The ability to reserve network bandwidth is critical for the success of high-performance grid applications. While reservation of lightpaths in dynamically switched optical networh facilitates guaranteed bandwidth, it is also imperative to eflectively schedule these bandwidth reservations so as to orchestrate worylows involving computational, storage, and network resources. However, reservation can often lead to bandwidth fragmentation which signijicantly reduces system utilization and increases the blockingprobability of requests. In this paper, we present a dynamic bandwidth scheduling scheme which exploits the quasi-flexible nature ofbandwidth reservations andmitigates the problem of bandwidth fragmentation in LambdaGrids.