A mathematical approach to Ullmann reaction: ANFIS computing of a chemical retrial queue model under hybrid vacation. (English) Zbl 1542.92232
Summary: Herein, we developed the first report on the chemical retrial queue and hybrid vacation process for the significant Ullmann coupling for enhanced high-throughput reaction discovery. The problem of controlling the waiting time for chemical retrials is addressed here. We incorporated the supplementary variables method (SVT) and generated the steady-state probability generating function (PGF) for system size and orbit size. Important cases are outlined, and a few key metrics are utilized to evaluate system performance. Additionally, the impact of changing certain system parameters has also been analyzed via numerical examples. One particularly interesting aspect of this research is the comparison of neuro-fuzzy technique results with validation results utilizing the “adaptive neuro-fuzzy inference system” (ANFIS).
MSC:
| 92E20 | Classical flows, reactions, etc. in chemistry |
Software:
ANFISReferences:
| [1] | W. Bohm, K. Hormik, On two-periodic random walks with bound-aries, Stoch. Models 26 (2010) 165-194. · Zbl 1202.60066 |
| [2] | W. H. Stockmeyer, W. Gobush, R. Norvich, Local-jump models for chain dynamics, Pure Appl. Chem. 26 (1971) 537-543. |
| [3] | B. W. Conolly, P. R. Parthasarathy, S. Dharmaraja, A chemical queue, Math. Sci. 22 (1997) 83-91. · Zbl 0898.60087 |
| [4] | A. M. K. Tarabia, A. H. El-Baz, Transient solution of a random walk with chemical rule, Phys. A Stat. Mech. 382 (2007) 430-438. |
| [5] | A. M. K. Tarabia, Analysis of random Walks with an absorbing Bar-rier and chemical rule, J. Comput. Appl. Math. 225 (2009) 612-620. · Zbl 1170.60033 |
| [6] | S. Tsitkov, T. Pesenti, H. Palacci, J. Blanchet, H. Hess, A queue-ing theory-based perspective of the kinetics of “channeled” enzyme cascade reactions, ACS Catal. 8 (2018) 10721-10731. |
| [7] | G. Alshreef, A. Tarabia, Transient analysis of chemical queue with catastrophes and server repair, Inf. Sci. Lett. 12 (2023) 541-545. |
| [8] | E. Sperotto, G. P. M. van Klink, G. van Koten, J. G. de Vries, The mechanism of the modified Ullmann reaction, Dalton Trans. 43 (2010) 10338-10351. |
| [9] | J. P. Finet, S. C. Fedorov, G. Boyer, Recent advances in Ullmann reaction: copper (II) diacetate C at alysed N-, O-and S-arylation involving polycoordinate hetero atomic derivatives, Curr. Org. Chem. 6 (2002) 597-626. |
| [10] | G. I. Falin, J. G. C. Templeton, Retrial Queues, Chapman and Hall, London, 1997. · Zbl 0944.60005 |
| [11] | J. R. Artalejo, Accessible bibliography on retrial queues, Math. Com-put. Model. 30 (1999) 1-6. |
| [12] | D. Arivudainambi, M. Godhandaraman, P. Rajadurai, Performance analysis of a single server retrial queue with working vacation, Opsearch. 33 (2013) 55-81. |
| [13] | V. M. Chandrasekaran, K. Indhira, M. C. Saravanarajan, P. Rajadu-rai, A survey on working vacation queueing models, Int. J. Pure. Appl. Math. 106 (2016) 33-41. |
| [14] | P. Rajadurai, Sensitivity analysis of an M/G/1 retrial queueing sys-tem with disaster under working vacations and working breakdowns, RAIRO Oper. Res. 52 (2018) 35-54. · Zbl 1394.60094 |
| [15] | C. Revathi, L. Francis Raj, Search of Arrivals of an M/G/1 retrial Queueing system with delayed repair and optional re-service using modified Bernoulli vacation, J. Comput. Math. 6 (2022) 200-209. |
| [16] | S. Maragathasundari, B. Balamurugan, Analysis of an M [X] /G/1 feedback queue with two stages of repair times, general delay time, Int. J. Appl. Eng. 10 (2015) 25165-25174. |
| [17] | M. M. N. GnanaSekar, I. Kandaiyan, Analysis of an M/G/1 retrial queue with delayed repair and feedback under working vacation policy with impatient customers, Symmetry 14 (2022) #2024. |
| [18] | A.G. Pakes, Some conditions for Ergodicity and recurrence of Markov chains, Oper. Res. 17 (1969) 1058-1061. · Zbl 0183.46902 |
| [19] | S. T. Humblet, Average drifts and the non-Ergodicity of Markov chains, Oper. Res. 31 (1983) 783-789. · Zbl 0525.60072 |
| [20] | H. Takagi, Vacation and Priority Systems, Part I. Queueing Analy-sis: A Foundation of Performance Evaluation, North-Holland, Ams-terdam, New York, (1991). · Zbl 0744.60114 |
| [21] | S. Gao, J. Wang, W. Li, An M/G/1 retrial queue with general re-trial times, working vacations and vacation interruption, Asia Pac. J. Oper. Res. 31 (2014) 6-31. · Zbl 1291.90071 |
| [22] | M. Zhang, Z. Hou, M/G/1 queue with single working vacation, J. Appl. Math. Comput. 39 (2012) 221-234. · Zbl 1296.60255 |
| [23] | J. S. R. Jang, ANFIS: adaptive-network-based fuzzy inference system, IEEE Trans. Syst. Man Cybern. 23 (1993) 665-685. |
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