Analysis of discrete-time TES/G/1 and TES/D/1-K queueing systems

Future B-ISDN (Broadband Integrated Services Data Network) and ATM (Asynchronous Transfer Mode) networks support several applications, e.g. speech and video sources. It is well recognized that the traffic streams and superposition of several traffic streams generated by such services have variable bit rates (VBR) with a high degree of burstiness and autocorrelation. TES (Transform Expand Sample) techniques can be applied to model such kinds of traffic streams. TES techniques are a versatile methodology for fitting and modelling stationary and autocorrelated time series. Although TES models can be easily implemented for simulation studies and predictions of the interesting performance quantities of queueing systems, e.g. waiting time and loss probability, the need arises for analytical results on the performance evaluation of queueing systems with autocorrelated arrival and/or service processes, as the performance quantities mentioned above may be difficult and time consuming to obtain via simulation models, when they become extremely small (typically 10−6 to 10−9). This study deals with exact and approximative analysis of TES/G/1 and TES/D/1-K queueing systems where the arriving packets/cells are served with FCFS (First Come First Serve) service strategy. DFT (Discrete Fourier Transformation) can be applied to reduce the computation overhead in the analysis of TES/G/1 and TES/D/1-K queueing systems.