Comparative Analysis of Heterogeneous Feedback Queue Model in Fuzzy Environment using L-R method and α-cut method

Vandana Saini; Deepak Gupta; A. K. Tripathi

doi:https://doi.org/10.14445/22315373/IJMTT-V69I3P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 3 | Year 2023 | Article Id. IJMTT-V69I3P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I3P505

Comparative Analysis of Heterogeneous Feedback Queue Model in Fuzzy Environment using L-R method and α-cut method

Vandana Saini, Deepak Gupta, A. K. Tripathi

Received	Revised	Accepted	Published
04 Feb 2023	05 Mar 2023	18 Mar 2023	31 Mar 2023

Abstract

The present paper is an attempt to discuss the behavior of a heterogeneous queue model in fuzzy environment. The objective of the paper is to discuss the various queue characteristics in fuzzy environment by using L-R method and α-cut method. The model consists of one server which is commonly connected to two heterogeneous servers. A numerical example is illustrated to check the validity and difference between all queue characteristics by applying both the techniques.

Keywords

Queuing, Feedback, Heterogeneous server, Fuzzy Environment, α-cut, L-R Method

References

[1] L. Takacs, “A Single-Server Queue with Feedback,” The Bell System Technical Journal, vol. 42, no. 2, pp. 505-519, 1963. [CrossRef] [Google Scholar] [Publisher Link]
[2] T. Suzuki, “Two Queues in Series,” Journal of Operational Research Society of Japan, vol. 5, 149-155, 1963.
[3] B. Krishnamootrhy, “On Poisson Queues with Heterogeneous Servers,” Operations Research, vol. 11, no. 3, pp. 321-330, 1963.
[Google Scholar] [Publisher Link]
[4] Parkash Lal Maggu, “Phase Type Service Queues with Two Servers in Biseries,” Journal of Operational Research Society of Japan, vol. 13, no.1, 1970.[Google Scholar]
[5] R.J. Li, and E.S. Lee, “Analysis of Fuzzy Queues,” Computers and Mathematics with Applications, vol.17, no. 7, pp. 1143-1147, 1989.
[CrossRef] [Google Scholar] [Publisher Link]
[6] T.P. Singh Kusum, and Gupta Deepak, “On Network Queue Model Centrally Linked with Common Feedback Channel,” Journal of Mathematics and System Sciences, vol. 6, no. 2, pp. 18-31, 2010.
[Google Scholar]
[7] Deepak Gupta, Sameer Sharma, and Naveen Gulati, “On Steady State Behaviour of a Network Queuing Model with Bi-serial and Parallel Channels Linked with a Common Server,” Computer Engineering and Intelligent Systems, vol. 2, no. 2, 2011.
[Google Scholar] [Publisher Link]
[8] Seema, Deepak Gupta, and Sameer Sharma, “Analysis of Biserial Servers Linked to a Common Server in Fuzzy Environment,” International Journal of computing science and Mathematics, vol. 68, no. 6, pp. 26-32, 2013.
[CrossRef] [Google Scholar]
[9] Sameer Sharma, Deepak Gupta, and Seema, “Network Analysis of Fuzzy Bi-serial and Parallel Servers with a Multistage Flow Shop Model,” 21st International Congress on Modelling and Simulation, Gold Coast, Australia, pp. 697-703, 2015.
[Google Scholar]
[10] A. Badamchi Zadeh, “A Batch Arrival Multi Phase Queuing System with Random Feedback in Service and Single Vacation Policy,” Opsearch, vol. 52, pp. 617-630, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Mittal Meenu, T.P. Singh, and Deepak Gupta, “Threshold Effect on a Fuzzy Queue Model with Batch Arrival,” Aryabhatta Journal of Mathematics & Informatics, vol. 7, no. 1, 2015.
[Google Scholar] [Publisher Link]
