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In this paper, we present for the first time an analytical model that quantifies the mechanism by which offset size affects priority in multiclass optical-burst switching (OBS) systems. Using the model, we derive an exact expression for the distribution of the number of bursts that contend with an arriving burst. The model is applicable to systems in which each class has an arbitrary burst-length distribution and an arbitrary offset size. We also derive accurate approximate expressions for the burst-blocking probability of premium-class traffic, as well as expressions for the sensitivity of premium-class performance to offset jitter and variations in the arrival rates of each class. In a case study, we find that scaling up a system in terms of the number of wavelengths and the traffic load significantly improves not only the burst-blocking performance of the premium class, but also its sensitivity to lower class traffic variations. We also use the model to dimension and provision the system to guarantee a minimum level of premium-class blocking and premium-class robustness to low-class load variations.