Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지

An Extension of the Level Crossing Technique

레벨횡단법의 확장에 대한 소고

  • 채경철 (한국과학기술원 산업공학과) ;
  • 이승원 (한국과학기술원 산업공학과)
  • Published : 2004.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

We demonstrate in this paper that the level crossing technique can be applied to such a system that not only the state vector is two-dimensional but Its two components are heterogeneous. As an example system, we use the GI-G/c/K queue whose state vector consists of the number of customers in the system and the total unfinished work.

Keywords

References

  1. 이호우, ‘대기행렬이론’, 개정판, 시그마프레스, 1998
  2. 채경철, 김남기, 최대원, ‘GI/G/c/K 대기행렬의 고객수 분포 방정식에 대한 해석’, ‘대한산업공학회지’, 제28권, 제4호(2002), pp.391-397
  3. Brill, P.H. and M.J.M. Posner, ‘Level Crossings in Point Processes Applied to Queues : Single-Server Case‘, Operations Research, Vol.25(1977), pp.662-674
  4. Cohen, J.W., 'On Up-and Downcrossings', J. of Applied Probability, Vol.14(1977), pp.405-410
  5. Doshi, B., 'Level-Crossing Analysis of Queues', Queueing and Related Models (Editors : U.N. Bhat et al), Clarendon Press, Oxford, 1992, pp.3-33
  6. Franken, P., D. Konig, U. Arndt and V. Schmidt, Queues and Point Processes, Wiley, New York, 1982
  7. Kim, S. and E.Y. Lee, 'A Level Crossing Approach to the Analysis of Finite Dam', J. of Korean Statistical Society, Vol.31, NO.3(2002), pp.405-413
  8. Perry, D. and B. Levikson, 'Continuous Production/Inventory Model with Analogy to Certain Queueing and Dam Models', Advances in Applied Probability, Vol.21(1989), pp.123-141
  9. Wolff, R.W., 'Poisson Arrivals See Time Averages', Operations Research, Vol.30, No.2(1982), pp.223-231 https://doi.org/10.1287/opre.30.2.223
  10. Wu, P. and M.J.M. Posner, 'A Level-Crossing Approach to the Solution of the Shortest-Queue Problem', Operations Research Letters, Vol.2l(1997), pp.181-189