[12] Mukeba Kanyinda Jean Pierre, Rostin Makengo Matendo Mabela, and B. Ulungu Ekunda Lukata, “Computing Fuzzy Queuing Performance Measures by L-R Method”, Journal of Fuzzy Sets Valued Analysis, vol. 1, pp. 57-67, 2015.
[CrossRef] [Google Scholar]
[13] J.P. Mukeba, “Application of L-R Method to Single Server Fuzzy Retrial Queue with Patient Customers,” Journal of Pure and Applied Mathematics: Advances and Applications, vol. 16, no. 1, pp. 43-59, 2016.
[CrossRef] [Google Scholar]
[14] T.P. Singh, Meenu Mittal, and Deepak Gupta, “Modelling of a Bulk Queue System in Triangular Fuzzy Numbers using α-cut,” International Journal of IT and Engineering, vol. 4, no. 9, pp. 72-79, 2016.
[Google Scholar]
[15] S. Kumar, and G. Tneja, “A Feedback Queuing Model with Chances of Providing Service at Most Twice by One or More out of Three Servers”, Aryabhatta Journal of Mathematics & Informatics , vol. 9, no.1, 2017.
[16] W. Ritha, and S. Josephine Vinnarasi, “Analysis of Priority Queuing Models: L-R Method,” Annals of Pure and Applied Mathematics, vol. 15, no. 2, pp. 271-276, 2017.
[CrossRef] [Google Scholar]
[17] Meenu Mittal, and Renu Gupta, “Modelling of Biserial Bulk Queue Network Linked with Common Server,” International Journal of Mathematics Trends and Technology, vol. 56, no. 6, pp. 430-436, 2018.
[CrossRef] [Google Scholar] [Publisher Link]
[18] B. Kalpana, and N. Anusheela, “Analysis of a Single Server Non-pre-emptive Fuzzy Priority Queue Using L-R Method,” ARPN Journal of Engineering and Applied Sciences, vol. 13, no. 23, pp. 9306-9310, 2018.
[Google Scholar] [Publisher Link]
[19] Kusum “Behaviorial Analysis of a Heterogeneous Feedback Queue System,” Aryabhatta Journal of Mathematics & Informatics, vol. 12, no. 1, 2020.
[20] Sachin Kumar Agrawal, Vipin Kumar, and Brahma Nand Agrawal, “Analysis of Tri-cum Biserial Bulk Queue Model Connected with a Common Server,” Journal of Mathematical and Computational Science, vol. 10, no. 6, pp. 2599-2612, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[21] Deepak Gupta, and Renu Gupta, “Time Independent Behaviour of Bulk Bi-serial Queuing Subsystems Connected to a Common Server,” Advances in Mathematics: Scientific Journal, vol. 9, no. 9, pp. 6525-6535, 2020. [CrossRef] [Google Scholar]
[22] Vandana Saini, Deepak Gupta, and A.K. Tripathi, “Analysis of a Feedback Bi-tandem Queue Network in Fuzzy Environment,” International journal of Mathematics Trends and Technology, vol. 68, no. 5, pp. 68-77, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[23] V. Saini, and D. Gupta, “Analysis of Heterogeneous Feedback Queue System with at most one Revisit,” Aryabhatta Journal of Mathematics & Informatics, vol. 13, no. 1, pp. 197-206, 2021.
[24] Vandana Saini, Deepak Gupta, and A.K. Tripathi, “Analysis of Heterogeneous Feedback Queue Model in Stochastic and in Fuzzy Environment using L-R Method,” Mathematics and Statistics, vol. 10, no. 5, pp. 918-924, 2022.
[CrossRef]
[25] G. Priscilla Pacifica, and J. Jenit Ajitha, “Steiner Domination in Fuzzy Graphs,” International Journal of Mathematics Trends and Technology, vol. 69, no. 1, pp. 17-23, 2023.
[CrossRef] [Google Scholar] [Publisher Link]

Citation :

Vandana Saini, Deepak Gupta, A. K. Tripathi, "Comparative Analysis of Heterogeneous Feedback Queue Model in Fuzzy Environment using L-R method and α-cut method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 3, pp. 31-38, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I3P505