Comparative Approach to Cost Computation of Arrival Control Queueing Model with Single Server Using SDM and GMIVM
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Abstract
In this article, we investigate the single server arrival control queuing system's cost optimization in an uncertain and fuzzy environment. This work aims to determine the optimal total-cost of the queuing model in the fuzzy environment, through its cost function. A single server arrival control queueing model was fuzzified using a triangular fuzzy number, and the Signed Distance Method (SDM) was employed to defuzzify the model. In order to achieve the paper's goal, we have additionally created parabolic and triangular, fuzzy numbers and used the Graded Mean Integration Value Method (GMIVM) for defuzzification of this model. In contrast to the standard crisp findings for the model, the computation of the fuzzy cost has been done in order to present a more realistic result to the model under discussion. Theoretical advancements for the systems that are crisp and fuzzy have been determined for each model independently, and estimated costs have made it easy to compare the two different approaches using computational tables. At the last, discussion and conclusion has also been given to gain better insight into the model.
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References
R.E. Bellman, L.A. Zadeh; Decision-making in a fuzzy environment, Management Science, 17-4 (1970), 141-164.
Baby, Saroja K., and V. Suvitha; Analysis of single server repairable queueing system with many kinds of service, single working vacation and standby server, YUJOR 34-2 (2024), 285-306.
Bouchentouf, Amina Angelika, and Abdelhak Guendouzi; Single server batch arrival Bernoulli feedback queueing system with waiting server, K-variant vacations and impatient customers, Operations Research Forum, 2 (2021), 1-23.
P.K. De and Apurva Rawat; A fuzzy inventory model without shortages using triangular fuzzy number, Fuzzy information and Engineering, 3-1 (2011), 59-68.
Arnold Kaufmann; Introduction to the theory of fuzzy subsets, Academic press, 1975.
Hans-Jürgen Zimmermann; Fuzzy set theory and its applications, Springer Science & Business Media, 2011.
Lotfi Akber Zadeh; Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1-1 (1978), 3-28.
Jing-Shing Yao and Wu Kweimei; Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy sets and Systems, 116-2 (2000), 275-288.
I.E. Khan and R. Paramasivam; Reduction in waiting time of single server markovian queuing encouraged arrival model, Reliability: Theory & Applications, 18-3 (2023), 776-784.
S. S. Mishra and D. K. Yadav; Computational approach to cost and profit analysis of clocked queueing networks, Contemporary Engineering Sciences, 3-8 (2010), 365-370.
S. S. Mishra and D. C. Shukla; A computational approach to the cost analysis of machine interference model, American Journal of Mathematical and Management Sciences, 29(1-2) (2009), 277-293.
S.S. Sanga and K. Antala; Fuzzy Cost Optimization for Single Server Queue under Admission Control F-policy and Balking, 2023.
Shree, Vaishnawi, Shweta Upadhyaya and Rakhee Kulshrestha; Cost scrutiny of discrete-time priority queue with cluster arrival and Bernoulli feedback, OPSEARCH (2024), 1-34.
M. Seenivasan and R. Ramesh; Cost Appraises of a Phosphorescent Bulk Arrival Queuing System by Wingspans Fuzzy Ranking Approach, Stochastic Processes and Their Applications in Artificial Intelligence, (2023), 50-64.
A. Vaithiyanathan; Analysis of a single server system with heterogeneous arrival, heterogeneous service, system failure and maintenance, Reliability: Theory & Applications 19-2 (78) (2024), 434-445.
M. S. Sundari and S. Palaniammal; Simulation of M/M/1 queuing system using ANN, Malaya Journal of Mathematik, S 1 (2015), 279-294.
M.J. Pardo and D. Fuente;; Fuzzy Markovian decision processes: Application to queuing systems, Computers & Mathematics with Applications, 60-9 (2010), 2526-2535.
R-J. Li and E. S. Lee; Analysis of fuzzy queues, Computers & Mathematics with Applications, 17-7 (1989), 1143-1147.
J.J. Buckley; Elementary queueing theory based on possibility theory, Fuzzy sets and systems, 37-1 (1990), 43-52.
D.S. Negi and E.S Lee; Analysis and simulation of fuzzy queue, Fuzzy Sets and Systems, 21 (1988), 43-57.
D Dubois, H Chirkova Prade; Fuzzy sets and systems, Academic Press, New York, 1980.
