NUMERICAL STUDY OF OPTIMAL BUFFER SIZE AND VACATION LENGTH IN M/G/1/K QUEUES WITH MULTIPLE VACATIONS

  • Kilhwan Kim Department of Management Engineering, Sangmyung University, South Korea
Keywords: M/G/1/K Queues, Multiple Vacations, Optimal Buffer Size, Optimal Vacation Length

Abstract

Nowadays, due to the advent of clouding computing, buffer size can be readily extended in a couple of minutes for computing servers, where the buffer size should not be considered as given when optimizing the system performance. In this context, we explore optimal combinations for the buffer size and the length of vacation time in M/G/1/K queues with multiple vacations numerically. We consider the cases of deterministic and exponentially distributed vacation and service times. In order to do this, we also formulate an optimal problem and define cost factors: the customer loss cost, the buffer holding cost, and the server operating cost. We present some numerical examples to investigate the impact of the system parameters such as the buffer size, the length of the vacation time, and the distribution of the service time, to performance measures and the total cost. We also investigate optimal combinations for the buffer size and the vacation length for various values of the cost factors.

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References

R. Zheng, J. C. Hou, and L. Sha, “Performance analysis of power management policies in wireless networks,” IEEE Transactions on Wireless Communications, vol. 5, no. 6, pp. 1351–1361, 2006.

K. De Turck, S. De Vuyst, D. Fiems, S. Wittevrongel, and H. Bruneel, “Performance of the sleepmode mechanism of the new ieee 802.16 m proposal for correlated downlink traffic,” in International conference on network control and optimization, 2009, pp. 152–165. DOI: https://doi.org/10.1007/978-3-642-10406-0_11

C.-Y. Chen, C.-H. Hsu, and K.-T. Feng, “Performance analysis and comparison of sleep mode operation for ieee 802.16 m advanced broadband wireless networks,” in Personal indoor and mobile radio communications (pimrc), 2010 ieee 21st international symposium on, 2010, pp. 1425–1430.

H. K. Aksoy and S. M. Gupta, “Optimal management of remanufacturing systems with server vacations,” The International Journal of Advanced Manufacturing Technology, vol. 54, nos. 9-12, pp. 1199–1218, 2011.

T. T. Lee, “M/g/1/n queue with vacation time and exhaustive service discipline,” Operations Research, vol. 32, no. 4, pp. 774–784, 1984. DOI: https://doi.org/10.1287/opre.32.4.774

T. T. Lee, “M/g/1/n queue with vacation time and limited service discipline,” Performance Evaluation, vol. 9, no. 3, pp. 181–190, 1989. DOI: https://doi.org/10.1016/0166-5316(89)90025-4

H. Takagi, “M/g/1/k queues with n-policy and setup times,” Queueing systems, vol. 14, nos. 1-2, pp. 79–98, 1993. DOI: https://doi.org/10.1007/BF01153527

S. Kasahara, Y. Takahashi, and T. Hasegawa, “Analysis of waiting time of m/g/1/k system with vacations under random scheduling and lcfs,” Performance evaluation, vol. 21, no. 3, pp. 239–259, 1995. DOI: https://doi.org/10.1016/0166-5316(93)E0046-8

A. Frey and Y. Takahashi, “A note on an m/gi/1/n queue with vacation time and exhaustive service discipline,” Operations research letters, vol. 21, no. 2, pp. 95–100, 1997. DOI: https://doi.org/10.1016/S0167-6377(97)00027-8

K.-H. Wang and J.-C. Ke, “A recursive method to the optimal control of an m/g/1 queueing system with finite capacity and infinite capacity,” Applied Mathematical Modelling, vol. 24, no. 12, pp. 899–914, 2000. DOI: https://doi.org/10.1016/S0307-904X(00)00024-X

K.-H. Wang, C.-C. Kuo, and W. Pearn, “Optimal control of an m/g/1/k queueing system with combined f policy and startup time,” Journal of Optimization Theory and Applications, vol. 135, no. 2, pp. 285–299, 2007. DOI: https://doi.org/10.1007/s10957-007-9253-6

Y. Park and G. U. Hwang, “An efficient power saving mechanism for delay-guaranteed services in ieee 802.16 e,” IEICE transactions on communications, vol. 92, no. 1, pp. 277–287, 2009. DOI: https://doi.org/10.1587/transcom.E92.B.277

Published
2019-02-28
How to Cite
Kim, K. (2019). NUMERICAL STUDY OF OPTIMAL BUFFER SIZE AND VACATION LENGTH IN M/G/1/K QUEUES WITH MULTIPLE VACATIONS . International Journal of Engineering Technologies and Management Research, 6(2), 1-13. https://doi.org/10.29121/ijetmr.v6.i2.2019.350