Parameter Estimation of Markovian Arrivals with Utilization Data

• LI Chen

  Department of Bioscience and Bioinformatics, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology

• ZHENG Junjun

  Department of Information Science and Engineering, Ritsumeikan University

• OKAMURA Hiroyuki

  Graduate School of Advanced Science Engineering, Hiroshima University

• DOHI Tadashi

  Graduate School of Advanced Science Engineering, Hiroshima University

Abstract

Utilization data (a kind of incomplete data) is defined as the fraction of a fixed period in which the system is busy. In computer systems, utilization data is very common and easily observable, such as CPU utilization. Unlike inter-arrival times and waiting times, it is more significant to consider the parameter estimation of transaction-based systems with utilization data. In our previous work [7], a novel parameter estimation method using utilization data for an Mt/M/1/K queueing system was presented to estimate the parameters of a non-homogeneous Poisson process (NHPP). Since NHPP is classified as a simple counting process, it may not fit actual arrival streams very well. As a generalization of NHPP, Markovian arrival process (MAP) takes account of the dependency between consecutive arrivals and is often used to model complex, bursty, and correlated traffic streams. In this paper, we concentrate on the parameter estimation of an MAP/M/1/K queueing system using utilization data. In particular, the parameters are estimated by using maximum likelihood estimation (MLE) method. Numerical experiments on real utilization data validate the proposed approach and evaluate the effective traffic intensity of the arrival stream of MAP/M/1/K queueing system. Besides, three kinds of utilization datasets are created from a simulation to assess the effects of observed time intervals on both estimation accuracy and computational cost. The numerical results show that MAP-based approach outperforms the exiting method in terms of both the estimation accuracy and computational cost.

Journal

• IEICE Transactions on Communications

  IEICE Transactions on Communications E105.B (1), 1-10, 2022-01-01

  The Institute of Electronics, Information and Communication Engineers

Keywords

• parameter estimation
• utilization data
• Markovian arrival process
• maximum likelihood estimation
• effective traffic intensity

Details

• CRID: 1390290617367652224
• NII Article ID: 130008138811
• DOI: 10.1587/transcom.2021ebp3007
• ISSN: 17451345
• ISSN: 09168516
• Web Site: https://www.jstage.jst.go.jp/article/transcom/E105.B/1/E105.B_2021EBP3007/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed