1. A system for providing low-latency computational capacity, the system comprising: a virtual compute system comprising one or more hardware computing devices executing specific computer-executable instructions and configured to at least: maintain a plurality of virtual machine instances on one or more physical computing devices, wherein the plurality of virtual machine instances comprises: a warming pool comprising a first sub-pool of virtual machine instances and a second sub-pool of virtual machine instances, wherein the first sub-pool of virtual machine instances are associated with one or more fixed resource constraints and the second sub-pool of virtual machine instances are associated with one or more variable resource constraints; and an active pool comprising virtual machine instances executing one or more program codes thereon; receive a first request to execute a first program code associated with a first user, the first request including an identity of a user account associated with the first user and one or more parameters for executing the first program code; determine, based on the identity of the user account, that the first program code is to be executed using a virtual machine instance associated with the second sub-pool that satisfies a first variable resource constraint; in response to a determination that the second sub-pool lacks a virtual machine instance satisfying the first variable resource constraint, wait until a first virtual machine instance satisfying the first variable resource constraint becomes available in the second sub-pool; cause the first virtual machine instance in the second sub-pool to be added to the active pool; and cause the first program code to be executed, using the one or more parameters, in a container created on the first virtual machine instance.