布,并描述了与粒子均衡分配到单元中的问题的联系。在相应的粒子平衡分配问题中,发现了范围的极限分布,即细胞中粒子的最大数量和最小数量之间的差异。
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来源期刊
CiteScore
0.60
自引率
20.00%
发文量
29
期刊介绍: The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.
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