An Unreliable Server Retrial Queue with Two Phases of Service and General Retrial Times Under Bernoulli Vacation Schedule

References

• Aissani, A. (1988). On the M/G/1 queueing system with repeated orders and unreliable. Journal of Technology, 6, 93–123.
   Google Scholar
• Aissani, A. (1993). Unreliable queueing with repeated orders. Microelectronics and Reliability, 33, 2093–2106.
   Google Scholar
• Aissani, A. (1994). A retrial queue with redundancy and unreliable server. Queueing Systems, 17, 431–449.
   Google Scholar
• Aissani, A. and Artalejo, J. R. (1998). On the single server retrial queue subject to breakdowns. Queueing System, 30, 309–321.
   Google Scholar
• Artalejo, J. R. (1997). Analysis of an M/G/1 queue with constant repeated attempts and server vacations. Computers and Operations Research, 24, 493–504.
   Google Scholar
• Artalejo, J. R. (1999). A classical bibliography of research on retrial queues: Progress in 1990–1999. TOP, 7, 187–211.
   Google Scholar
• Artalejo, J. R. (1999). Accessible bibliography on retrial queues. Mathematical and Computer Modelling, 30, 1–6.
   Google Scholar
• Artalejo, J. R. (2010). Accessible bibliography on retrial queue: Progress in 2000–2009. Mathematical and Computer Modelling, 51, 1071–1081.
   Google Scholar
• Artalejo, J. R. and Choudhury, G. (2004). Steady state analysis of an M/G/1 queue with repeated attempts and two-phase service. Quality Technology & Quantitative Management, 1, 189–199.
   Google Scholar
• Artalejo, J. R. and Falin, G. (2002). Standard and retrial queueing systems: A comparative analysis. Revista Mathematica Computens, 15, 101–129.
   Google Scholar
• Atencia, I. and Moreno, P. (2005). A single server retrial queue with general retrial time and Bernoulli schedule. Applied Mathematics and Computation, 162, 855–880.
   Google Scholar
• Avi-Itzhak, B. and Naor, P. (1963). Some queueing problems with the service station subject to breakdowns. Operations Research, 11, 303–320.
   Google Scholar
• Chang, F. M. and Ke, J. C. (2009). On a batch retrial model with J vacations. Journal of Computational and Applied Mathematics, 232, 402–414.
   Google Scholar
• Choi, B. D., Park, K. K. and Pearce, C. E. M (1993). An M/M/1 retrial queue with control policy and general retrial time. Queueing Systems, 14, 275–292.
   Google Scholar
• Choi, B.D., Rhee, K.H. and Park, K.K. (1993). The M/G/1 retrial queue with retrial rate control policy. Probability in Engineering and Information Sciences, 7, 29–46.
   Google Scholar
• Choudhury, G. and Deka, K. (2008). An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair. Performance Evaluation, 65, 714–724.
   Google Scholar
• Choudhury, G. and Deka, K. (2009). An MX/G/1 unreliable retrial queue with two phases of service and Bernoulli admission mechanism. Applied Mathematics and Computation, 215, 936–949.
   Google Scholar
• Choudhury, G. and Ke, J. C. (2012). A batch arrival retrial queue with general retrial times under Bernoulli vacation schedule for unreliable server and delaying repair. Applied Mathematical Modelling, 36, 255–269.
   Google Scholar
• Choudhury, G. and 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.
   Google Scholar
• Choudhury, G. and 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.
   Google Scholar
• Choudhury, G. and Paul, M. (2006). A two phase queueing system with Bernoulli vacation schedule under multiple vacation policy. Statistical Methodology, 3, 174–185.
   Google Scholar
• Choudhury, G., Tadj, L. and Deka, K. (2010). A batch arrival retrial queueing system with two phases of service and service interruption. Computers and Mathematics with Applications, 59, 437–450.
   Google Scholar
• Choudhury, G., Tadj, L. and Paul, M. (2007). Steady state analysis of an M/G/1 queue with two phases of service and Bernoulli vacation schedule under multiple vacation policy. Applied Mathematical Modelling, 31, 1079–1091.
   Google Scholar
• Cooper, R. B. (1981). Introduction to Queueing Theory, Elsevier, Amsterdam.
   Google Scholar
• Cox, D. R. (1955). The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Proceeding of Cambridge Philosophical Society, 51, 433–441.
   Google Scholar
• Diamond, J. E. and Alfa, A. S. (1999). Approximation method for M/PH/1 retrial queues with phase type inter-retrial times. European Journal of Operational Research, 113, 620–631.
   Google Scholar
• Doshi, B. T. (1986). Queueing systems with vacations-A survey, Queueing Systems, 1, 29–66.
   Google Scholar
• Efrosinin, D. and Sztrik, J. (2011). Performance analysis of a two-server heterogeneous retrial queue with threshold policy. Quality Technology & Quantitative Management, 8, 211–236.
   Google Scholar
• Falin, G. I. (1986). Single line repeated orders queueing systems. Optimization, 17, 649–677.
   Google Scholar
• Falin, G. I. (1990). A survey of retrial queues. Queueing Systems, 7, 127–168.
   Google Scholar
• Falin, G. I. and Templeton, J. G. C. (1997). Retrial Queues, Chapman and Hall, London.
   Google Scholar
• Farahmand, K. (1990). Single line queue with repeated attempts. Queueing Systems, 6 223–228.
   Google Scholar
• Fayolle, G. in Boxma, O. J., Cohen, J. W. and Tijms, H. C. (Eds.) (1986). “A simple telephone exchange with delayed feedback”, Teletraffic Analysis and Computer Performance Evaluation. Elsevier, Amsterdam, 245–253.
