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Previously, we proposed a data buffering system that makes use of a pair of white light cavities. For application to telecommunication systems, it would be convenient to realize such a device using fiber-optic resonators. In this paper, we present the design of such a system, where the white light cavity effect is produced by using stimulated Brillouin scattering. The system consists of a pair of fiber-optic white light cavities placed in series. As in the original proposal, the delay time can be controlled independently of the bandwidth of the data pulses. Furthermore, we show how the bandwidth of the system can be made as large as several times the Brillouin frequency shift. We also show that the net delay achievable in such a buffer can be significantly larger than what can be achieved using a conventional recirculating loop buffer.