A batch arrival unreliable server delaying repair queue with two phases of service and Bernoulli vacation under multiple vacation policy

References

• Avi-Itzhak, B., & Naor, P. (1963). Some queuing problems with the service station subject to breakdown. Operations Research, 11, 303–320.10.1287/opre.11.3.303
   Web of Science ®Google Scholar
• Baba, Y. (1986). On the MX/G/1 queue with vacation time. Operations Research Letters, 5, 93–98.10.1016/0167-6377(86)90110-0
   Web of Science ®Google Scholar
• Chaudhry, M. L., & Templeton, J. G. C. (1983). A first course in bulk queues. New York, NY: John Wiley.
   Google Scholar
• Choudhury, G. (2002). A batch arrival queue with a vacation time under single vacation policy. Computers & Operations Research, 29, 1941–1955.10.1016/S0305-0548(01)00059-4
   Web of Science ®Google Scholar
• Choudhury, G., & Madan, K. C. (2004). A two phase batch arrival queueing system with a vacation time under Bernoulli schedule. Applied Mathematics and Computation, 149, 337–349.10.1016/S0096-3003(03)00138-3
   Web of Science ®Google Scholar
• 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, 71–85.10.1016/j.mcm.2005.04.003
   Web of Science ®Google Scholar
• Choudhury, G., & Paul, M. (2006). A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy. Statistical Methodology, 3, 174–185.10.1016/j.stamet.2005.09.003
   Google Scholar
• Choudhury, G., Tadj, L., & Paul, M. (2007). Steady state analysis of an Mx/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy. Applied Mathematical Modelling, 31, 1079–1091.10.1016/j.apm.2006.03.032
   Web of Science ®Google Scholar
• Choudhury, G., & Tadj, L. (2011). The optimal control of an MX/G/1 unreliable server queue with two phases of service and Bernoulli vacation schedule. Mathematical and Computer Modelling, 54, 673–688.10.1016/j.mcm.2011.03.010
   Web of Science ®Google Scholar
• Choudhury, G., & Deka, M. (2012). A single server queueing system with two phases of service subject to server breakdown and Bernoulli vacation. Applied Mathematical Modelling, 36, 6050–6060.10.1016/j.apm.2012.01.047
   Web of Science ®Google Scholar
• Cox, D. R. (1955). The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Mathematical Proceedings of the Cambridge Philosophical Society, 51, 433–441.10.1017/S0305004100030437
   Google Scholar
• Doshi, B.T. (1986). Queueing systems with vacations – A survey. Queueing Systems, 1, 29–66.10.1007/BF01149327
   Google Scholar
• Fiems, D., Maertens, T., & Bruneel, H. (2008). Queueing systems with different types of server interruptions. European Journal of Operational Research, 188, 838–845.10.1016/j.ejor.2007.05.010
   Web of Science ®Google Scholar
• Fuhrmann, S. W., & Cooper, R. B. (1985). Stochastic decompositions in the M/G/1 queue with generalized vacations. Operations Research, 33, 1117–1129.10.1287/opre.33.5.1117
   Web of Science ®Google Scholar
• Gaver, D. P. (1962). A waiting line with interrupted service including priorities. Journal of Royal Statistical Society, Ser-B, 24, 73–90.
   Google Scholar
• Heathcote, C. R. (1959). The time-dependent problem for a queue with preemptive priorities. Operations Research, 7, 670–680.10.1287/opre.7.5.670
   Google Scholar
• Heyman, D. P. (1977). The T-policy for the M/G/1 Queue. Management Science, 23, 775–778.10.1287/mnsc.23.7.775
   Web of Science ®Google Scholar
• Ibe, O. C., & Trivedi, K. S. (1990). Two queues with alternating service and server breakdown. Queueing Systems, 7, 253–268.10.1007/BF01154545
   Google Scholar
• Ke, J. C., Wu, C. H., & Zhang, Z. G. (2010). Recent developments in vacation queueing models: A short survey. International Journal Of Operations Research, 7, 3–8.
