Analyzing a degenerate buffer with general inter-arrival and service times in discrete time |
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Authors: | W. Rogiest K. Laevens J. Walraevens H. Bruneel |
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Affiliation: | (1) SMACS Research Group, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium |
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Abstract: | In novel switching approaches such as Optical Burst Switching, the involved buffers can only provide a degenerate waiting room, with delays restricted to multiples of a basic value, the granularity. Although the resulting performance loss was already studied analytically, previous work is either limited by the assumption of independent arrivals, or it involves a matrix with size growing fast with buffer size or arrival process complexity. Overcoming this, we developed a generic and accurate loss performance model for a degenerate GI/G/1 buffer in discrete time, that yields results instantly for any constellation of burst sizes, inter-arrival times, granularity, load and buffer size. This paper presents our model and compares its results to simulations, illustrating the impact of different types of correlation in the arrival process on loss performance. Our basic model is general and accurate, it can thus serve as a basic tool for optical switch design. |
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Keywords: | Degenerate buffer Optical buffer FDL buffer Cyclic waiting Lakatos-type queueing system Correlated traffic Granularity Discrete-time queueing Generating functions |
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