Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
권호 표지

An Interpretation of the Equations for the GI/GI/c/K Queue Length Distribution

GI/GI/c/K 대기행렬의 고객수 분포 방정식에 대한 해석

  • Chae, Kyung-Chul (Department of Industrial Engineering, Korea Advanced Institute of Science and Technology) ;
  • Kim, Nam-Ki (Department of Mathematics & Computer Science, Royal Military College of Canada) ;
  • Choi, Dae-Won (Department of Industrial Engineering, Korea Advanced Institute of Science and Technology)
  • 채경철 (한국과학기술원 산업공학과) ;
  • 김남기 (캐나다 왕립국방대학교수 수학 및 컴퓨터과학부) ;
  • 최대원 (한국과학기술원 산업공학과)
  • Published : 2002.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

We present a meaningful interpretation of the equations for the steady-state queue length distribution of the GI/GI/c/K queue so that the equations are better understood and become more applicable. As a byproduct, we present an exact expression of the mean queue waiting time for the M/GI/c queue.

Keywords

References

  1. Chae, K. C., Chang, S. H. and Lee, H. W. (2002a), Analysis of the M/$G^{b}$/1 Queue by the Arrival Time Approach, Journal of the Korean Institute of Industrial Engineers, 28(1), 36-43
  2. Chae, K. C., Choi, D. W. and Lee, H. W. (2002b), A Note on the Decomposition Property for $M^{X}$/G/1 Queues with Generalized Vacations, Journal of the Korean Institute of Industrial Engineers, 28(3), 247-255
  3. Chae, K. C. and Lee, H. W. (1995), $M^{X}$/G/1 Vacation Models with N-Policy: Heuristic Interpretation of the Mean Waiting Time, Journal of the Operational Research Society, 46(2), 258-264 https://doi.org/10.1057/jors.1995.31
  4. De Boer, P. T., Nicola, V. F. and Van Ommeren, J. C. W. (2001), The Remaining Service Time upon Reaching a High Level in M/G/1 Queues, Queueing Systems, 39(1), 55-78 https://doi.org/10.1023/A:1017935616446
  5. Franken, P., Konig, D., Arndt, U. and Schmidt, V. (1982), Queues and Point Processes, John Wiley & Sons, New York
  6. Kim, N. K. and Chae, K. C. (2003), Transform-Free Analysis of the GI/G/1/K Queue through the Decomposed Little's Formula, Computers & Operations Research, 30(3), 353-365 https://doi.org/10.1016/S0305-0548(01)00101-0
  7. Kimura, T. (1996), A Transform-Free Approximation for the Finite Capacity M/G/s Queue, Operations Research, 44(6), 984-988 https://doi.org/10.1287/opre.44.6.984
  8. Lee, H. W. (1998), Queueing Theory, Sigma Press, Seoul, Korea (written in Korean)
  9. Li, J. (1997), An Approximation Method for the Analysis of GI/G/1 Queues, Operations Research, 45(1), 140-144 https://doi.org/10.1287/opre.45.1.140
  10. Wolff, R. W. (1982), Poisson Arrivals See Time Averages, Operations Research, 30(2), 223-231 https://doi.org/10.1287/opre.30.2.223
  11. Wolff, R. W. (1989), Stochastic Modeling and the Theory of Queues, Prentice-Hall, Englewood Cliffs, New Jersey