Abstract
General service batch arrival feedback retrial G-queue with vacation is considered. Along with the essential service, the server provides service in S phases. There are several different optional services available at each level. The server’s status determines whether or not each individual customer is admitted to the system. According to the Poisson process, positive customers arrive in batches. When a negative consumer enters the system, the server goes down and the customer in service is removed from the system. The failing server is immediately dispatched for repair. If the server is idle, one of the admitted customer instantly enters the service and the others join the orbit; otherwise, all admitted customers enter the orbit. After the completion of essential or optional services, the server may join the queue if they are dissatisfied with the service. The server will leave on vacation with certain probability, after providing service to a customer. The system’s probability generating functions are carried out using the supplemental variable approach, and various performance measurements are developed. Stochastic decomposition property is verified and the special cases are deduced. The joint distributions of the server state and the number of customers in the retrial group are obtained. The influence of parameters on system performance metrics is investigated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abdollahi, S., Salehirad, M.R.: On an M/G/1 queueing model with K-Phase optional services and Bernoulli feedback. J. Serv. Sci. Manage. 5, 280–288 (2012)
Arivudainambi, D., Gowsalya, M.: Performance analysis of an M/G/1 feedback retrial queue with two types of service and Bernoulli vacation. Stochastic Process. Models Oper. Res. 38–54 (2016)
Artalejo, J.R., Atencia, I., Moreno, P.: A discrete time Geo[X]/G/1 retrial queue with control of admission. Appl. Math. Model. 29, 1100–1120 (2005)
Bagyam, J.E.A., Udaya Chandrika, K.: Bulk arrival two phase retrial queue with two types service and extended Bernoulli vacation. Int. J. Math. Trends Technol. 4(7), 116–124 (2013)
Bagyam, J.E.A., Udaya Chandrika, K.: Multi-stage retrial queueing system with Bernoulli feedback. Int. J. Sci. Eng. Res. 4(9), 496–499 (2013)
Choudhury, G., Ke, J.C.: A batch arrival retrial queue with general retrial times under Bernoulli vacation schedule for unreliable server and delaying repair. Appl. Math. Model. 36, 255–269 (2012)
Dimitriou, I.: A batch arrival priority queue with recurrent repeated demands, admission control and hybrid failure recovery discipline. Appl. Math. Comput. 219, 11327–11340 (2013)
Dimitriou, I., Langaris, C.: Analysis of a retrial queue with two-phase service and server vacations. Queueing Syst. Theo. Appl. 60(1–2), 111–129 (2008)
Gelenbe, E.: Random neural networks with negative and positive signals and product form solution. Neural Comput. 1, 502–510 (1989)
Jain, M., Kaur, S.: Bernoulli vacation model for MX/G/1 unreliable server retrial queue with Bernoulli feedback. Balking Opt. Ser. RAIRO-Oper. Res. 55, S2027–S2053 (2021)
Li, T., Zhang, L.: An M/G/1 retrial G-Queue with general retrial times and working breakdowns. Math. Comput. Appl. 22(15), 1–17 (2017)
Niranjan, S.P., Chandrasekaran, V.M., Indhira, K.: State dependent arrival in bulk retrial queueing system with immediate Bernoulli feedback, multiple vacations and threshold, IOP Conf. Ser. Mater. Sci. Eng. 263, 1–15 (2017)
Sharma, P.: M/G/1 retrial queueing system with Bernoulli feedback and modified vacation. Int. J. Math. Trends Technol. 61(1), 10–21 (2018)
Radha, J., Indhira, K., Chandrasekaran, V.M.: A group arrival retrial g - queue with multi optional stages of service, orbital search and server breakdown. IOP Conf. Ser. Mater. Sci. Eng. 263, 1–16 (2017b)
Rajadurai, P., Chandrasekaran, V.M., Saravanarajan, M.C.: Analysis of an M[X]/G/1 unreliable G-queue with orbital search and feedback under Bernoulli vacation schedule. Opsearch 53(1), 197–223 (2015)
Salehirad, M.R., Badamchi Zadeh, A.: On the multi–phase M/G/1 queueing system with random feedback. Central Eur. J. Oper. Res. 17(2), 131–139 (2009)
Sangeetha, N., Udaya Chandrika, K.: Batch arrival multi-stage retrial G-Queue with fluctuating modes of services and feedback. Adv. Math. Sci. J. 8(3), 438–450 (2019)
Sangeetha, N., Udaya Chandrika, K.: Multi stage and multi optional retrial G-Queue with feedback and starting failure. In: AIP Conference Proceedings, vol. 2261, no. 030077, pp. 1–11 (2020)
Santhi, K.: An M/G/1 retrial queue with second optional service and multiple working vacation. Adv. Appl. Math. Sci. 20(6), 1129–1146 (2021)
Wang, J., Li, J.: A single server retrial queue with general retrial times and two-phase service. J. Syst. Sci. Complexity 22(2), 291–302 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Sangeetha, N., Ebenesar Anna Bagyam, J., Udayachandrika, K. (2022). Performance Analysis of Retrial Queueing System in Wireless Local Area Network. In: Giri, D., Mandal, J.K., Sakurai, K., De, D. (eds) Proceedings of International Conference on Network Security and Blockchain Technology. ICNSBT 2021. Lecture Notes in Networks and Systems, vol 481. Springer, Singapore. https://doi.org/10.1007/978-981-19-3182-6_10
Download citation
DOI: https://doi.org/10.1007/978-981-19-3182-6_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-3181-9
Online ISBN: 978-981-19-3182-6
eBook Packages: EngineeringEngineering (R0)