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Research Article

An analytical approach of Markov modulated Poisson input with feedback queue and repeated service under N-policy with setup time

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Pages 257-285 | Received 24 Mar 2022, Accepted 05 Feb 2023, Published online: 27 Mar 2023

References

  • Al-Khedhairi, A., & Tadj, L. (2007). A bulk service queue with a choice of service and re-service under Bernoulli schedule. International Journal of Contemporary Mathematical Sciences, 2(23), 1107–1120. https://doi.org/10.12988/ijcms.2007.07112
  • Ammar, S. (2020). Behavior analysis of an M/M/1 vacation queue in random environment. Quality Technology & Quantitative Management, 18(4), 397–417. https://doi.org/10.1080/16843703.2020.1846268
  • Anabosi, R. F., & Madan, K. C. (2003). A single server queue with two types of service, Bernoulli schedule server vacations and a single vacation policy. Pakistan Journal of Statistics, 19(3), 331–342.
  • Barbhuiya, F. P., & Gupta, U. C. (2020). Analytical and computational aspects of the infinite buffer single server N policy queue with batch renewal input Computers &. Operations Research, 118, 104916. https://doi.org/10.1016/j.cor.2020.104916
  • Barbhuiya, F. P., Kumar, N., & Gupta, U. C. (2022). Analysis of the GI/M/c queue with N-threshold policy. Quality Technology & Quantitative Management, 19(4), 490–510. https://doi.org/10.1080/16843703.2022.2046308
  • Baruah, M., Madan, K. C., & Eldabi, T. (2012). Balking and re-service in a vacation queue with batch arrival and two types of heterogeneous service. Journal of Mathematics Research, 4(4), 114. https://doi.org/10.5539/jmr.v4n4p114
  • Bohm, W. (1992). A transient analysis of M/G/1 queues with N-policy. Statistical Papers, 33(1), 151–157. https://doi.org/10.1007/BF02925320
  • Bouchentouf, A. A., Boualem, M., YahiaouiL, A. H., & Ahmad, H. (2022). A multi-station unreliable machine model with working vacation policy and customers’ impatience. Quality Technology & Quantitative Management, 19(6), 1–31. https://doi.org/10.1080/16843703.2022.2054088
  • Choudhury, G., & Kalita, C. R. (2018). An M/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server’s breakdown and delayed repair. Quality Technology & Quantitative Management, 15(5), 622–654. https://doi.org/10.1080/16843703.2017.1331499
  • Choudhury, G., & Madan, K. C. (2005). A two-stage batch arrival queueing system with a modified Bernoulli schedule vacation under N-policy. Mathematical and Computer Modelling, 42(1–2), 71–85. https://doi.org/10.1016/j.mcm.2005.04.003
  • Choudhury, G., & Paul, M. (2004). A batch arrival queue with an additional service channel under N-policy. Applied Mathematics and Computation, 156(1), 115–130. https://doi.org/10.1016/j.amc.2003.07.006
  • Cox, D. R. (1955). The analysis of non-markovian stochastic processes by the inclusion of supplementary variables. In: Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, vol 51, pp 433–441
  • El-Hadidy, M. A. A., & Fakharany, M. (2021). A transient analysis algorithm to control the quality and performance of the queuing system. Quality Technology & Quantitative Management, 18(6), 683–700. https://doi.org/10.1080/16843703.2021.1932053
  • Fischer, W., & Meier-Hellstern, K. (1993). The Markov-modulated Poisson process (MMPP) cookbook. Performance Evaluation, 18(2), 149–171. https://doi.org/10.1016/0166-5316(93)90035-S
  • Fuhrmann, S. W., & Cooper, R. B. (1985). Stochastic decompositions in the M/G/1 queue with generalized vacations. Operations Research, 33(5), 1117–1129. https://doi.org/10.1287/opre.33.5.1117
  • Heyman, D. P. (1968). Optimal operating policies for M/G/1 queuing systems. Operations Research, 16(2), 362–382. https://doi.org/10.1287/opre.16.2.362
  • Hur, S., Kim, J., & Kang, C. (2003). An analysis of the M/G/1 system with N and T policy. Applied Mathematical Modelling, 27(8), 665–675. https://doi.org/10.1016/S0307-904X(03)00074-X
