Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

[1] E. Altman, U. Yechiali, Analysis of customers’ impatience in queues with server vacation, Queueing Syst, 52(2006), 261–279.10.1007/s11134-006-6134-x Search in Google Scholar

[2] E. Altman, U. Yechiali, Infinite server queues with systems’ additional task and impatient customers, Probab. Eng. Inf. Sci, 22(4) (2008), 477–493.10.1017/S0269964808000296 Search in Google Scholar

[3] S. I. Ammar, Transient solution of an M/M/1 vacation queue with a waiting server and impatient customers, Journal of the Egyptian Mathematical Society, 25(3) (2017), 337–342.10.1016/j.joems.2016.09.002 Search in Google Scholar

[4] G. Ayyappan, J. Udayageetha, Transient solution of M^[X₁], M^[X₂]/G₁,G₂/1 with priority services, modified Bernoulli vacation, Bernoulli feedback, breakdown, delaying repair and reneging, Appl. Appl. Math, 12(2) (2017), 633–657.10.1504/IJMOR.2023.10056402 Search in Google Scholar

[5] Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations, Oper. Res. Lett, 33(2) (2005), 201–209.10.1016/j.orl.2004.05.006 Search in Google Scholar

[6] Y. Baba, The M^X/M/1 queue with multiple working vacation, Am. J. Oper. Res, 2(2) (2012), 217–224.10.4236/ajor.2012.22025 Search in Google Scholar

[7] M. Baruah, K. C. Madan, T. Eldabi, A two stage batch arrival queue with reneging during vacation and breakdown periods, American Journal of Operations Research, 3 (2013), 570–580.10.4236/ajor.2013.36054 Search in Google Scholar

[8] A. Bhagat, M. Jain, N-policy for M^X/G/1 unreliable retrial G-queue with preemptive resume and multi-services, J. Oper. Res. Soc. China, 4(2016), 437–459.10.1007/s40305-016-0128-0 Search in Google Scholar

[9] A. A. Bouchentouf, A. Guendouzi, Cost optimization analysis for an M^X/M/c vacation queueing system with waiting servers and impatient customers, SeMA Journal, 76 (2019), 309–341.10.1007/s40324-018-0180-2 Search in Google Scholar

[10] A. A. Bouchentouf, A. Guendouzi, The M^X/M/c Bernoulli feedback queue with variant multiple working vacations and impatient customers: performance and economic analysis, Arab. J. Math., 9, (2020), 309–327.10.1007/s40065-019-0260-x Search in Google Scholar

[11] A. A. Bouchentouf, A. Guendouzi, S. Majid, On impatience in M/M/1/N/DWV queue with vacation interruption, Croatian Operational Research Review, 11(1) (2020), 21–37.10.17535/crorr.2020.0003 Search in Google Scholar

[12] A. A. Bouchentouf, L. Yahiaoui, On feedback queueing system with reneging and retention of reneged customers, multiple working vacations and Bernoulli schedule vacation interruption, Arab. J.Math., 6 (2017), 1–11.10.1007/s40065-016-0161-1 Search in Google Scholar

[13] O. J. Boxma, S. Schlegel, U. Yechiali, On an M/G/1 queue with a waiting server timer and vacations, American Mathematical society Translations, 2(207) (2002), 25–35.10.1090/trans2/207/02 Search in Google Scholar

[14] M. Jain, A. Jain, Working vacations queueing model with multiple types of server breakdowns, Appl. Math. Model, 34(1) (2010), 1–13.10.1016/j.apm.2009.03.019 Search in Google Scholar

[15] M. Jain, S. Rani, M. Singh, Transient analysis of Markov feedback queue with working vacation and discouragement. In: Deep K., Jain M., Salhi S. (eds) Performance prediction and analytics of fuzzy, reliability and queuing models. Asset analytics (Performance and safety management). Springer, Singapore, (2019).10.1007/978-981-13-0857-4_18 Search in Google Scholar

