Modern research and education networks, such as ESnet and Internet2, offer the capability to increase the reliability and predictability of big data transfers through the reservation of bandwidth in the form of dynamic (on-demand) virtual circuits interconnecting pairs of geographically distant end sites. Because each end site utilizes a circuit in the same manner as a VLAN, the number of circuits that can be simultaneously active is limited. In this paper, we address the problem of maximizing the number of bandwidth reservations that can be serviced by a set of virtual circuits while minimizing the number of required virtual circuits. We develop an algorithm, called CA, that solves this problem and compare its performance with a simplified version, called S-CA, and a baseline FCFS algorithm, through both offline and online simulations. We demonstrate that CA performs up to 30% better than S-CA and up to three times better than FCFS.