WAVELET COMPRESSION OF NETWORK DELAY MEASUREMENTS Konstantinos G. Kyriakopoulos, Professor David J. Parish High Speed Networks, Electronic and Electrical Engineering, Loughborough University Lougborough, Leicestershire, LE11 3TU, U.K. k.kyriakopoulos@lboro.ac.uk Abstract Monitoring high-speed networks produces a large amount of network performance measurements over a long period of time making their storage impractical. This paper looks at the Wavelet Transform as a method of compressing the information describing network delay measurements while maintaining quality of important signal features. A wavelet coefficient thresholding technique is used along with an efficient method for storing wavelet coefficients. Experimental results are obtained to compare soft and hard thresholding techniques by using the mean square error (MSE) statistic and the file size of the compressed output. In addition, those two techniques are compared against the lossless compression tool bzip2. Results show that the proposed method achieves 6.5 times more compression than bzip2 while preserving the peaks and bursty segments of the examined signals. Keywords UKLight, MASTS, network performance measurements, compression, wavelets 1. INTRODUCTION This paper is motivated by the need to measure the performance of high-speed communication networks of the future and specifically of the UKLight experimental network. The UKLight initiative is a 10 Gb/s, high capacity research network facility that interconnects JANET, the UK’s research and educational network, with several other continental research networks [1]. The MASTS (Measurement and Analysis in all Scales of Time and Space) project has been initiated to provide a traffic monitoring system for the UKLight network capable of recording data at various time scales and replying to real-time queries. There are two main challenges in the MASTS project that should be considered. The first challenge is the high volume of traffic transport that UKLight is capable of delivering. The second challenge is the long duration of the network’s active status, during which the traffic is recorded. At the heart of the MASTS project is the need to derive an efficient method of data analysis and reduction in order to archive and store the enormous amount of monitored traffic [2]. In this paper, wavelet analysis is applied to network delay measurements in order to compress the size of the information without reducing the quality in important features of the signal. This work is not looking in ways of using wavelets to measure the delay. Delay signals were taken from the BT project of High Speed Networks in Loughborough. Experimental results are obtained to compare soft and hard thresholding techniques by using the mean square error (MSE) statistic and the file size of the compressed output. In addition, the results from those two techniques are compared against the lossless compression tool bzip2. The rest of the paper is structured as follows. In section 2 the concepts of wavelet analysis, wavelet compression and thresholding are introduced. In Section 3 the methodology of this work is presented. Section 4 discusses the results of the proposed methodology after being applied to thirty signals. Finally, the conclusions and the future work are given in Section 5. 2. WAVELETS, THRESHOLDS AND DENOISING In contrast with other techniques that use a constant window size to analyze a section of a signal (DCT, STFT), wavelet analysis has the benefit of varying the window size. For that reason, wavelets can adapt to various time-scales and perform local analysis. Local analysis is the ability to analyze a localized section of a larger signal [3].