Paper title: |
Optimal Policy for M^{X}/G/1 Queueing System with Bernoulli Feedback |

Published in: |
Issue 3, (Vol. 4) / 2010Download |

Publishing date: |
2010-10-26 |

Pages: |
114-121 |

Author(s): |
SHINDE Vikas , KALRA Mukta, WADHWA Kamal |

Abstract. |
We deal with M^{x}/G/1 Queueing System with
Bernoulli feedback under N-Policy. The probability generating
function and supplementary variable technique are utilized to
evaluate the steady state probability distribution of the number
of units in the system. The steady state results are used to
establish the explicit expressions for the average number of
units in the system and the mean response time for three
different series time distribution. Some of the existing results
are deduced as special cases. Cost analysis is performed to
design the optimal N-policy at minimum cost. In order to
validate the analytical approach by taking illustration we
compute numerical results. |

Keywords: |
M^{x}/G/1 Queue, Supplementary Variable, N-policy, Bernoulli Feedback, Response Time, Cost Analysis. |

References: | 1. Ayyappan, G., A. Muthu Ganapathi Subramanian, Sekar G.(2010): M/M/1 Retrial Queueing system with N-policy multiple vacation under Non-Pre-Emptive Priority service by Matrix Geometric Method, Applied Mathematical Sciences, Vol. 4, No. 2, pp-1141-1154. 2. Bell, C.E.(1972): Optimal operation of an M/G/1 priority queue with removable server, Operation Research, Vol. 21, pp. 1281-1289. 3. Boxma, Onno,J. and Yechiali, Urli (1997): An M/G/1 queue with multiple types of feedback and gated vacations, J. Appl. Prob., Vol. 34, pp. 773-784. 4. Choi, B. D., Kim, Y. C., Shin, Y. W. & Pearce, C. E. M.(2002): The Mx /G/1 queue with queue length dependent service times, J. of Applied Mathematics & Stochastic Analysis, Vol.14, No. 4, pp. 399-419. 5. Cohen, J. W. (1969): The Single Server Queue, NorthHolland, Amsterdam. 6. Cox, D. R. (1995): The analysis of non-markovian stochastic processes by the inclusion of supplementary variables, Proceedings of the Cambridge Philosophical Society Vol. 51, pp. 433-441. 7. Disney, R. L.(1981): A note on sojourn times in M/G/1 queues with instantaneous, Bernaulli feedback, Naval Res. Logist. Quart., Vol.27, pp. 679-684. 8. Disney, R. L., McNickle, D. C. and Simon, B. (1980): The M/G/1 queue with instantaneous, Bernaulli feedback, Naval Res. Logist. Quart., Vol.27, pp. 635- 644. 9. Fontana, B. and Berzosa, C. D. (1984): stationary queue-length distribution in an M/G/1 queue with two non-preemptive priorities and general feedback in Performance of Computer- Communication Systems, ed. W. Bux and H. Rudin, Elsevier, North-Holland, Amsterdam. 10. Jain, M.(2003): N-policy for redundant repairable system with additional repairman, OPSEARCH, Vol. 4, pp.97- 114. 11. Jain, Madhu and Bhargava, Charu (2009): Unreliable server M/G/1 Queueing system with Bernoulli Feedback, Repeated Attempts, Modified vacation, Phase repair and Discouragement, JKAU: Eng. Sci, Vol. 20, No. 2, pp. 45-77. 12. Lillo, R. E. and Martin, M. (2000): On optimal exhaustive policies for the M/G/1 queue, Operation Research Letters, Vol. 27, pp. 39-46. 13. Medhi, J. (2001): Response time in an M/G/1 queueing system with Bernoulli feedback, in Recent Developments in Operations Research, ed. M. L. Agarwal and K. Sen, Narosa Publishing House, New Delhi, India, pp. 249- 259. 14. Simon, B. (1984): Priority queues with feedback, J. Assoc. Comput. Mach., Vol. 31, pp. 134-149. 15. Takine, T., Takagi, H. and Hasegawa, T. (1991): Sojourn times in vacation and polling systems with Bernoulli feedback, J. Appl. Prob., Vol. 28, pp. 422-432. 16. Takagi, H. (1987): Analysis and applications of a multiqueue cyclic service system with feedback, IEEE Trans. Commun., Vol.35, pp.248-250. 17. Takagi, H. (1996): A note on the response time in M/G/1 queue with service in random order and Bernoulli feedback, J. Operational Res. Soc. Of Japan, Vol. 39, No. 4, pp. 486-500. 18. Wang, K. H. and Ke, J. C.(2000): A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity, Applied Mathematical Modeling, Vol. 24, pp. 899-914. 19. Zhang, Z. G. and Love, C. E. (1998): The threshold policy in the M/G/1 queue with an exponential first vacation, INFOR, Vol. 36, No. 4, pp. 193-204. |

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