Joining strategies under two kinds of games for a multiple vacations retrial queue with N-policy and breakdowns
Motivated by cost control and information guidance, in this work, we study a multiple vacations retrial queue with N-policy and breakdowns. This service system has the characteristics that there is no waiting space in front of the server and the waiting list is virtual. If the arriving customer find...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2021-06-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021527?viewType=HTML |
| _version_ | 1819098197247655936 |
|---|---|
| author | Zhen Wang Liwei Liu Yuanfu Shao Yiqiang Q. Zhao |
| author_facet | Zhen Wang Liwei Liu Yuanfu Shao Yiqiang Q. Zhao |
| author_sort | Zhen Wang |
| collection | DOAJ |
| description | Motivated by cost control and information guidance, in this work, we study a multiple vacations retrial queue with N-policy and breakdowns. This service system has the characteristics that there is no waiting space in front of the server and the waiting list is virtual. If the arriving customer finds that the system is available, he immediately receives the complete service. Otherwise, the customer leaves the system or joins the orbit (virtual waiting list). For cost control, the system is activated only when the current vacation is completed and at least N customers are waiting in the system, otherwise, the server continues to the next vacation until the number of customers in the system is not less than N. Two types of customer joining cases apply to this paper, i.e., non-cooperative customers aim to optimize individual interests, and the social planner in the cooperative case considers the profit of the whole service system. The equilibrium joining strategy for the non-cooperative case and the socially optimal joining strategy for the cooperative case are determined. Since it is difficult to obtain analytical characterization, an improved particle swarm optimization (PSO) algorithm is used to explore the impact of system parameters on the profit of the service provider. At the same time, a large number of numerical experiments visualize the influence of parameters on the system. |
| first_indexed | 2024-12-22T00:27:09Z |
| format | Article |
| id | doaj.art-fef5f1ca750647cead6f2b5e3f44a9a0 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-22T00:27:09Z |
| publishDate | 2021-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-fef5f1ca750647cead6f2b5e3f44a9a02022-12-21T18:45:02ZengAIMS PressAIMS Mathematics2473-69882021-06-01689075909910.3934/math.2021527Joining strategies under two kinds of games for a multiple vacations retrial queue with N-policy and breakdownsZhen Wang0Liwei Liu1Yuanfu Shao 2Yiqiang Q. Zhao31. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, Guangxi, China2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China3. School of Science, Guilin University of Technology, Guilin 541004, Guangxi, China4. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, CanadaMotivated by cost control and information guidance, in this work, we study a multiple vacations retrial queue with N-policy and breakdowns. This service system has the characteristics that there is no waiting space in front of the server and the waiting list is virtual. If the arriving customer finds that the system is available, he immediately receives the complete service. Otherwise, the customer leaves the system or joins the orbit (virtual waiting list). For cost control, the system is activated only when the current vacation is completed and at least N customers are waiting in the system, otherwise, the server continues to the next vacation until the number of customers in the system is not less than N. Two types of customer joining cases apply to this paper, i.e., non-cooperative customers aim to optimize individual interests, and the social planner in the cooperative case considers the profit of the whole service system. The equilibrium joining strategy for the non-cooperative case and the socially optimal joining strategy for the cooperative case are determined. Since it is difficult to obtain analytical characterization, an improved particle swarm optimization (PSO) algorithm is used to explore the impact of system parameters on the profit of the service provider. At the same time, a large number of numerical experiments visualize the influence of parameters on the system.https://www.aimspress.com/article/doi/10.3934/math.2021527?viewType=HTMLtwo joining casesmultiple server vacationsbreakdownsjoining strategiesimproved pso algorithm |
| spellingShingle | Zhen Wang Liwei Liu Yuanfu Shao Yiqiang Q. Zhao Joining strategies under two kinds of games for a multiple vacations retrial queue with N-policy and breakdowns AIMS Mathematics two joining cases multiple server vacations breakdowns joining strategies improved pso algorithm |
| title | Joining strategies under two kinds of games for a multiple vacations retrial queue with N-policy and breakdowns |
| title_full | Joining strategies under two kinds of games for a multiple vacations retrial queue with N-policy and breakdowns |
| title_fullStr | Joining strategies under two kinds of games for a multiple vacations retrial queue with N-policy and breakdowns |
| title_full_unstemmed | Joining strategies under two kinds of games for a multiple vacations retrial queue with N-policy and breakdowns |
| title_short | Joining strategies under two kinds of games for a multiple vacations retrial queue with N-policy and breakdowns |
| title_sort | joining strategies under two kinds of games for a multiple vacations retrial queue with n policy and breakdowns |
| topic | two joining cases multiple server vacations breakdowns joining strategies improved pso algorithm |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021527?viewType=HTML |
| work_keys_str_mv | AT zhenwang joiningstrategiesundertwokindsofgamesforamultiplevacationsretrialqueuewithnpolicyandbreakdowns AT liweiliu joiningstrategiesundertwokindsofgamesforamultiplevacationsretrialqueuewithnpolicyandbreakdowns AT yuanfushao joiningstrategiesundertwokindsofgamesforamultiplevacationsretrialqueuewithnpolicyandbreakdowns AT yiqiangqzhao joiningstrategiesundertwokindsofgamesforamultiplevacationsretrialqueuewithnpolicyandbreakdowns |