The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Multiclass loss systems with several server allocation methods

여러 서버배정방식의 멀티클래스 손실시스템 연구

  • Na, Seongryong (Department of Information and Statistics, Yonsei University)
  • 나성룡 (연세대학교 정보통계학과)
  • Received : 2016.03.04
  • Accepted : 2016.05.09
  • Published : 2016.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study multiclass loss systems with different server allocation methods. The Markovian states of the systems are defined and their effective representation is investigated. The limiting probabilities are derived based on the Markovian property to determine the performance measures of the systems. The effects of the assignment methods are compared using numerical solutions.

이 논문에서는 서로 다른 서버배정방식을 가지는 멀티클래스 손실시스템을 연구한다. 마코프 성질을 유지하도록 상태를 정의하고 상태를 효율적으로 표현하는 방법을 살펴본다. 시스템 성능척도를 산출하기 위하여 마코프 성질에 기초한 극한확률 유도를 연구한다. 해석해 혹은 수치해를 구하여 배정방식이 시스템 성능에 미치는 영향을 비교한다.

Keywords

References

  1. Kelly, F. P. (1991). Loss networks, Annals of Applied Probability, 1, 319-378. https://doi.org/10.1214/aoap/1177005872
  2. Koo, I., Yang, J., Ahmad, A., and Kim, K. (2002). Erlang capacity analysis of hybrid FDMA/CDMA systems supporting multi-class services according to channel assignment methods, International Journal of Communication Systems, 15, 867-880. https://doi.org/10.1002/dac.569
  3. Koo, I., Yang, J., and Kim, K. (2000). Analysis of Erlang capacity for DS-CDMA systems supporting multiclass services with the limited number of channel elements. In Proceedings of IEEE Conference on Wireless Communications and Networking 2000, USA, 355-359.
  4. Lee, J., Na, S., Choi, Y., and Lim, S. (2002). Performance analysis on channel distribution algorithm of selector in CDMA2000 1x system. In Proceedings of Korea Information and Communications Society, Summer 2002.
  5. Na, S. (2006). Exact performance evaluation of multi-class loss systems with applications to telecommunications networks, Telecommunications Review, 16, 1084-1091.
  6. Na, S. (2010). Markov modeling of multiclass loss systems, The Korean Journal of Applied Statistics, 23, 747-757. https://doi.org/10.5351/KJAS.2010.23.4.747
  7. Na, S. (2014). Numerical iteration for stationary probabilities of Markov chains, Communications for Statistical Applications and Methods, 21, 513-520. https://doi.org/10.5351/CSAM.2014.21.6.513
  8. Nesterov, Y. and Nemirovski, A. (2015). Finding the stationary states of Markov chains by iterative methods, Applied Mathematics and Computation, 255, 58-65. https://doi.org/10.1016/j.amc.2014.04.053
  9. O'Leary, D. P. (1993). Iterative methods for finding the stationary vector for Markov chains, Linear Algebra, Markov Chains, and Queueing Models (C.D. Meyer and R.J. Plemmons (ed.)), The IMA volumes in mathematics and its applications, 48, 125-136, Springer, New York. https://doi.org/10.1007/978-1-4613-8351-2_9
  10. Ross, K. W. (1995). Multiclass Loss Models for Broadband Telecommunication Networks, Springer, London.
  11. Ross, S. M. (1996). Stochastic Processes (2nd Ed), Wiley, New York.
  12. Stewart, W. J. (2000). Numerical methods for computing stationary distributions of finite irreducible Markov chains. In W.K. Grassmann (Ed.), Computational Probability, International series in operations research and management science, 24, 81-111, Springer, New York.
  13. Zhao, D., Li, H., and Su, D. (2012). A numerical algorithm on the computation of the stationary distribution of a discrete time homogeneous finite Markov chain, Mathematical Problems in Engineering, 2012.