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This paper presents a new analytical model for calculating the blocking probability in Just-Enough-Time (JET)-based optical burst switching networks. Relationship to the problem of calculating the reservation probability in advance reservation systems is also discussed. The proposed analytical model takes into consideration the effects of the burst offset time and the burst length on the blocking probability. We use a (M+1)-state non-homogenous Markov chain to describe the state of an output link carrying M wavelength channels. In addition, we model each wavelength channel by a 2-state Markov chain. The offset time is drawn from a specified distribution so that wavelength reservation requests, made before a given time, build up to be a workload whose mean value declines with the reservation starting time. Furthermore, we express the blocking probability in terms of first passage time distributions to account for the burst length. To verify its accuracy, the model results are compared with the results of a sophisticated discrete-event simulation model. The model results were found to be in satisfactory agreement with simulation results.