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An enhanced mathematical model is introduced to study and evaluate the performance of a core node in an optical burst switched network. In the proposed model, the exact Poisson traffic arrivals to the OBS node is approximated by assuming that the maximum allowed number of arrivals to the OBS node, in a given time slot, is two (instead of infinity). A detailed state diagram is outlined to illustrate the problem, and then a mathematical model based on the equilibrium point analysis (EPA) technique is presented. The steady-state system throughput is derived from the model which is built in the absence of wavelength conversion capability. Our proposed model is aided by a simulation work which studies the performance of an OBS core node under the assumption of Poisson traffic arrivals (the exact case) and calculates the steady- state system throughput. The results obtained from the proposed mathematical model are consistent with that of simulation when assuming Poisson traffic arrivals and this consistency holds for a wide range of traffic load.