   Google Scholar
• Fuhrmann, S. W. and Cooper, R. B. (1985). Stochastic decomposition in M/G/1 queue with generalized vacations. Operations Research, 33, 1117–1129.
   Google Scholar
• Gao, S. and Wang, J. (2013). Discrete-time GeoX/G/1 retrial queue with general retrial times, working vacations and vacation interruption. Quality Technology & Quantitative Management, 10, 495–512.
   Google Scholar
• Gaver, D. P. (1962). A waiting line with interrupted service including priorities. Journal of the Royal Statistical Society, Series-B, 24, 73–90.
   Google Scholar
• Gomez-Corral, A. (1999). Stochastic analysis of a single server retrial queue with general retrial time. Naval Research Logistic, 46, 561–581.
   Google Scholar
• Gomez-Corral, A. (2006). A bibliographical guide to analysis of retrial queues through matrix analytic techniques. Annals of Operations Research, 141, 163–191.
   Google Scholar
• Kapyrim, V. A. (1977). A study of stationary distributions of a queueing system with recurring demands. Cybernatics, 13, 548–590.
   Google Scholar
• Ke, J. C. and Chang F. M. (2009). M[x]/(G1,G2)/1 retrial queue under Bernoulli vacation schedules with general repeated attempts and starting failures. Applied Mathematical Modelling, 33, 3186–3196.
   Google Scholar
• Ke, J. C. and Chang, F. M. (2009). Modified vacation policy for M/G/1 retrial queue with balking and feedback. Computers and Industrial Engineering, 57, 433–443.
   Google Scholar
• Keilson, J. and Servi, L. D. (1986). Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedule. Journal of Applied Probability, 23, 790–802.
   Google Scholar
• Kella, O. (1990). Optimal control of vacation scheme in an M/G/1 queue. Operations Research, 38, 724–728.
   Google Scholar
• Krishnakumar, B. and Arivudainambi, D. (2002). The M/G/1 retrial queue with Bernoulli schedule and general retrial time. Computers and Mathematics with Applications, 43, 15–30.
   Google Scholar
• Krishnakumar, B., Arivudainambi, D. and Vijay Kumar, A. (2002). On the Mx/G/1 retrial queue with Bernoulli schedule and general retrial times. Asia Pacific Journal of Operational Research, 19, 61–79.
   Google Scholar
• Krishnakumar, B., Vijay Kumar, A. and Arivudainambi, D. (2002). An M/G/1 retrial queueing system with two phase service and preemptive resume. Annals of Operations Research, 113, 61–79.
   Google Scholar
• Kulkarni, V. G. and Choi, B. D. (1990). Retrial queues with server subject to breakdowns and repairs, QQueueingSystems, 7, 191–208.
   Google Scholar
• Kulkarni, V. G. and Liang, H. M. in Dshalalow, J. H. (Ed) (1997). “Retrial queues revisited”. Frontiers in QQueueing, CRC, New York, 19–34.
   Google Scholar
• Langaries, G. (1999). Gated pooling models with customers in orbit. Mathematical and Computer Modelling, 30, 171–187.
   Google Scholar
• Li, W., Shi, D. and Chao, X. (1997). Reliability analysis of M/G/1 queueing system with server breakdowns and vacations. Journal of Applied Probability, 34, 546–555.
   Google Scholar
• Mitrany, I. L. and Avi-Itzhak, B. (1968). A many server queue with service interruptions. Operations Research, 16, 628–638.
   Google Scholar
• Moreno, P. (2004). An M/G/1 retrial queue with recurrent customers and general retrial times. Applied Mathematics and Computation, 159, 651–666.
   Google Scholar
• Neuts, M. F. and Ramalhoto, M. F. (1984). A service model in which the server is required to search customers. Journal of Applied Probability, 21, 157–166.
   Google Scholar
• Sengupta, B. (1990). A queue with service interruptions in an alternating random environment. Operations Research, 38, 308–318.
   Google Scholar
• Sennot, L. I., Humblet, P. A. and Tweedie, R. L. (1983). Mean drifts and the non-ergodicity of Markov chain. Operations Research, 31, 783–789.
   Google Scholar
• Senthil Kumar, M. and Arumuganathan, R. On the single server batch arrival retrial queue with general vacation time under Bernoulli schedule and two phases of heterogeneous service. Quality Technology & Quantitative Management, 5, 145–160.
   Google Scholar
• Takine, T. and Sengupta, B. (1998). A single server queue with service interruptions. Queueing Systems, 26, 285–300.
   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.
   Google Scholar
• Thirurengadan, K. (1963). Queueing with breakdowns. Operations Research, 11, 62–71.
   Google Scholar
• Wang, J. and Li, J. (2008). A repairable M/G/1 retrial queue with Bernoulli vacation and two-phase service. Quality Technology & Quantitative Management, 5, 179–192.
   Google Scholar
• Wang, J. and Li, J. (2009). A single server retrial queue with general retrial times and two phases of service. Journal of System Science and Complexity, 22, 291–302.
   Google Scholar
• Wang, J., Cao, J. and Li, Q. (2001). Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Systems, 38, 363–380.
   Google Scholar
• Wenhui, Z. (2005). Analysis of a single server retrial queue with FCFS orbit and Bernoulli vacation. Applied Mathematics and Computation, 161, 353–364.
   Google Scholar
• Yang, T. and Templeton, J. G. C. (1987). A survey on retrial queues. Queueing Systems, 2, 201–233.
   Google Scholar
• Yang, T., Posner, M. J. M., Templeton, J. G. C. and Li, H. (1994). An approximation method for the M/G/1 retrial queue with general retrial times. European Journal of Operational Research, 76, 552–562.
   Google Scholar