Abstract: Systems and methods are described for allocating resources on an on-demand code execution system under conditions of scarcity, when demand for resources exceeds threshold limits. Under such conditions, a single high-demand resource consumer—such as a function or an account on the system—might monopolize available resources, denying access to the system to other resource consumers. Embodiments of the present disclosure prevent that monopolization by implementing constrained equal awards allocation, whereby resource consumers with relatively low-demand are allocated their requested resources, and remaining resources are divided substantially equally among remaining consumers of relatively high demand. The allocation techniques described herein may be implemented even under varying demand levels, without requiring each consumer to positively state their desired portion prior to allocation.