James J. Buckley, Thomas Feuring and Yoichi Hayashi; Fuzzy queueing theory revisited, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9-5 (2001), 527-537.
S.P. Chen; A bulk arrival queuing model with fuzzy parameters and varying batch sizes, Applied Mathematical Modeling, 30 (2006), 920-929.
Panta, Ananda Prasad, Ram Prasad Ghimire, Dinesh Panthi, and Shankar Raj Pant; Optimization of M/M/s/N queueing model with reneging in a fuzzy environment, American Journal of Operations Research, 11-3 (2021), 121.
Ke, Jau-Chuan and Chuen-Horng Lin; Fuzzy analysis of queueing systems with an unreliable server: A nonlinear programming approach, Applied mathematics and computation 175-1 (2006), 330-346.
Julia V. Chirkova and Vladimir V. Mazalov; Optimal arrivals to preemptive queueing system, International Conference on Mathematical Optimization Theory and Operations Research, (2022), 169-181. Springer International Publishing.
Laxmi, P. Vijaya, Hasan A. Qrewi and Andwilile A. George; Analysis of batch arrival general service queue with balking, feedback and second optional service, Contemporary Mathematics (2023) 1109-1124.
Fazlollahtabar, Hamed and Hadi Gholizadeh; Economic analysis of the M/M/1/N queuing system cost model in a vague environment, International Journal of Fuzzy Logic and Intelligent Systems 19-3 (2019), 192-203.
Prameela, K. Usha and Pavan Kumar; FM/FEk/1 queuing model with Erlang service under various types of fuzzy numbers, International Journal of Recent Technology and Engineering 8-1 (2019), 2277-3878.
B. Palpandi and G. Geetharamani; Evaluation of performance measures of bulk arrival queue with fuzzy parameters using robust ranking technique, International Journal of Computational Engineering Research, 3-10 (2013), 53-57.
S.S. Sanga and M. Jain; FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach, Applied Mathematics and Computation, 362 (2019), 124542.
S. Barak and M. S. Fallahnezhad; Cost analysis of fuzzy queuing systems, (2012), 25-36.
Fathi-Vajargah, Behrouz and S.A.R.A. Ghasemalipour; Simulation of a random fuzzy queuing system with multiple servers, Journal of Contemporary Mathematical Analysis 51 (2016), 103-110.
M. Enrique and H. R. Enrique; Simulation of Fuzzy Queuing Systems with a Variable Number of Servers, Arrival and Service Rates, IEEE Transactions on Fuzzy Systems 22-4 (2014), 892-903.
G. Kannadasan and N. Sathiyamoorth; The analysis of M/M/1 queue with working vacation in fuzzy environment, Applications and Applied Mathematics: An International Journal (AAM) 13-2 (2018), 1.
Chen, Gang, Zaiming Liu and Jingchuan Zhang; Analysis of strategic customer behavior in fuzzy queueing systems, Journal of Industrial & Management Optimization 16-1 (2020).
Andrew J. Keith, and Darryl K. Ahner; A survey of decision making and optimization under uncertainty, Annals of Operations Research 300-2 (2021), 319-353. https://doi.org/10.1007/s10479-019-03431-8.
B.B. Singh, S. Rawat, S Yadav and S.S Mishra; Optimization of Markovian arrival and service queuing model under fuzziness, Int. J. Agricult. Stat. Sci. 16-2 (2020), 567-572. ISSN: 0973-1903, e-ISSN: 0976-3392, Scopus/ Elsevier, ESCI.
Yi Zheng, Juxihong Julaiti and Guodong Pang; Adaptive service rate control of an M/M/1 queue with server breakdowns, Queueing Systems 106-1 (2024), 159-191.
S. S. Mishra; Cost Analysis of M/M/1 and MF/MF/1 Queuing Model using ANN and Signed Distance Method, Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12-12 (2021), 1547-1562.
S.P. Subhapriya and M. Thiagarajan; M/M/1 Interdependent Queuing Model with Vacation and Controllable Arrival Rates, Indian Journal of Science and Technology 17-14 (2024), 1497-1506.
S.S. Mishra, B.B. Singh, S.K. Yadav, S. Rawat, P.P. Mishra and A. Singh; Cost Optimization of Arrival and Service Control Queueing Model with Single Server in Fuzzy Environment of Uncertainty, Turkish Journal of Computer and Mathematics Education, (2021) 12(12), 1626-1639.