Computation of the Unreliable M^x / M /1 Model for Multiple Working Vacations Queuing System with Encouraged Arrivals
DOI:
https://doi.org/10.21123/bsj.2024.9154Keywords:
Breakdowns, Encouraged Arrivals, Multiple Working Vacations, Probability Generating Function, Queuing System, Stochastic DecompositionAbstract
This research analyzed queuing system with encouraged arrivals under multiple working vacations and server breakdowns. It is based on a Mx/M/1 model, where the customers arrive in batches or bulk. In addition, the arrival follows a Poisson process and the service time is distributed exponentially. Moreover, in this queuing system, breakdowns can occur at any time, and it is affecting the server’s service time. The repair time is independent. Server resume the service as soon as returns from the service facility. Repair time follows exponential distribution. Encouraged arrival in queuing models involves external factors or incentives that prompt the firms. This strategy for mitigating may include preventing maintenance or minimizing the service disruptions and maintain the system efficiency. Encouraged arrival in queuing model conscious effort to increase customers or other entities to a service system during specific periods. Encouraged arrival improves the system performance and service efficiency of the model. Finally, this research solved the Chapman-Kolmogorov balancing equations for the steady state system, analyzed the queuing model using probability generating function and discussed, the stochastic decomposition property and the expected system size.
Received 31/05/2023
Revised 02/06/2023
Accepted 04/06/2024
Published Online First 20/09/2024
References
Abdelmawgoud MTA, Dawood AA, Moussa MBH. The Impact of Prolonged Waiting Time of Food Service on Customers' Satisfaction. Minia J Tour Manag Res. 2016; 1(1): 247-251. https://doi.org/10.21608/mjthr.2016.262117 .
Agraval PK, Jain A, Jain M. M/M/1 queueing model with working vacation and two types of server breakdowns. 2nd National Conference on Recent Advancement in Physical Sciences, (NCRAPS) 2020, 19-20 December 2020, Uttarakhand, INDIA. J Phys Conf Ser. 2021; 1849(1): 1-15. https://doi.org/10.1088/1742-6596/1849/1/012021 .
Alqaysi M, Behadili S, Salam A. Spatiotemporal modelling in wireless communication Networks. Baghdad Sci J. 2022; 20(3): 904-918. https://doi.org/10.21123/bsj.2022.6848.
Bouchentouf A, Guendouzi A, Meriem H, Shakir M. Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience. Operations Research and Decisions. 2022; 32(2): 16-33. https://doi.org/10.37190/ord220202 .
Erlang AK. The Theory of Probabilities and Telephone Conversations. Nyt Tidsskrift for Matematik B. 1909; 20(33): 131-137.
Jain M, Jain A. Working vacations queuing model with multiple types of server Breakdowns. Appl Math Model. 2010; 34(1): 1-13. https://doi.org/10.1016/j.apm.2009.03.019.
Krishnamoorthy A, Joshua A, Kozyrev D. Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation. Mathematics. 2021; 9(4): 1-29. https://doi.org/10.3390/math9040419.
Lakshmi PV, Kassahun TW. Analysis of variant working vacation queue with reneging under a multi-server environment. Int J Manag Sci Eng. 2020; 15(2): 130-137. https://doi.org/10.1080/17509653.2019.1653237.
Laxmi PV, Rajesh P, Kassahun TW. Analysis of a variant working vacation queue with customer impatience and server breakdown. Int J Oper Res. 2021; 40(4): 437-459. https://doi.org/10.1504/IJOR.2021.114839.
Mary K, Remona JM, Rajalakshmi J. Analysis of Mx/M/1/MWV/BD Queuing Systems. Int J Comput Appl. 2016; 141(7): 1-4.
Malik S, Gupta R. Analysis of Finite Capacity Queueing System with Multiple Vacations and Encouraged Customers. Int J Sci Res Math Stat Sci. 2022; 9(2): 17-22.
Moussa MHBE, Abd Elmawgoud MTA, Elias AN. Measuring Service Time Characteristics in Fast Food Restaurants in Cairo: A Case Study. Tour Today. 2015; 1(15): 90-104.
Panta AP, Ghimire RP, Panthi D, Pant SR. A Review of Vacation Queuing Models in Different Framework. Ann Pure Appl Math. 2021; 24(2): 99-121. http://dx.doi.org/10.22457/apam.v24n2a02849.
Seenivasan M, Chandiraleka S. Single Server Queueing Model with Multiple Working Vacation and with Breakdown. Second International Conference on Advances in Electrical, Computing Communication and Sustainable Technologies (ICAECT), Bhilai, India. IEEE. 2022; 1-5: https://doi.org/10.1109/ICAECT54875.2022.9807852
Servi LD, Finn SG. M/M/1 Queue with Working Vacations (M/M/1/WV). Perform Eval. 2002; 50(1): 41-52. https://doi.org/10.1016/S0166-5316(02)00057-3.
Sindhu S, Krishnamoorthy A, Kozyrev D. On queues with working vacation and interdependence in arrival and service processes. Mathematics. 2023; 11(10): 1-16. https://doi.org/10.3390/math11102280.
Som BK, Seth S. An M/M/1/N Queuing system with Encouraged Arrivals. Glob J Pure Appl Math. 2017; 13(7): 3443-3453.
Som BK, Seth S. M/M/c/N Queuing Systems with Encouraged Arrivals, Reneging Retention and Feedback Customer. Yugosl. J Oper Res. 2018; 28(3): 333-344. https://doi.org/10.2298/YJOR170620006S.
Xu X, Liu M, Zhao Xh. The bulk input M[x]/M/1 queue with working vacations. J Syst Sci Syst Eng. 2009; 18(3): 358-368. https://doi.org/10.1007/s11518-009-5111-4.
Yusof AL, Halim H, Ya'acob N, Hanapiah NH. Performance Analysis of Propagation in VHF Military Tactical Communication System. Baghdad Sci J. 2021; 18(4(Suppl.)): 1378-1386. https://doi.org/10.21123/bsj.2021.18.4(Suppl.).1378.
Baba Y. Analysis of a GI/M/1 Queue with Multiple Working Vacations. Oper Res Lett. 2005; 33(2): 201-209. https://doi.org/10.1016/j.orl.2004.05.006.
Downloads
Issue
Section
License
Copyright (c) 2024 Sujipriya A, Julia Rose Mary K
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
