Bi-objective optimization and reliability analysis in unreliable M/G/1 retrial queues with rational customers, reserved idle times and setup times

References

• Akutsu, K., & Phung-Duc, T. (2019). Analysis of retrial queues for cognitive wireless networks with sensing time of secondary users. In International Conference on Queueing Theory and Network Applications, Ghent (pp. 77–91). Springer.
   Google Scholar
• Artalejo, J. R. (1995). A queueing system with returning customers and waiting line. Operations Research Letters, 17(4), 191–199. https://doi.org/10.1016/0167-6377(95)00017-E
   Web of Science ®Google Scholar
• Artalejo, J. R. (2010). Accessible bibliography on retrial queues: Progress in 2000–2009. Mathematical and Computer Modelling, 51(9–10), 1071–1081. https://doi.org/10.1016/j.mcm.2009.12.011
   Google Scholar
• Artalejo, J. R., Economou, A., & Lopez-Herrero, M. J. (2005). Analysis of a multiserver queue with setup times. Queueing Systems, 51(1–2), 53–76. https://doi.org/10.1007/s11134-005-1740-6
   Web of Science ®Google Scholar
• Barroso, L. A., Clidaras, J., & Hölzle, U. (2013). The datacenter as a computer: An introduction to the design of warehouse-scale machines. Synthesis Lectures on Computer Architecture, 8(3), 1–154.
   Google Scholar
• Barroso, L. A., & Hölzle, U. (2007). The case for energy-proportional computing. Computer, 40(12), 33–37. https://doi.org/10.1109/MC.2007.443
   Web of Science ®Google Scholar
• Bischof, W. (2001). Analysis of M/G/1-queues with setup times and vacations under six different service disciplines. Queueing Systems, 39(4), 265–301. https://doi.org/10.1023/A:1013992708103
   Web of Science ®Google Scholar
• Chambari, A., Azimi, P., & Najafi, A. A. (2021). A bi-objective simulation- based optimization algorithm for redundancy allocation problem in series- parallel systems. Expert Systems with Applications, 173, 114745–114753. https://doi.org/10.1016/j.eswa.2021.114745
   Web of Science ®Google Scholar
• Chang, J., & Wang, J. (2018). Unreliable M/M/1/1 retrial queues with set-up time. Quality Technology & Quantitative Management, 15(5), 589–601. https://doi.org/10.1080/16843703.2017.1320459
   Web of Science ®Google Scholar
• Choudhury, G., & Deka, K. (2008). An retrial queueing system with two phases of service subject to the server breakdown and repair. Performance Evaluation, 65(10), 714–724. https://doi.org/10.1016/j.peva.2008.04.004
   Web of Science ®Google Scholar
• Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. https://doi.org/10.1109/4235.996017
   Web of Science ®Google Scholar
• Falin, G., & Templeton, J. G. (1997). Retrial queues (Vol. 75). CRC Press.
   Google Scholar
• Gao, S., Zhang, J., & Wang, X. (2020). Analysis of a retrial queue with two-type breakdowns and delayed repairs. IEEE Access, 8, 172428–172442. https://doi.org/10.1109/ACCESS.2020.3023191
   Web of Science ®Google Scholar
• Garraghan, P., Moreno, I. S., Townend, P., & Xu, J. (2014). An analysis of failure-related energy waste in a large-scale cloud environment. IEEE Trans- Actions on Emerging Topics in Computing, 2(2), 166–180. https://doi.org/10.1109/TETC.2014.2304500
   Web of Science ®Google Scholar
• Hirogaki, M. (2014). Service quality management in retailing: Theory and empirical analysis of customer satisfaction with checkout services. International Journal of Trade, Economics and Finance, 5(3), 270–276. https://doi.org/10.7763/IJTEF.2014.V5.383
   Google Scholar
• Khan, K. N., Scepanovic, S., Niemi, T., Nurminen, J. K., Von Alfthan, S., & Lehto, O. P. (2019). Analyzing the power consumption behavior of a large scale data center. SICS Software-Intensive Cyber-Physical Systems, 34(1), 61–70. https://doi.org/10.1007/s00450-018-0394-7
   Google Scholar
• Liu, T. H., Chang, F. M., Ke, J. C., & Sheu, S. H. (2022). Optimization of retrial queue with unreliable servers subject to imperfect coverage and reboot delay. Quality Technology & Quantitative Management, 19(4), 428–453. https://doi.org/10.1080/16843703.2021.2020952
   Web of Science ®Google Scholar
• Li, K., & Wang, J. (2021). Equilibrium balking strategies in the single-server retrial queue with constant retrial rate and catastrophes. Quality Technology & Quantitative Management, 18(2), 156–178. https://doi.org/10.1080/16843703.2020.1760464
   Web of Science ®Google Scholar
• Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica: Journal of the Econometric Society, 37(1), 15–24. https://doi.org/10.2307/1909200
   Web of Science ®Google Scholar
• Nazarov, A., Moiseev, A., Phung-Duc, T., & Paul, S. (2020). Diffusion limit of multi-server retrial queue with setup time. Mathematics, 8(12), 2232–2252. https://doi.org/10.3390/math8122232
   Web of Science ®Google Scholar
• Phung-Duc, T. (2017). Single server retrial queues with setup time. Journal of Industrial & Management Optimization, 13(3), 1329–1345. https://doi.org/10.3934/jimo.2016075
   Web of Science ®Google Scholar
• Phung-Duc, T., & Kawanishi, K. (2019). Multiserver retrial queue with setup time and its application to data centers. Journal of Industrial & Management Optimization, 15(1), 15–35. https://doi.org/10.3934/jimo.2018030
   Web of Science ®Google Scholar
• Pries, R., Jarschel, M., Schlosser, D., Klopf, M., & Tran-Gia, P. (2011). Power consumption analysis of data center architectures. In International conference on green communications and networking, Colmar (pp. 114–124). Springer.
