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Research Article

Queueing system with server breakdowns and individual customer abandonment

ORCID Icon, , &
Pages 441-460 | Received 17 Nov 2022, Accepted 16 Apr 2023, Published online: 22 May 2023

References

  • Asmussen, S. (2003). Applied probability and queues (Vol. 2). Springer.
  • Avi-Itzhak, B., & Naor, P. (1963). Some queuing problems with the service station subject to breakdown. Operations Research, 11(3), 303–320. https://doi.org/10.1287/opre.11.3.303
  • Banerjee, A., Gupta, U. C., & Chakravarthy, S. R. (2015). Analysis of a finite-buffer bulk-service queue under Markovian arrival process with batch-size-dependent service. Computers & Operations Research, 60, 138–149. https://doi.org/10.1016/j.cor.2015.02.012
  • Bouchentouf, A. A., Boualem, M., Yahiaoui, L., & Ahmad, H. (2022). A multi-station unreliable machine model with working vacation policy and customers’ impatience. Quality Technology & Quantitative Management, 19(6), 766–796. https://doi.org/10.1080/16843703.2022.2054088
  • Chai, X., Jiang, T., Li, L., Xu, W., & Liu, L. (2022). On a many-to-many matched queueing system with flexible matching mechanism and impatient customers. Journal of Computational and Applied Mathematics, 416, 114573. https://doi.org/10.1016/j.cam.2022.114573
  • Chakravarthy, S. R. (2001). The batch Markovian arrival process: A review and future work. Advances in Probability Theory and Stochastic Processes, 1(1), 21–49.
  • Chakravarthy, S. R. (2009). A disaster queue with Markovian arrivals and impatient customers. Applied Mathematics and Computation, 214(1), 48–59. https://doi.org/10.1016/j.amc.2009.03.081
  • Chakravarthy, S. R. (2010). Markovian arrival processes. In Wiley Encyclopedia of Operations Research and Management Science.
  • Chakravarthy, S. R. (2017). A catastrophic queueing model with delayed action. Applied Mathematical Modelling, 46, 631–649. https://doi.org/10.1016/j.apm.2017.01.089
  • Chakravarthy, S. R. (2022a). Introduction to matrix-analytic methods in queues 1: Analytical and simulation approach – basics. ISTE Ltd, London and John Wiley and Sons.
  • Chakravarthy, S. R. (2022b). Introduction To matrix-analytic methods in queues 2: Analytical and simulation approach – queues and simulation. ISTE Ltd, London and John Wiley and Sons.
  • Chakravarthy, S. R. (2022c). Analysis of a queueing model with MAP arrivals and heterogeneous phase-type group services. Mathematics, 10(19), 3575. https://doi.org/10.3390/math10193575
  • Chakravarthy, S. R., Kulshrestha, S., & Kulshrestha, R. (2020). A queueing model with server breakdowns, repairs, vacations, and backup server. Operations Research Perspectives, 7, 100131. https://doi.org/10.1016/j.orp.2019.100131
  • Chakravarthy, S. R., Rumyantsev, S., & Rumyantsev, A. (2021). Analysis of a queueing model with batch markovian arrival process and general distribution for group clearance. Methodology and Computing in Applied Probability, 23(4), 1551–1579. https://doi.org/10.1007/s11009-020-09828-4
  • Chen, A., & Renshaw, E. (1997). The M/M/1 queue with mass exodus and mass arrivals when empty. Journal of Applied Probability, 34(1), 192–207. https://doi.org/10.2307/3215186
  • Choi, B. D., & Kim, B. (2000). Sharp results on convergence rates for the distribution of GI/M/1/K queues as K tends to infinity. Journal of Applied Probability, 37(4), 1010–1019. https://doi.org/10.1239/jap/1014843080
  • Dudin, A. N., Klimenok, V. I., & Vishnevsky, V. M. (2020). The theory of queuing systems with correlated flows. Springer Nature.
