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Analysis of a M[X]/G/1 queueing system with an unreliable server and delaying vacations using maximum entropy | ||
| Computational Sciences and Engineering | ||
| دوره 4، شماره 2، آذر 2024، صفحه 319-330 اصل مقاله (428.61 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22124/cse.2025.30255.1101 | ||
| نویسندگان | ||
| Moein Mohsenzadeh* 1؛ Mahdi Doustparast2؛ Abdolrahim Badamchizadeh3؛ Mohammad Jelodari Mamaghani4 | ||
| 1Ph.D. student of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 2Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 3Department of Statistics, Allameh Tabataba’i University, Tehran, Iran. | ||
| 4Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran | ||
| چکیده | ||
| This paper deals with a single unreliable server and with delaying vacations which has Poisson arrivals and general distribution for the service times. The server can be activated at arrival epochs or deactivated at service completion epochs. The maximum entropy principle is increasingly relevant to queueing systems. The principle of maximum entropy (PME) presents an impartial framework as a promising method to examine complex queuing processes. 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^([X])/G/1 queueing system؛ Delaying vacations؛ Unreliable server | ||
| مراجع | ||
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[1] Ke, Jau-Chuan & Lin, Chuen-Horng. (2006). Maximum entropy solutions for batch-arrival with an unreliable server and delaying vacations. Applied Mathematics and Computation. 183. 1328-1340.
[2] Jain, Madhu & Kaur, Sandeep. (2020). Bernoulli vacation model for unreliable server retrial queue with Bernoulli feedback, balking and optional service. RAIRO - Operations Research, 55, S2027-S2053.
[3] Nithya, R.P., & Haridass, M. (2020b). Stochastic modelling and analysis of maximum entropy of queuing system with balking, startup and vacation interruption. International Journal of Services and Operations Management, 37(3), 343-371.
[4] Nithya, R.P., & Haridass, M. (2020a). Cost optimisation and maximum entropy analysis of a bulk queueing system with breakdown, controlled arrival and multiple vacations. International Journal of Operational Research, 39(3), 279-305.
[5] Malik, G., Upadhyaya, S., & Sharma, R. (2021b). Particle swarm optimization and maximum entropy results for retrial G-queue with delayed repair. International Journal of Mathematical, Engineering and Management Sciences, 6(2), 541-563.
[6] 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), 809.
[7] Nisha,Upadhyaya, S., & Shekhar, C. (2024). Maximum Entropy Solution for Priority Reiterate G-queue Under Working Breakdown and Working Vacation. International Journal of Mathematical, Engineering and Management Sciences, 9(1), 163-187.
[8] Mohsenzadeh, M., Badamchizadeh, A., & Jelodari Mamaghani, M. (2024). A maximum entropy approach for the N policy M/G/1 queueing system with a removable server. Computational Sciences and Engineering, 3(2), 219-229.
[9] U. Yechiali, On the M[x] /G/1 queue with a waiting server and vacations. Sankhya 66 (2004) 159–174.
[10] K.-H. Wang, J.-C. Ke. (2002). Control policies of an M/G/1 queueing system with a removable and non-reliable server. International Transactions in Operations Research, 9, 195–212.
[11] M.A. El-Affendi, D.D. Kouvatsos. (1983). A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium. Acta Information, 19, 339–355. | ||
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