Internal switches in all-photonic networks do not perform data conversion into the electronic domain, thereby eliminating a potential capacity bottleneck, but the inability to perform efficient optical buffering introduces network scheduling challenges. In this paper we focus on the problem of scheduling fixed-length frames in allphotonic star-topology networks with the goal of minimizing rejected demand. We formulate the task as an optimization problem and characterize its complexity. We describe the Minimum Rejection Algorithm (MRA), which minimizes total rejection, and demonstrate that the Fair Matching Algorithm (FMA) minimizes the maximum percentage rejection of any connection. We analyze through OPNET simulation the rejection and delay performance.