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In this paper, an exact analytical model for computation of burst length distribution under time-correlated input sources, at the output of an edge optical burst switching node, has been developed. Approximation techniques, to reduce time complexity of the model, have also been suggested. Effects of time correlation is successfully captured and it is found that for constant load, the variance of burst length increases with increased correlation. It is also observed that the variance of burst length reaches its peak value for a particular value of load, depending on the source correlation. The analytical results were verified with simulation studies.