   Google Scholar
• Sennott, L. I., Humblet, P. A., & Tweedie, R. L. (1983). Mean drifts and the non-ergodicity of Markov chains. Operations Research, 31(4), 783–789. https://doi.org/10.1287/opre.31.4.783
   Web of Science ®Google Scholar
• Tian, R., Wu, X., He, L., Han, Y., & Lopez-Ruiz, R. (2023). Strategic analysis of retrial queues with setup times, breakdown and repairs. Discrete Dynamics in Nature & Society, 2023, 1–19. https://doi.org/10.1155/2023/4930414
   Web of Science ®Google Scholar
• Uchechukwu, A., Li, K., & Shen, Y. (2014). Energy consumption in cloud computing data centers. International Journal of Cloud Computing and Services Science (IJ-CLOSER), 3(3), 31–48.
   Google Scholar
• Wang, J., Cao, J., & Li, Q. (2001). Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Systems, 38(4), 363–380. https://doi.org/10.1023/A:1010918926884
   Web of Science ®Google Scholar
• Wang, J., & Li, L. (2019). Strategic joining in an M/M/1 constant retrial queue with reserved idle time under N-policy. In International Conference of Celebrating Professor Jinhua Cao’s 80th Birthday, Singapore (pp. 374–388). Springer.
   Google Scholar
• Wang, Z., Liu, L., Zhao, Y. Q., Li, L., & Xu, W. (2023). Joining strategies of noncooperative and cooperative in a single server retrial queue with N- policy and multiple server vacations. Communications in Statistics – Theory and Methods, 52(4), 1076–1100. https://doi.org/10.1080/03610926.2021.1923747
   Web of Science ®Google Scholar
• Wang, J., & Zhang, F. (2013). Strategic joining in M/M/1 retrial queues. European Journal of Operational Research, 230(1), 76–87. https://doi.org/10.1016/j.ejor.2013.03.030
   Web of Science ®Google Scholar
• Zhang, Y., & Wang, J. (2017). Equilibrium pricing in an M/G/1 retrial queue with reserved idle time and setup time. Applied Mathematical Modelling, 49, 514–530. https://doi.org/10.1016/j.apm.2017.05.017
   Web of Science ®Google Scholar
• Zhang, Y., & Wang, J. (2023). Managing retrial queueing systems with boundedly rational customers. Journal of the Operational Research Society, 74(3), 748–761. https://doi.org/10.1080/01605682.2022.2053305
   Web of Science ®Google Scholar
• Zhang, F., Wang, J., & Liu, B. (2012). On the optimal and equilibrium retrial rates in an unreliable retrial queue with vacations. Journal of Industrial and Management Optimization, 8(4), 861–875. https://doi.org/10.3934/jimo.2012.8.861
   Web of Science ®Google Scholar
• Zhang, F., Wang, J., & Liu, B. (2013). Equilibrium joining probabilities in observable queues with general service and setup times. Journal of Industrial & Management Optimization, 9(4), 901–917. https://doi.org/10.3934/jimo.2013.9.901
   Web of Science ®Google Scholar
• Zhang, Y., Wang, J., & Wang, F. (2016). Equilibrium pricing strategies in retrial queueing systems with complementary services. Applied Mathematical Modelling, 40(11–12), 5775–5792. https://doi.org/10.1016/j.apm.2016.01.029
   Web of Science ®Google Scholar
• Zhu, S., & Wang, J. (2018). Strategic behavior and optimal strategies in an M/G/1 queue with Bernoulli vacations. Journal of Industrial & Management Optimization, 14(4), 1297–1322. https://doi.org/10.3934/jimo.2018008
   Web of Science ®Google Scholar
• Zhu, S., Wang, J., & Liu, B. (2020). Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs. Operational Research, 20(4), 2163–2187. https://doi.org/10.1007/s12351-018-0407-0
   Web of Science ®Google Scholar