We demonstrate an optical time buffer technology that meets the requirements of an all-optical packet router with a load-balancing architecture. The buffer is based on wavelength switching and an arrayed waveguide grating, which selects one of the delays in an array of fiber delay lines of increasing length. This buffer is unique because it enables the maximal sharing of delay lines among multiple input ports. Each of the N delays can simultaneously support N different wavelengths; therefore, for N input ports, the total buffer capacity is of the order of N3 packets. Measurements performed with data at 10 Gbits/s and N=3 show that there is only a 2 dB bit error rate (BER) penalty resulting from wavelength switching.