Operations Research Transactions >
2022 , Vol. 26 >Issue 2: 1 - 15
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2022.02.001
Equilibrium analysis in the retrial queue with an unreliable server
Received date: 2021-10-14
Online published: 2022-05-27
This paper studies customers' equilibrium joining strategy in an M/M/1 constant retrial queue with an unreliable server, where the server may break down under the busy and idle states. In this system, there is no waiting space in front of the server. If a customer finds the server idle upon arrival, he occupies the server immediately. Otherwise, if the server is found busy, the customer can choose to leave a message so that the server can search for customers in the retrial orbit who have left messages before in order to serve them when it is free. Once the server breaks down, the customer being served will be squeezed out of the system and new customers are not allowed to join again. According to the different information provided for customers, this paper investigates the system characteristics at steady state and customers' equilibrium joining strategies based on a reward-cost function. Further, the server's revenue and social welfare functions are established. Through comparisons, it is found revealing the queue length may not bring a greater revenue for the server or a larger social welfare.
Yu ZHANG, Jinting WANG . Equilibrium analysis in the retrial queue with an unreliable server[J]. Operations Research Transactions, 2022 , 26(2) : 1 -15 . DOI: 10.15960/j.cnki.issn.1007-6093.2022.02.001
| 1 | Naor P . The regulation of queue size by levying tolls[J]. Econometrica, 1969, 37 (1): 15- 24. |
| 2 | Edelson N M , Hilderbrand D K . Congestion tolls for poisson queuing processes[J]. Econometrica, 1975, 43 (1): 81- 92. |
| 3 | Hassin R , Haviv M . To Queue or not to Queue: Equilibrium Behavior in Queueing Systems[M]. Boston: Kluwer Academic Publishers, 2003. |
| 4 | Hassin R . Rational Queueing[M]. Boca Raton: CRC Press, 2016. |
| 5 | 王金亭. 排队博弈论基础[M]. 北京: 科技出版社, 2016. |
| 6 | 孙微, 李世勇. 经济学视角下的随机服务系统[M]. 北京: 电子工业出版社, 2017. |
| 7 | Wang J , Zhang F . Strategic joining in M/M/1 retrial queues[J]. European Journal of Operational Research, 2017, 240, 76- 87. |
| 8 | Wang J , Zhang F . Monopoly pricing in a retrial queue with delayed vacations for local area network applications[J]. IMA Journal of Management Mathematics, 2018, 27 (2): 315- 334. |
| 9 | Zhang Y , Wang J , Wang F . Equilibrium pricing strategies in retrial queueing systems with complementary services[J]. Applied Mathematical Modelling, 2016, 40 (11-12): 5775- 5792. |
| 10 | Zhang Y , Wang J . Equilibrium pricing in an M/G/1 retrial queue with reserved idle time and setup time[J]. Applied Mathematical Modelling, 2017, 49, 514- 530. |
| 11 | Economou A , Kanta S . Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue[J]. Naval Research Logistics, 2011, 58 (2): 107- 122. |
| 12 | 张淞钛, 徐秀丽. 具有两类故障特性的M/M/1排队系统均衡分析[J]. 运筹学学报, 2019, 23 (4): 131- 142. |
| 13 | 张淞钛, 徐秀丽. 具有两类平行顾客的不完全故障排队系统均衡分析[J]. 系统科学与数学, 2019, 39 (4): 637- 647. |
| 14 | Wang J , Zhang X , Huang P . Strategic behavior and social optimization in a constant retrial queue with the N-policy[J]. European Journal of Operational Research, 2017, 256 (3): 841- 849. |
| 15 | Zhang Y . Strategic behavior in the constant retrial queue with a single vacation[J]. RAIRO-Operations Research, 2020, 54 (2): 569- 583. |
| 16 | Zhang Z , Wang J , Zhang F . Equilibrium customer strategies in the single-server constant retrial queue with breakdowns and repairs[J]. Mathematical Problems in Engineering, 2014, 2014, 379572. |
| 17 | Wang F , Wang J , Zhang F . Strategic behavior in the single-server constant retrial queue with individual removal[J]. Quality Technology and Quantitative Management, 2015, 12, 323- 340. |
| 18 | 钟瑶, 唐应辉. 具有两类失效模式的D策略M/G/1可修排队系统分析[J]. 运筹学学报, 2020, 24 (1): 40- 56. |
/
| 〈 |
|
〉 |
