Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

DISCRETE-TIME QUEUE WITH VARIABLE SERVICE CAPACITY

  • LEE YUTAE (Department of Information and Communication Engineering Dongeui University)
  • Published : 2005.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper considers a discrete-time queueing system with variable service capacity. Using the supplementary variable method and the generating function technique, we compute the joint probability distribution of queue length and remaining service time at an arbitrary slot boundary, and also compute the distribution of the queue length at a departure time.

Keywords

References

  1. H. Bruneel, Performance of discrete-time queueing systems, Comput. Oper. Res. 20 (1993), 303-320 https://doi.org/10.1016/0305-0548(93)90006-5
  2. H. Bruneel and B. Kim, Discrete-time Models for Communication Systems Including ATM, Kluwer Academic Publishers, 1993
  3. M. L. Chaudhry and S. H. Chang, Analysis of the discrete-time bulk-service queue $Geo/G^Y$ /1/n + B, Oper. Res. Lett. 2003
  4. M. L. Chaudhry and J. G. C. Templeton, A First Course in Bulk Queues, John Wiley & Sons, 1983
  5. B. D. Choi, D. I. Choi, Y. Lee and D. K. Sung, Priority queueing system with fixed-length packet-train arrivals, IEE Proceedings-Communications 145 (1998), no. 5, 331-336
  6. B. D. Choi, Y. Lee and D. I. Choi, $Geo^{X_{1}}$, $Geo^{X_{2}}$/D/c HOL priority queueing system with random order selection within each priority class, Probab. Engrg. Inform. Sci. 12 (1998), no. 1, 125-139 https://doi.org/10.1017/S026996480000509X
  7. E. Cinlar, Introduction to Stochastic Processes, Prentice-Hall, Inc., Englewood Cliff, New Jersey, 1975
  8. T. J. J. Denteneer, J. S. H. van Leeuwaarden and J. A. C. Resing, Bounds for a discrete-time multi server queue with an application to cable networks, ITC 18, Berlin, 2003
  9. J. H. Dshalalow, Frontiers in queueing, CRC Press, Boca Raton, Florida, 1997
  10. M. A. Dummler and A. K. Schomig, Using discrete-time analysis in the performance evaluation of manufacturing systems, 1999 International Conference on Semiconductor Manufacturing Operational Modeling and Simulation(SMOMS'99), San Francisco, California, January, 1999, 18-20
  11. U. C. Gupta and V. Goswami, Performance analysis of finite buffer discrete-time queu with bulk service, Comput. Oper. Res. 29 (2002), 1331-1341 https://doi.org/10.1016/S0305-0548(01)00034-X
  12. G. U. Hwang and K. Sohraby, Power tail aymptotic results of a discrete time queue with long range dependent input, J. Korean Math. Soc. 40 (2003), no. 1, 87-107
  13. N. K. Kim and M. L. Chaudhry, An invariance relation and a unified method to derive stationary queue-length distributions, Oper. Res. 52 (2004), no. 5
  14. J. Lamperti., Criteria for the recurrence or transience of stochastic process, I, J. Math. Anal. Appl. 1 (1960) 314-330 https://doi.org/10.1016/0022-247X(60)90005-6
  15. Y. Lee, Discrete Time Analysis of GI /G /1 Priority Queueing Systems, M.S. dissertation, Korea Advanced Institute of Science and Technology(KAIST), Korea, 1993
  16. Y. Lee, Discrete-time $Geo^X$/G/1 queue with preemptive resume priority, Math. Comput. Modelling 34 (2001), 243-250 https://doi.org/10.1016/S0895-7177(01)00057-7
  17. Y. Lee and B. D. Choi, Queueing system with multiple delay and loss priorities for ATM networks, Inform. Sci. 138 (2001), no. 1-4, 7-29 https://doi.org/10.1016/S0020-0255(01)00151-7
  18. Y. Lee and K. S. Lee, Discrete-time $Geo^X$/G/1 queue with preemptive repeat different priority, Queueing Syst. Theory Appl. 44 (2003) no. 4, 399-411 https://doi.org/10.1023/A:1025199506212
  19. Y. Lee, Y. H. Kim and J. D. Huh, Discrete-time $Geo^X$/G/1 queue with nonpreemptive priority, Comput. Math. Appl. 46 (2003), no. 10-11, 1625-1632
  20. A. G. Pakes, Some conditions for ergodicity and recurrence of Markov chains, Oper. Res. 17 (1969), 1058-1061 https://doi.org/10.1287/opre.17.6.1058
  21. T. L. Saaty, Elements of queueing theory with applications, McGraw-Hill Book company, 1961
  22. H. Takagi, Queueing Analysis Vol.3: Discrete-time systems, North-Holland, Amsterdam, 1993