On Burst Length Distribution and Preemption Probabilities in OBS Networks with Burst Segmentation

Recently, preemption techniques have attracted considerable attention as a means to provide differentiated quality of service in optical burst switching (OBS) networks. This paper is focused on the analysis of preemption probabilities for bursts within the same priority class. As proposed by Vokkarane and Jue ((2003)* IEEE J Select Areas Commun 21(7): 1198–1209) an incoming burst will preempt the burst in service, within the same priority class, if the residual length of the burst in service is smaller than the incoming burst length. For a general case with wavelength conversion, the preemption probability of contending bursts with a generic service distribution, not necessarily exponential, is analyzed. First, we show that the size distribution for the preempting bursts is shifted to larger values, in comparison to the original burst size distribution. Second, we obtain an upper and lower bound for the preemption probability. Finally, the asymptotic behavior of the OBS switch is analyzed showing that preemption will always occur for a very large number of wavelengths.