Retrial G-queue With Precipitous Breakdown and Non-tenacious Customers
DOI:
https://doi.org/10.2298/YJOR230915001BKeywords:
Retrial queue, bulk arrival, non-tenacious customers, precipitous breakdown, modified Bernoulli vacationAbstract
We perform an analysis on an M/G/1 system that has bulk arrival Poisson process as well as instantaneous service, Precipitous breakdown and random repair, Gqueue, and operation under an MBV (Modified Bernoulli vacation) policy. The positive outcome of a customer retrial is lost when an Anti-positive customer arrives during a positive (good) customer’s assistance period. If a new customer enters and notices that the server is currently undergoing repairs or on vacation, they may renege or balk from the system. To obtain a wide variety of additional outcomes, we use the details provided by the supplementary variable method regarding the rates at which different events occur and it is possible to determine the probability-generating functions of queue length distributions as well as the explicit formulations of important performance metrics. The numerical data confirm the analytical findings about the major performance metrics.References
T. Van Do, “Bibliography on g-networks, negative customers and applications,” Mathematical and Computer Modelling, vol. 53, no. 1, pp. 205-212, 2011. doi: 10.1016/j.mcm.2010.08.006
B. K. Kim and D. H. Lee, “The m/g/1 queue with disasters and working breakdowns,” Applied Mathematical Modelling, vol. 38, no. 5, pp. 1788-1798, 2014. doi: 10.1016/j.apm.2013.09.016
S. P. Madheswari and P. Suganthi, “An m/g/1 retrial queue with second optional service and unreliable server under single exhaustive vacation,” Nonlinear Studies, vol. 24, no. 2, 2017.
C. Ancker and A. V. Gafarian, “Some queuing problems with balking and reneging,” Operations Research, vol. 11, no. 1, pp. 88-100, 1963. doi: 10.1287/opre.11.1.88
A. Choudhury and P. Medhi, “Balking and reneging in multiserver markovian queuing system,” International Journal of Mathematics in Operational Research, vol. 3, no. 4, pp. 377-394, 2011. doi: 10.1504/IJMOR.2011.040874
J. Radha, K. Indhira, and V. Chandrasekaran, “A group arrival retrial g-queue with multi optional stages of service, orbital search and server breakdown,” vol. 263, no. 4, 2017. doi: 10.1088/1757-899X/263/4/042150
K. Madan, “A bulk input queue with a stand-by,” South African Statistical Journal, vol. 29, no. 1, pp. 1-7, 1995.
J. Keilson and L. Servi, “Oscillating random walk models for gi/g/1 vacation systems with bernoulli schedules,” Journal of applied Probability, vol. 23, no. 3, pp. 790-802, 1986. doi: 10.2307/3214016
“The m/g/1 retrial queue with bernoulli schedules and general retrial times,” Computers and Mathematics with Applications, vol. 43, no. 1-2, pp. 15-30, 2002.
R. Tripathi, “Optimal ordering policy under two stage trade credits financing for deteriorating items using discounted cash flow approach,” International Journal of Process Management and Benchmarking, vol. 7, no. 1, pp. 120-140, 2017. doi: 10.1504/IJPMB.2017.080942
J. E. A. Bagyam and K. U. Chandrika, “Multi-stage retrial queueing system with bernoulli feedback,” International Journal of Scientific and Engineering Research, vol. 4, no. 9, pp. 496-499, 2013.
M. Baruah, K. C. Madan, and T. Eldabi, “Balking and re-service in a vacation queue with batch arrival and two types of heterogeneous service,” Journal of Mathematics Research, vol. 4, no. 4, pp. 114-124, 2012.
H. Li and T. Yang, “Geo/g/1 discrete time retrial queue with bernoulli schedule,” European Journal of Operational Research, vol. 111, no. 3, pp. 629-649, 1998. doi: 10.1016/S0377- 2217(97)90357-X
S. Gao, J. Wang, and T. Van Do, “A repairable retrial queue under bernoulli schedule and general retrial policy,” Annals of Operations Research, vol. 247, no. 1, pp. 169-192, 2016. doi: 10.1007/s10479-015-1885-6
E. Gelenbe, “Product-form queueing networks with negative and positive customers,” Journal of applied probability, vol. 28, no. 3, pp. 656-663, 1991. doi: 10.2307/3214499
E. Gelenbe, P. Glynn, and K. Sigman, “Queues with negative arrivals,” Journal of applied probability, vol. 28, no. 1, pp. 245-250, 1991. doi: 10.2307/3214756
A. Begum and G. Choudhury, “Analysis of an m/g 1 g 2/1 queue with bernoulli vacation and server breakdown,” International Journal of Applied and Computational Mathematics, vol. 9, no. 1, 2023.
L. Lakaour, D. Aissani, K. Adel-Aissanou, K. Barkaoui, and S. Ziani, “An unreliable single server retrial queue with collisions and transmission errors,” Communications in Statistics- Theory and Methods, vol. 51, no. 4, pp. 1085-1109, 2022.
G. Malik, S. Upadhyaya, and R. Sharma, “Particle swarm optimization and maximum entropy results for mx/g/1 retrial g-queue with delayed repair,” International Journal of Mathematical, Engineering and Management Sciences, vol. 6, no. 2, 2021. doi: 10.33889/IJMEMS.2021.6.2.033
W. Xu, L. Liu, L. Li, Z. Wang, and S. Wittevrongel, “Analysis of a collision-affected m/gi/1//n retrial queuing system considering negative customers and transmission errors,” Mathematics, vol. 11, no. 16, p. 3532, 2023.
S. I. Ammar and P. Rajadurai, “Performance analysis of preemptive priority retrial queueing system with disaster under working breakdown services,” Symmetry, vol. 11, no. 3, 2019. doi: 10.3390/sym11030419
C. J. Singh, S. Kaur, and M. Jain, “Unreliable server retrial g-queue with bulk arrival, optional additional service and delayed repair,” International Journal of Operational Research, vol. 38, no. 1, pp. 82-111, 2020. doi: 10.1504/IJOR.2020.106362
Z. Nesrine, P. Spiteri, and N. Djellab, “Numerical solution for the performance characteristics of the m/m/c/k retrial queue with negative customers and exponential abandonments by using value extrapolation method,” RAIRO-Operations Research, vol. 53, no. 3, pp. 767-786, 2019. doi: 10.1051/ro/2017059
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
