The offset-time-based QoS scheme has been proposed for the next generation Optical Internet as a way to improve current IP's best effort service. For a single node, it has been shown that the offset-time-based scheme efficiently achieves service differentiation without requiring any buffer at the WDM layer. In this paper, the offset-time-based scheme is applied to the multi-hop base. To this end, we consider various policies to handle blocked bursts such as drop, retransmission, deflection routing and buffering in the multi-hop very high performance Backbone Network Service (vBNS), and compare their performance in terms of average wavelength utilization, the average wavelength efficiency and the average end-to-end extra delay. It is shown that the buffering policy is useful with scarce network resource (e.g., bandwidth), but the dropping policy in conjunction with the offset-time-based scheme is good enough with abundant resources.