DISCRETE-TIME Geo/G/1 RETRIAL QUEUES WITH GENERAL RETRIAL TIME AND BERNOULLI VACATION

• Published in: Journal of systems science and complexity Vol. 25; no. 3; pp. 504 - 513
• Main Author: Wang, Jinting
• Format: Journal Article
• Language: English
• Published: Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.06.2012
• Subjects: Bernoulli; Complex Systems; Control; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Statistics; Systems Theory; 休假; 排队系统; 搜索过程; 服务器; 离散时间; 轨道系统; 马尔可夫链; vacation; stochastic decomposition; Discrete-time queue; general retrial time; retrial queue
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-012-0254-7

This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.