[16] R. F. Khalaf, K. C. Madan, C. A. Lukas, An M^X/G/1 with Bernoulli Schedule General Vacation Times, General Extended Vacations, Random Breakdown, General Delay Time for Repairs to Start and General Repair Times, Applied Mathematical Sciences, 3(4) (2011), 35–51.10.5539/jmr.v3n4p8 Search in Google Scholar

[17] W. M. Kempa, M. Kobielnik, Transient solution for queue-size distribution in a certain finite-bu er model with server working vacations, In International Conference on Information and Software Technologies, CCIS, (2016), 426–440.10.1007/978-3-319-46254-7_34 Search in Google Scholar

[18] S. Majid, P. Manoharan, Stationary analysis of a multiserver queue with multiple working vacation and impatient customers, App. App. Math., 12(2) (2017), 658–670. Search in Google Scholar

[19] R. Padmavathy, K. Kalidass, K. Ramanath, Vacation queues with impatient customers and a waiting server, Int. Jour. of Latest Trends in Soft. Eng., 1(1) (2011), 10–19. Search in Google Scholar

[20] L. D. Servi, S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Perform. Eval., 50(1) (2002), 41–52.10.1016/S0166-5316(02)00057-3 Search in Google Scholar

[21] C. J. Singh, M. Jain, B. Kumar, Analysis of MX/G/1 queueing model with balking and vacation, Int. J. Oper. Res., 19(2) (2014), 154–173.10.1504/IJOR.2014.058952 Search in Google Scholar

[22] R. Sudhesh, A. Azhagappan, S. Dharmaraja, Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience, RAIRO Oper Re., 51(3) (2017), 591–606.10.1051/ro/2016046 Search in Google Scholar

[23] R. Sudhesh, L. F. Raj, Computational analysis of stationary and transient distribution of single server queue withworking vacation, Glob Trends Computers Commun Sys Commun Comput Info Sci., 269 (2012), 480–489.10.1007/978-3-642-29219-4_55 Search in Google Scholar

[24] P. Vijaya Laxmi, K. Jyothsna, Impatient customer queue with Bernoulli schedule vacation interruption, Computers and Operations Research, 56 (2014), 1–7.10.1016/j.cor.2014.08.018 Search in Google Scholar

[25] P. Vijaya Laxmi, P. Rajesh, Analysis of variant working vacations queue with customer impatience, International Journal of Management Science and Engineering Management, 12(3) (2017), 186–195.10.1080/17509653.2016.1218306 Search in Google Scholar

[26] L.Yahiaoui, A.A. Bouchentouf, M. Kadi, Optimum cost analysis for an Geo/Geo/c/N feedback queue under synchronous working vacations and impatient customers, Croatian Operational Research Review, 10(2) (2019), 211–226.10.17535/crorr.2019.0019 Search in Google Scholar

[27] D. Yue, W. Yue, Y. Sun, Performance analysis of an M/M/c/N queueing system with balking, reneging and synchronous vacations of partial servers, In The Sixth International Symposium on Operations Research and Its Applications (ISORA’06), Xinjiang, China, (2006), 128–143. Search in Google Scholar

[28] D. Yue, W. Yue, G. Xu, Analysis of customers’ impatience in an M/M/1 queue with working vacations, Journal of Industrial & Management Optimization, 8(4) (2012), 895–908.10.3934/jimo.2012.8.895 Search in Google Scholar

[29] D. Yue, W. Yue, G. Zhao, Analysis of an M/M/c queueing system with impatient customers and synchronous vacations, Journal of Applied Mathematics, Volume 2014, Article ID 893094, 11 pages, doi: 10.1155/2014/893094 Open DOISearch in Google Scholar

[30] H. Zhang, An analysis of the M^X/M/1 queue with multiple working vacations by GI/M/1 type Markov process, Acta Informatica, 55(2018), 613–624.10.1007/s00236-018-0316-y Search in Google Scholar

[31] H. Zhang, G. Zhou, M/M/1 queue with m kinds of di erentiated working vacations, J. Appl. Math. Comput., 54(2017), 213–227.10.1007/s12190-016-1005-z Search in Google Scholar