Journal of the Institute of Electronics Engineers of Korea CI (전자공학회논문지CI)

The Institute of Electronics and Information Engineers (대한전자공학회)
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Fuzzy M/M/l/K Queueing Network Model for Performance Evaluation of Network System

네트워크 시스템의 성능평가를 위한 퍼지 M/M/l/K 큐잉네트워크모델

  • Choo, Bong-Jo (Division of Computer Information Processing, Kimcheon College) ;
  • Jo, Jung-Bok (Dept. of Computer Engineering., School of System Engineering, Dongseo Univ.) ;
  • Woo, Chong-Ho (School of Electrical and Computer Engineering, Pukyong National Univ.)
  • 추봉조 (금천대학 컴퓨터정보처리계열) ;
  • 조정복 (동서대학교 시스템공학부 컴퓨터공학과) ;
  • 우종호 (부경대학교 전자컴퓨터정보통신공학부)
  • Published : 2001.07.25
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Abstract

In this paper, we propose Fuzzy M/M/1/K queueing network model which has derived by appling the fuzzy set theory to M/M/l/K queueing network model in which has single server and system capacity K. When the arriving rate of input job and the servicing rate of a server arc represented as the linguistic attributes, the system analysis can be performed by using this model. The major evaluation measures of system such as the average number of jobs existing in the system, the average number of jobs into system, and the average spending time of job in system etc. are derived for the evaluation of system. Computer simulation was performed for verifying the effectiveness of these result equations. In which the various fuzzy arriving rates and fuzzy servicing rates according to varying the system capacity K were given for the system evaluation. We verified that the results of simulation are in accord with the expected evaluations in the proposed fuzzy model.

본 논문에서는 한 개의 서버와 시스템용량 K를 갖는 M/M/1/K 큐잉네트워크모델에 펴지집합이론을 적용한 퍼지 M/M/1/K 큐잉네트워크모델을 제안하였다. 작업의 도착율과 서버의 서비스율의 형태가 언어적 속성으로 표현될 때， 이 모델을 사용하여 시스템의 해석이 가능해진다. 시스템의 평가를 위해서 시스템내 평균작업수， 작업 평균진입률， 그리고 작업 평균소요시간 등 시스템의 주요 평가측도를 유도하였다. 퍼지 작업 환경에서 이러한 결과식들의 유효함을 검증하기 위하여， 제안된 모델에 다양한 퍼지도착율 ${\lambda}$와 퍼지서비스율 ${\mu}$에 대하여 시스템용량 K 값의 변화에 따른 성능평가를 컴퓨터 시뮬레이션하였다. 그 결과가 제안한 퍼지 모델에서 예측한 평가와 일치함을 확인하였다.

Keywords

References

  1. A O. Allen, Probability, Statistics, and Queueing Theory with Computer Science Applications, Academic Press, California, 1990
  2. T. G. Robertazzi, Computer networks and systems : queueing theory and performance evaluation, Springer-Verlag, New York, 1994
  3. Randolph Nelson, Probability, stochastic processes, and queueing theory the mathematics of computer performance modelling, Springer Verlag, New York, 1995
  4. Yue Ma, James J. Han, and Kishor S. Trivedi, 'Composite Performance and Availability Analysis of Communications Networks: A Comparison of Exact and Approximate Approaches,' IEEE GLOBECOM, vol. 3, pp. 1771-1777, 2000 https://doi.org/10.1109/GLOCOM.2000.891940
  5. J. B. Jo, Y. Tsujimura, M. Gen, and G. Yamazaki, 'Performance Evaluation of Computer System with Failure Based on Fuzzy Set Theory,' J. of the Operations Research Society of Japan, vol. 38, no. 4, pp.409-422, 1995
  6. J. B. Jo, Y. Tsujimura, M. Gen, and G. Yamazaki, 'Performance Evaluation of Network Models based on Fuzzy Queueing System,' J. of Japan Society for Fuzzy Theory and Systems, vol. 8, no. 3, pp. 50-55, 1996
  7. Y. A. Philis and Runtong Zang, 'Fuzzy Service Control of Queueing System,' IEEE Tran. on Syst. Man Cyber, vol. 29, no. 4, pp, 503-517, 1999 https://doi.org/10.1109/3477.775266
  8. Nico M. van Dijk, 'On Hybrid Combination of Queueing and Simulation,' 2000 Winter Simulation Conference Proceedings, vol. 1, pp. 147-150, 2000 https://doi.org/10.1109/WSC.2000.899709
  9. J. J. Buckley and Y Qu, 'Solving Systems of Fuzzy Equations: A New Solution Concept,' Fuzzy Sets and Systems, vol. 39, pp. 291-301, 1991 https://doi.org/10.1016/0165-0114(91)90099-C
  10. A. Kaufmann and M. M. Gupta, Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold, 1985
  11. J. J. Buckley, 'Elementary Queueing Theory Based on Possibility Theory,' Fuzzy Sets and Systems, vol. 37, pp, 43-52, 1990 https://doi.org/10.1016/0165-0114(90)90062-B