Modern data-intensive applications move vast amounts of data between multiple locations around the world. To enable predictable and reliable data transfers, next generation networks allow such applications to reserve network resources for exclusive use. In this paper, we solve an important problem (called SMR3) to accommodate multiple and concurrent network reservation requests between a pair of end sites. Given the varying availability of bandwidth within the network, our goal is to accommodate as many reservation requests as possible while minimizing the total time needed to complete the data transfers. First, we prove that SMR3 is an NP-hard problem. Then, we solve it by developing a polynomial-time heuristic called RRA. The RRA algorithm hinges on an efficient mechanism to accommodate large number of requests in an iterative manner. Finally, we show via numerical results that RRA constructs schedules that accommodate significantly larger number of requests compared to other, seemingly efficient, heuristics.