Generalized Variance-Based Markovian Fitting for Self-Similar Traffic Modelling(<Special Section>Internet Technology V)

• SHAO Shou Kuo

  Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University Network Operation Supporting Technology Lab., Chunghwa Telecommunication Laboratories

• REDDY PERATI Malla

  Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University

• TSAI Meng Guang

  Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University

• TSAO Hen Wai

  Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University

• WU Jingshown

  Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University

Abstract

Most of the proposed self-similar traffic models are asymptotic in nature. Hence, they are less effective in queueing-based performance evaluation when the buffer sizes are small. In this paper, we propose a short range dependent (SRD) process modelling by a generalized variance-based Markovian fitting to provide effective queueing-based performance measures when buffer sizes are small. The proposed method is to match the variance of the exact second-order self-similar processes. The fitting procedure determines the related parameters in an exact and straightforward way. The resultant traffic model essentially consists of a superposition of several two-state Markov-modulated Poisson processes (MMPPs) with distinct modulating parameters. We present how well the resultant MMPP could emulate the variance of original self-similar traffic in the range of the specified time scale, and could provide more accurate bounds for the queueing-based performance measures, namely tail probability, mean waiting time and loss probability. Numerical results show that both the second-order statistics and queueing-based performance measures when buffer capacity is small are more accurate than that of the variance-based fitting where the modulating parameters of each superposed two-state MMPP are equal. We then investigate the relationship between time scale and the number of superposed two-state MMPPs. We found that when the performance measures pertaining to larger time scales are not better than that of smaller ones, we need to increase the number of superposed two-state MMPPs to maintain the accurate and reliable queueing-based performance measures. We then conclude from the extensive numerical examples that an exact second-order self-similar traffic can be well represented by the proposed model.

Journal

• IEICE transactions on communications

  IEICE transactions on communications 88 (4), 1493-1502, 2005-04-01

  The Institute of Electronics, Information and Communication Engineers

Keywords

• index of dispersion for counts
• MMPP
• self-similarity
• variance-time

Details

• CRID: 1573105975069694464
• NII Article ID: 10016563858
• NII Book ID: AA10826261
• ISSN: 09168516
• Text Lang: en
• Data Source:
  • CiNii Articles