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A maximum entropy approach for the N policy M/G/1 queueing system with a removable server

Document Type : Original Article

Authors

1 Department of Statistics, Allameh Tabataba’i University, Tehran, Iran.

2 Department of Statistics, Allameh Tabataba’i University, Tehran, Iran.

3 Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran

Abstract

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.

Keywords

References
[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
Computational Sciences and Engineering
Volume 3, Issue 2
September 2023
Pages 219-229
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