1. A system for providing low-latency computational capacity from a virtual compute fleet, the system comprising: an electronic data store configured to store at least a program code of a user; and a virtual compute system comprising one or more hardware computing devices executing specific computer-executable instructions, said virtual compute system in communication with the data store, 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 comprise: a warming pool comprising virtual machine instances having one or more software components loaded thereon; and an active pool comprising virtual machine instances assigned to one or more users, wherein the virtual compute system is configured to add a first number of virtual machine instances to the warming pool in response to a first virtual machine instance being removed from the warming pool; monitor incoming code execution requests to execute program codes on the virtual compute system, the incoming code execution requests comprising information usable for identifying the respective program codes to be executed on the virtual compute system; determine a current rate at which the incoming code execution requests are received; determine whether the current rate at which the incoming code execution requests are received satisfies a threshold condition for adjusting the warming pool; and in response to determining that the current rate at which the incoming code execution requests are received satisfies the threshold condition, adjust a rate at which additional virtual machine instances are added to the warming pool such that a second number of virtual machine instances are added to the warming pool in response to a second virtual machine instance being removed from the warming pool, wherein the second number and is different from the first number and determined based on the current rate at which the incoming code execution requests are received.