  • Kalita, C. R., & Choudhury, G. (2019). Analysis of an unreliable MX/(G1 G2)/1 repeated service queue with delayed repair under randomized vacation policy. Communications in Statistics-Theory and Methods, 48(21), 5336–5369. https://doi.org/10.1080/03610926.2018.1513142
  • Ke, J. -C., & Ke JC. (2003). The operating characteristic analysis on a general input queue with N policy and a startup time. Mathematical Methods of Operations Research, 57(2), 235–254. https://doi.org/10.1007/s001860200255
  • Ke, J. C., Huang, H. I., & Chu, Y. K. (2010). Batch arrival queue with n-policy and at most j vacations. Applied Mathematical Modelling, 34(2), 451–466. https://doi.org/10.1016/j.apm.2009.06.003
  • Krishnamoorthy, A., & Deepak, T. (2002). Modified N-policy for M/G/1 queues. Computers & Operations Research, 29(12), 1611–1620. https://doi.org/10.1016/S0305-0548(00)00108-8
  • Kumar, B. K., Arivudainambi, D., & Vijayakumar, A. (2002). On the N-policy of M/G/1 feedback queue with varying arrival rates. Opsearch, 39(5), 296–314. https://doi.org/10.1007/BF03399191
  • Kumar, B. K., Rukmani, R., Thangaraj, V., & Krieger, U. R. (2010). A single server retrial queue with Bernoulli feedback and collisions. Journal of Statistical Theory and Practice, 4(2), 243–260. https://doi.org/10.1080/15598608.2010.10411984
  • Lan, S., & Tang, Y. (2017). Performance and reliability analysis of a repairable discrete-time Geo/G/1 queue with Bernoulli feedback and randomized policy. Applied Stochastic Models in Business and Industry, 33(5), 522–543. https://doi.org/10.1002/asmb.2253
  • Madan, K. C., Al-Nasser, A. D., & Al-Masri, A. Q. (2004). On M[x]G1G21 queue with optional re-service. Applied Mathematics and Computation, 152(1), 71–88. https://doi.org/10.1016/S0096-3003(03)00545-9
  • Medhi, J., & Templeton, J. G. (1992). A Poisson input queue under N-policy and with a general start up time. Computers & Operations Research, 19(1), 35–41. https://doi.org/10.1016/0305-0548(92)90057-C
  • Melikov, A., Aliyeva, S., & Sztrik, J. (2019). Analysis of queueing system MMPP/M/K/K with delayed feedback. Mathematics, 7(11), 1128. https://doi.org/10.3390/math7111128
  • Mytalas, G. C., & Zazanis, M. A. (2022). Performance analysis for Bernoulli feedback queues subject to disasters: A system with batch Poisson arrivals under a multiple vacation policy. Quality Technology & Quantitative Management.
  • Pearn, W. L., Ke, J. C., & Chang, Y. C. (2004). Sensitivity analysis of the optimal management policy for a queuing system with a removable and non-reliable server. Computers & Industrial Engineering, 46(1), 87–99. https://doi.org/10.1016/j.cie.2003.11.001
  • Rajadurai, P., Saravanarajan, M. C., & Chandrasekaran, V. M. (2018). A study on M/G/1 feedback retrial queue with subject to server breakdown and repair under multiple working vacation policy. Alexandria Engineering Journal, 57(2), 947–962. https://doi.org/10.1016/j.aej.2017.01.002
  • Tadj, L., & Choudhury, G. (2005). Optimal design and control of queues. Top, 13(2), 359–412. https://doi.org/10.1007/BF02579061
  • Tadj, L., & Ke, J. C. (2008). A hysteretic bulk quorum queue with a choice of service and optional re-service. Quality Technology & Quantitative Management, 5(2), 161–178. https://doi.org/10.1080/16843703.2008.11673394
  • Takács, L. (1962). Introduction to the theory of queues. Technical Report.
  • Takagi, H. (1991). A Foundation of performance evaluation: Vacation and priority systems. North-Holland.
  • Upadhyaya, S. (2016). Performance prediction of a discrete-time batch arrival retrial queue with Bernoulli feedback. Applied Mathematics and Computation, 283, 108–119. https://doi.org/10.1016/j.amc.2016.02.026
  • Yadin, M., & Naor, P. (1963). Queueing systems with a removable service station. The Journal of the Operational Research Society, 14(4), 393–405. https://doi.org/10.1057/jors.1963.63
  • Yen, T. C., Wang, K. H., & Chen, J. Y. (2020). Optimization analysis of the N policy M/G/1 queue with working breakdowns. Symmetry, 12(4), 583. https://doi.org/10.3390/sym12040583

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