Abstract  Scheduling resources on Grids is a well-known problem. The extension of Grids to LambdaGrids requires the scheduling of lambdas, i.e., end-to-end high-speed circuits. In this paper, we propose a scheduling heuristic for such lambdas in support of large-scale scientific applications that require high-throughput transfers of large files. We refer to this heuristic as Varying-Bandwidth List Scheduling (VBLS) because the scheduler returns a Time-Range-Capacity (TRC) allocation vector with varying bandwidth levels assigned for different time ranges within the duration of a transfer. The advantage of VBLS over a fixed-bandwidth allocation scheme is that it allows the scheduler to backfill any holes left in resource allocations. Enabling VBLS requires end host applications to specify the file size in their transfer requests. To characterize VBLS, we ran simulation experiments that show that VBLS performance approaches packet-switching performance. This result means that file transfers can take advantage of bandwidth that becomes available subsequent to the start of transfers, a current and critical drawback of typical fixed-bandwidth allocation schemes in circuit-switched networks. Next, we identify the key features needed in a transport protocol that works in conjunction with VBLS and develop the Varying Bandwidth Transport Protocol (VBTP). VBTP is a rate based flow control scheme that is coupled with Selective-ARQ based error control. Finally, the paper concludes with a discussion on the impact of transport problems on VBLS scheduling.