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A maximum entropy approach for the N policy M/G/1 queueing system with a removable server | ||
| Computational Sciences and Engineering | ||
| مقاله 5، دوره 3، شماره 2، آذر 2023، صفحه 219-229 اصل مقاله (433.34 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22124/cse.2024.27465.1079 | ||
| نویسندگان | ||
| Moein Mohsenzadeh* 1؛ Abdolrahim Badamchizadeh2؛ Mohammad Jelodari Mamaghani3 | ||
| 1Department of Statistics, Allameh Tabataba’i University, Tehran, Iran. | ||
| 2Department of Statistics, Allameh Tabataba’i University, Tehran, Iran. | ||
| 3Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran | ||
| چکیده | ||
| The maximum entropy principle has grown progressively more pertinent to queueing systems. The principle of maximum entropy presents an impartial framework as a promising method to examine complex queuing processes. In this research, the N policy M/G/1 queueing system with a removable server was analyzed by using the maximum entropy method. We use maximum entropy principle to derive the approximate formulas for the steady-state probability distributions of the queue length. The maximum entropy approach is then used to give a comparative perusal between the system’s exact and estimated waiting times. We demonstrate that the maximum entropy approach is efficient enough for practical purpose and is a feasible method for approximating the solution of complex queueing systems. | ||
| کلیدواژه‌ها | ||
| Maximum entropy؛ M/G/1 queueing system؛ N policy؛ Removable server | ||
| مراجع | ||
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[1] Wang, K. H., Chuang, S. L., & Pearn, W. L. (2002). Maximum entropy analysis to the N policy M/G/1 queueing system with a removable server. Applied Mathematical Modelling, 26(12), 1151-1162. [2] Upadhyaya, S., Ghosh, S., & Malik, G. (2022). Cost investigation of a batch arrival retrial G-Queue with working malfunction and working vacation using particle swarm optimization. Nonlinear Studies, 29(3). [3] Bounkhel, M., Tadj, L., & Hedjar, R. (2020). Entropy analysis of a flexible Markovian queue with server breakdowns. Entropy, 22(9), 979. [4] Chauhan, D. (2018). Maximum entropy analysis of unreliable queue with Bernoulli vacation schedule. International Journal of Statistics and Applied Mathematics, 3(6), 110-118. [5] Singh, C. J., Kaur, S., & Jain, M. (2017). Waiting time of bulk arrival unreliable queue with balking and Bernoulli feedback using maximum entropy principle. Journal of Statistical theory and practice, 11, 41-62. [6] Parkash, O., & Mukesh. (2016). Contribution of maximum entropy principle in the field of queueing theory. Communications in Statistics-Theory and Methods, 45(12), 3464-3472. [7] Upadhyaya, S., & Shekhar, C. (2024). Maximum Entropy Solution for M X/G/1 Priority Reiterate G-queue Under Working Breakdown and Working Vacation. International Journal of Mathematical, Engineering & Management Sciences, 9(1). [8] Jain, M., & Kaur, S. (2021). Bernoulli vacation model for MX/G/1 unreliable server retrial queue with bernoulli feedback, balking and optional service. RAIRO-Operations Research, 55, S2027-S2053. [9] Wang, K. H., & Ke, J. C. (2000). A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity. Applied Mathematical Modelling, 24(12), 899-914. [10] Heyman, D. P. (1968). Optimal operating policies for M/G/1 queuing systems. Operations Research, 16(2), 362-382. [11] Tijms, H. C. (1986). Stochastic Modelling and Analysis, Wiley, New York. [12] B.D. Sivazlian, B. D., & Stanfel, L.E., (1975). Analysis of Systems in Operations Research, Engle-wood Cliffs, New Jersey. [13] Wang, K. H., Chang, K. W., & Sivazlian, B. D. (1999). Optimal control of a removable and non-reliable server in an infinite and a finite M/H2/1 queueing system. Applied mathematical modelling, 23(8), 651-666. [14] Wang, K. H., & Huang, H. M. (1995). Optimal control of an M/E k/1 queueing system with a removable service station. Journal of the operational research society, 46(8), 1014-1022 | ||
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