   Google Scholar
• Ke, J. C., & Huang, K. B. (2010). Analysis of an unreliable server M [ X ] /G/1 system with a randomized vacation policy and delayed repair. Stochastic Models, 26, 212–241.10.1080/15326341003756262
   Web of Science ®Google Scholar
• Ke, J. C., Huang, K. B., & Pearn, W. L. (2011). The performance measures and randomized optimization for an unreliable server M[x]/G/1 vacation system. Applied Mathematics and Computation, 217, 8277–8290.10.1016/j.amc.2011.03.008
   Google Scholar
• Ke, J. C., Huang, K. B., & Pearn, W. L. (2012). A batch arrival queue under randomised multi-vacation policy with unreliable server and repair. International Journal of Systems Science, 43, 552–565.10.1080/00207721.2010.517863
   Web of Science ®Google Scholar
• Keilson, J. (1962). Queues subject to service interruption. The Annals of Mathematical Statistics, 33, 1314–1322.10.1214/aoms/1177704364
   Google Scholar
• Keilson, J., & Servi, L. D. (1986). Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules. Journal of Applied Probability, 23, 790–802.10.2307/3214016
   Web of Science ®Google Scholar
• Kella, O. (1990). Optimal control of the vacation scheme in an M/G/1 queue. Operations Research, 38, 724–728.10.1287/opre.38.4.724
   Web of Science ®Google Scholar
• Krishnamoorthy, A., Pramod, P. K., & Deepak, T. G. (2009). On a queue with interruptions and repeat or resumption of service. Nonlinear Analysis: Theory, Methods & Applications, 71, e1673–e1683.10.1016/j.na.2009.02.056
   Web of Science ®Google Scholar
• Kuo, C. C., Ke, J. C., & Choudhury, G. (2015). Optimal NT policies for a two-phase service M/G/1 system with Bernoulli vacation schedule. Quality Technology and Quantitative Management, 12, 341–351.
   Web of Science ®Google Scholar
• Lee, H. W., Seo, W. J., & Lee, S. W. (2011). Analysis of the M/G/1 queueing system under the triadic (N,D,T)-policies. Quality Technology and Quantitative Management, 8, 333–357.
   Google Scholar
• Levy, Y., & Yechiali, U. (1975). Utilization of idle time in an M / G /1 queueing system. Management Science, 22, 202–211.10.1287/mnsc.22.2.202
   Web of Science ®Google Scholar
• Li, Q., Xu, D., & Cao, J. (1997). Reliability approximation of a Markov queueing system with server breakdown and repair. Microelectronics and Reliability, 37, 1203–1212.10.1016/S0026-2714(96)00291-0
   Google Scholar
• Li, Q., & Lin, C. (2006). The M/G/1 processor-sharing queue with disasters. Computers and Mathematics with Applications, 51, 987–998.10.1016/j.camwa.2005.10.012
   Google Scholar
• Madan, K. C. (2003). On a single server queue with two stage heterogeneous service and deterministic server vacations. International Journal of System Sciences, 32, 837–844.
   Google Scholar
• Mitrany, I. L., & Avi-Itzhak, B. (1968). A many-server queue with service interruptions. Operations Research, 16, 628–638.10.1287/opre.16.3.628
   Web of Science ®Google Scholar
• Sengupta, B. (1990). A queue with service interruptions in an alternating random environment. Operations Research, 38, 308–318.10.1287/opre.38.2.308
   Web of Science ®Google Scholar
• Tadj, L. (2003). On an M/G/1 quorum queueing system under T-policy. Journal of the Operational Research Society, 54, 466–471.10.1057/palgrave.jors.2601536
   Web of Science ®Google Scholar
• Takagi, H. (1990). Queueing analysis (Vol. 1). Amsterdam: Elsevier.
   Google Scholar
• Takine, T., & Sengupta, B. (1998). A single server queue with service interruptions. Queueing Systems, 26, 285–300.
   Web of Science ®Google Scholar
• Tang, Y. (1997). A single-server M/G/1 queueing system subject to breakdowns – some reliability and queueing problems. Microelectronics and Reliability, 37, 315–321.10.1016/S0026-2714(96)00018-2
   Web of Science ®Google Scholar
• Thirurengadan, K. (1963). Queueing with breakdowns. Operations Research, 11, 303–320.
   Web of Science ®Google Scholar
• Wang, K. H., Wang, T. Y., & Pearn, W. L. (2007). Optimal control of the N-policy M/G/1 queueing system with server breakdowns and general startup times. Applied Mathematical Modelling, 31, 2199–2212.10.1016/j.apm.2006.08.016
   Web of Science ®Google Scholar
• White, H., & Christie, L. S. (1958). Queuing with preemptive priorities or with breakdown. Operations Research, 6, 79–95.10.1287/opre.6.1.79
   Web of Science ®Google Scholar
• Wolff, R. W. (1982). Poisson arrivals see time averages. Operations Research, 30, 223–231.10.1287/opre.30.2.223
   Web of Science ®Google Scholar