Journal of Internet of Things and Convergence (사물인터넷융복합논문지)

The Korea Internet of Things Society (한국사물인터넷학회)
권호 표지
DOI QR코드

DOI QR Code

Estimation of maximum object size satisfying mean response time constraint in web service environment

웹 서비스 환경에서 평균 응답 시간의 제약조건을 만족하는 최대 객체 크기의 추정

  • Yong-Jin Lee (Department of Technology Education, Korea National University of Education)
  • 이용진 (한국교원대학교 기술교육과 )
  • Received : 2023.03.16
  • Accepted : 2023.04.23
  • Published : 2023.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

One of the economical ways to satisfy the quality of service desired by the user in a web service environment is to adjust the size of the object. To this end, this study finds the maximum size of objects that satisfy this constraint when the mean response time is given below an arbitrary threshold for quality of service. It can be inferred that in the steady state of system, the mean response time in the deterministic model by using the round-robin will be the same as that of the queueing model following the general distribution. Based on this, analytical formulas and procedures for finding the maximum object size are obtained. As a service distribution of web traffic, the Pareto distribution is appropriate, so the maximum object size is computed by applying the M/G(Pareto)/1 model and the M/G/1/PS model using exponential distribution as computational experience. Performance evaluation through numerical calculation shows that as the shape parameter in the Pareto distribution increases, the M/G(Pareto)/1 model and M/G/1/PS model have the same maximum object size. The results of this study can be used to environments where objects can be sized for economical web service control.

웹 서비스 환경에서 사용자가 원하는 서비스 품질을 만족하는 경제적인 방법의 하나는 객체의 크기를 조절하는 것이다. 이를 위해 본 연구에서는 서비스 품질로 평균 응답 시간이 임의의 임계값 이하로 주어질 때, 이 제약 조건을 만족하는 최대 객체의 크기를 구한다. 시스템이 정상 상태일 때, 라운드-로빈을 사용하는 결정 모델의 평균 응답 시간은 일반 분포를 따르는 큐잉 모델에서의 평균 응답 시간과 같아질 것으로 추론할 수 있다. 이를 기반으로 최대 객체 크기를 발견하기 위한 해석적 수식과 절차를 수립한다. 웹 트래픽은 서비스 분포로 Pareto 분포가 적합하므로 M/G(Pareto)/1 모델과 지수 분포를 사용한 M/G/1/PS를 적용하여 최대 객체의 크기를 구한다. 수치 계산을 통한 성능평가는 Pareto 분포의 형상 파라미터(shaping parameter)가 커짐에 따라 M/G(Pareto)/1 모델과 M/G/1/PS 모델의 최대 객체 크기가 같아짐을 보여준다. 본 연구의 결과는 경제적인 웹 서비스 제어를 위해 객체의 크기를 조절하는 환경에 사용될 수 있다.

Keywords

References

  1. M. Hachol-Balter, Performance Modeling and Design of Computer Systems, pp.13-15, Cambridge Press, 2013.
  2. S. Ross, Introduction to Probability and Statistics for Engineers and Scientists, pp.538-540, Academic Press, 2012.
  3. M. E. Crovella and A. Bestavros, "Self-similarity in World Wide Web Traffic: Evidence and Possible Causes", IEEE/ACM Transactions on Networking, Vol.5, No.6, pp.835-846, 1997. https://doi.org/10.1109/90.650143
  4. W. Stallings, High-speed Networks, pp.182-198, Prentice Hall, 2002.
  5. V. Paxson and S. Floyd, "Wide Area Traffic: The Failure of Poisson Modeling," IEEE/ACM Transactions on Networking, Vol.3, No.3, pp.226-244, 1995. https://doi.org/10.1109/90.392383
  6. V. Paxson, "End-to-End Routing Behavior in the Internet," ACM SIGCOMM Communication Review, Vol.36, No.5, pp.41-56, 1996. https://doi.org/10.1145/1163593.1163602
  7. J. Reeds and M. Jorgensen, "The Double Pareto-Lognormal Distribution- A New Parametric Model for Size Distributions," Communications in Statistics- Theory and Methods, Vol.33, No.8, pp.1733-1753, 2004. https://doi.org/10.1081/STA-120037438
  8. Y. M. Tripathi, C. Petropoulos, and M. Jha, "Estimation of the Shape Parameter of a Pareto Distribution," Communications in Statistics- Theory and Methods, Vol.47, No.18, pp.4459-4468, 2018. https://doi.org/10.1080/03610926.2017.1376088
  9. R. Khayari, R. Sadre and B. R. Haverkort, "Fitting World-wide Web Request Traces with the E-M-algorithm", Performance Evaluation, Vol.52, No.2, pp.175-191, 2003. https://doi.org/10.1016/S0166-5316(02)00179-7
  10. A. Riska, V. Diev and E. Smirni, "Efficient Fitting of Long-tailed Data Sets into Hyper-exponential Distributions," in Proceedings of the IEEE Global Telecommunication Conference, Vol.3, pp.3513-2517, 2002.
  11. H. Lee, Queuing Systems for Engineers, Hong-Reung, 2008.
  12. Y. Lee, "Mean Object Size Comparison of M/G/1/PS and TDM System," ICIC Express Letters, Vol.12, No.5, pp.417-423, 2018.
  13. Y. Lee, "On the Comparison of Mean Object Size in M/G/1/PS Model and M/BP/1 Model for Web Service," International Journal of Internet, Broadcasting and Communication, Vol.14, No.3, pp.1-7, 2022.
  14. Y. -J. Lee, "Mean Object Size considering Average Waiting Latency in M/BP/1 System", International Journal of Computer Networks and Communications, Vol.12, No.5, pp.73-80, 2020. https://doi.org/10.5121/ijcnc.2020.12505
  15. Y. Lee, "Maximum Web Object Size satisfying M/G/1 Queueing Delay constraint in Multiple User Access Environment", The Journal of Korean Institute of Information Technology, Vol.12, No.6, pp.119-124, 2014.  https://doi.org/10.14801/kiitr.2014.12.6.119