Analysis of the M/G/1 Queueing System under the Triadic (N, D, J)-Policies

References

• Agarwal, R. P. and Dshalalow, J. H. (2005). New fluctuation analysis of D-policy bulk queues with multiple vacations. Mathematical and Computer Modelling, 41, 253–269.
   Google Scholar
• Artalejo, J. R. (2001). On the M/G/1 queue with D-policy. Applied Mathematical Modelling, 25, 1055–1069.
   Google Scholar
• Artalejo, J. R. (2002). A note on the optimality of the N- and D-policies for the M/G/1 queue. Operations Research Letters, 30, 375–376.
   Google Scholar
• Balachandran, K. R., Control policies for a single server system. Management Science, 19, 1013–1018, 1973
   Google Scholar
• Balachandran, K. R. and Tijms, H. (1975). On the D-policy for the M/G/1 queue. Management Science, 21, 1073–1076.
   Google Scholar
• Boxma, O. J. (1976). Note on a control problem of Balachandran and Tijms. Management Science, 22, 916–917.
   Google Scholar
• Boxma, O. J. (1989). Workloads and waiting times in single-server systems with multiple customer classes. Queueing Systems, 5(1–3), 185–214.
   Google Scholar
• Boxma, O. J. and Groenendijk, W. P. (1987). Pseudo-conservation laws in cyclic-service systems. Journal of Applied Probability, 24(4), 949–964.
   Google Scholar
• Chae, K. C. and Park, Y. I. (2001). The queue length distribution for the M/G/1 queue under the D-policy. Journal of Applied Probability, 38, 278–279.
   Google Scholar
• Crabill, T. B., Gross, D. and Magazine, M. J. (1977). A classified bibliography of research on optimal design and control of queue. Operations Research, 25, 219–232.
   Google Scholar
• Doshi, B. T. (1990). Generalizations of the stochastic decomposition results for single server queues with vacations. Stochastic Models, 6(2), 307–333.
   Google Scholar
• Dshalalow, J. H. (1998). Queueing processes in bulk systems under D-policy. Journal of Applied Probability, 35(4), 976–989.
   Google Scholar
• Erlang, A. K. (1909). The Theory of Probabilities and Telephone Conversations. Nyt Tidsskrift for Matematik, B., 20, 33–39. Reproduced in The Life and Works of A. K. Erlang, Brockmeyer et al. 1948, 131–137. Translated by Danish Academy of Technical Science.
   Google Scholar
• Heyman, D. P. (1977). The T-policy for the M/G/1 queue. Management Science, 23, 775–778.
   Google Scholar
• Lee, H. W., Lee, S. S. and Chae, K. C. (1994). Operating characteristics of M X/G/1 queue with N-policy. Queueing systems, 15, 387–399.
   Google Scholar
• Lee, H. W., Baek, J. W. and Jeon, J. (2005). Analysis of the M X/G/1 queue under D -policy. Stochastic Analysis and Application, 23, 785–808.
   Google Scholar
• Lee, H. W., Cheon, S. H. and Seo, W. J. (2006). Queue length and waiting time of the M/G/1 queue under the D-policy and multiple vacations. Queueing Systems, 54, 261280.
   Google Scholar
• Lee, H. W. and Seo, W. J. (2007). A mean value formula for the M/G/1 queue controlled by workload. Operations Research Letters, 35, 472–476.
   Google Scholar
• Lee, H. W. and Seo, W. J. (2008). The performance of the M/G/1 queue under the dyadic Min(N, D)-policy and its cost optimization. Performance Evaluation, 65, 742–758.
   Google Scholar
• Levy, H. and Yechiali, U. (1975). Utilization of idle time in an M/G/1 queueing system. Management Science, 22(2), 202–211.
   Google Scholar
• Rubin, I. and Zhang, Z. (1988). Switch-on policies for communications and queueing systems, In De Moraes, L.F.M, de Souza e Solva E. and Soares, L.F.G. (Editors), Data Communication Systems and Their Performance, Elsevier Science Publishers B.V. (North-Holland), 315–325.
   Google Scholar
• Shanthikumar, J. G. (1988). On stochastic decomposition in M/G/1 type queues with generalized server vacations. Operations Research, 36(4), 566–569.
   Google Scholar
• Tadj, L. and Choudhury, G. (2005). Optimal design and control of queues. TOP, 13(2), 359–412.
   Google Scholar
• Takagi, H. (1991). Queueing Analysis: A Foundation of Performance Evaluation, Vol I, Vacation and Priority Systems, Part I, North-Holland.
   Google Scholar
• Teghem, J. Jr. (1986). Control of the service process in a queueing system. European Journal of Operational Research, 23, 141–158.
   Google Scholar
• Tijms, H. C. (1976). On a switch-over policy for controlling the workload in a queueing system with two constant service rates and fixed switch-over costs. Statistics, 7, 933–943.
   Google Scholar
• Tijms, H. C. (1986). Stochastic Modelling and Analysis: A Computational Approach. John Wiley & Sons, Chichester.
   Google Scholar
• Wolff, R. W. (1982). “Poisson arrivals see time averages”. Operations Research, 30(2), 223–231.
   Google Scholar
• Yadin, M. and Naor, P. (1963). Queueing systems with a removable server station. Operational Research Quarterly, 14, 393–405.
   Google Scholar