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 optical burst switching (OBS) node is approximated by assuming that the maximum allowed number of arrivals to the OBS node, in a given time slot, is 2 (instead of ∞). A detailed state diagram is outlined to illustrate the problem, and then a mathematical model based on the equilibrium point analysis technique is presented. Two performance measures, namely, the steady-state system throughput and the average blocking probability, are derived from the model, which is built in the absence of wavelength conversion capability. Our proposed model is aided by a simulation work that 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 certain range of traffic load. The effect of varying different network parameters on the average blocking probability is discussed.