Streaming computations often exhibit substantial data parallelism that makes them well-suited to SIMD architectures. However, many such computations also exhibit irregularity, in the form of data-dependent, dynamic data rates, that makes efficient SIMD execution challenging. One aspect of this challenge is the need to schedule execution of a computation realized as a pipeline of stages connected by finite queues. A scheduler must both ensure high SIMD occupancy by gathering queued items into vectors and minimize costs associated with switching execution between stages. In this work, we present the AFIE (Active Full, Inactive Empty) scheduling policy for irregular streaming applications on SIMD processors. AFIE provably groups inputs to each stage of a pipeline into a minimal number of SIMD vectors while incurring a bounded number of switches relative to the best possible policy. These results apply even though irregularity forbids a priori knowledge of how many outputs will be generated from each input to each stage. We have implemented AFIE as an extension to the MERCATOR system  for building irregular streaming applications on NVIDIA GPUs.We describe how the AFIE scheduler simplifies MERCATOR's runtime code and empirically measure the new scheduler's improved performance on irregular streaming applications.