In this paper, the optical burst switching with burst dropping (OBS/BD) technique is proposed to be implemented in an all-optical backbone network to support IP traffic. The OBS/BD is based on two main features: i) several IP packets are assembled in a single macro-packet, called burst; ii) the burst contention in an optical switch is handled by the means of two techniques: the wavelength dimension and the "burst dropping". In the optical burst switching (OBS), the entire burst is discarded when all of the output wavelengths are engaged at its arrival instant. Whereas, the OBS/BD technique discards only the initial part of the burst and forwards the final part of the burst beginning at the instant in which one wavelength becomes free. Obviously, the OBS/BD, respect to the OBS, allows to increase the switch throughput, i.e. the number of forwarded IP packets. We develop the analytical models that quantify this increase tacking into account of several system parameters.