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In optical burst switching (OBS) networks, class differentiation and isolation can be achieved by assigning adequately long time offsets between the control packet and payload of high-class bursts. While it has been recognized that the length distribution of low-class bursts plays a role in determining the size of the offsets required, there have been no studies on the effect of other factors that may also be significant. In this paper we examine the effect of the ratio of the arrival rates of low-class and high-class traffic on the level of isolation achieved in OBS networks with quality of service offsets. We show that the level of isolation in the network depends on the arrival rate of low-class traffic, especially when the amount of low-class and high-class traffic in the system is comparable. When we vary the ratio between low and high-class arrival rates from 0.1 to 10, an additional offset of three times the mean low-class burst length is required to achieve the same level of isolation. These results imply that it is important for researchers and network designers to take into account the amount of low-class traffic in the network when provisioning offsets for class differentiation in OBS networks.