  • Dudin, A. N., & Nishimura, S. (1999). A BMAP/SM/1 queueing system with Markovian arrival input of disasters. Journal of Applied Probability, 36(3), 868–881. https://doi.org/10.1239/jap/1032374640
  • Gantmacher, F. R. (1967). Theory of matrices (1st ed.). Science.
  • Graham, A. (1981). Kronecker products and matrix calculus with applications. Ellis Horwood.
  • Hoseinpour, P. (2021). Improving service quality in a congested network with random breakdowns. Computers & Industrial Engineering, 157, 107226. https://doi.org/10.1016/j.cie.2021.107226
  • Jain, M., Kaur, S., & Singh, P. (2021). Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI). Operational Research, 21(4), 2203–2246. https://doi.org/10.1007/s12351-019-00519-8
  • Jain, G., & Sigman, K. (1996). A Pollaczek–Khintchine formula for M/G /1 queues with disasters. Journal of Applied Probability, 33(4), 1191–1200. https://doi.org/10.2307/3214996
  • Kim, J., & Kim, B. (2007). Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure. Queueing Systems, 57(1), 47–55. https://doi.org/10.1007/s11134-007-9045-6
  • Krishnamoorthy, A., Pramod, P. K., & Chakravarthy, S. R. (2014). Queues with interruptions: A survey. Top, 22(1), 290–320. https://doi.org/10.1007/s11750-012-0256-6
  • Liu, T. -H., Chang, F. -M., Ke, J. -C., & Sheu, S. -H. (2022). Optimization of retrial queue with unreliable servers subject to imperfect coverage and reboot delay. Quality Technology & Quantitative Management, 19(4), 428–453. https://doi.org/10.1080/16843703.2021.2020952
  • Lucantoni, D. (1991). New results on the single server queue with a batch Markovian arrival process. Communications in Statistics Stochastic Models, 7(1), 1–46. https://doi.org/10.1080/15326349108807174
  • Lucantoni, D., Meier-Hellstern, K. S., & Neuts, M. F. (1990). A single-server queue with server vacations and a class of non-renewal arrival processes. Advances in Applied Probability, 22(3), 676–705. https://doi.org/10.2307/1427464
  • Medhi, A., & Choudhury, P. (2012). Aspects of impatience in a finite buffer queue. RAIRO - Operations Research, 46(3), 189–209. https://doi.org/10.1051/ro/2012014
  • Mitrani, I. L., & Avi-Itzhak, B. (1968). A many-server queue with server interruptions. Operations Research, 16(3), 628–638. https://doi.org/10.1287/opre.16.3.628
  • Neuts, M. F. (1979). A versatile Markovian point process. Journal of Applied Probability, 16(4), 764–779. https://doi.org/10.2307/3213143
  • Neuts, M. F. (1981). Matrix-geometric solutions in stochastic models -an algorithmic approach. Dover Publications (originally published by Johns Hopkins University Press).
  • Neuts, M. F. (1989). Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekker.
  • Neuts, M. F. (1992). Models based on the Markovian arrival processes. IEICE Transactions on Communications, E75-B(12), 1255–1265.
  • Neuts, M. F., & Lucantoni, D. (1979). A Markovian queue with N servers subject to breakdowns and repair. Management Science, 25(9), 849–861. https://doi.org/10.1287/mnsc.25.9.849
  • Simonot, F. (1997). Convergence rate for the distributions of GI/M/1/n and M/GI/1/n as n tends to infinity. Journal of Applied Probability, 34(4), 1049–1060. https://doi.org/10.2307/3215017
  • Thiruvengadam, K. (1963). Queuing with breakdowns. Operations Research, 11(1), 62–71. https://doi.org/10.1287/opre.11.1.62
  • White, H., & Christie, L. S. (1958). Queuing with preemptive priorities or with breakdown. Operations Research, 6(1), 79–95. https://doi.org/10.1287/opre.6.1.79

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