1. A computer-implemented method comprising: as implemented by one or more computing devices configured with specific executable instructions, maintaining an active pool of virtual machine instances assigned to one or more users, wherein each virtual machine instance in the active pool has one or more software components loaded thereon; receiving a request to acquire compute capacity for executing a program code of a user on the virtual compute system, the request including metadata indicating the program code, the user associated with the program code, and a first amount of computing resources to be allocated for executing the program code on the virtual compute system; determining whether the active pool contains a container that has the program code loaded thereon; in response to determining that the active pool does not contain a container that has the program code loaded thereon, determining whether the active pool contains a virtual machine instance that is assigned to the user and has at least the first amount of computing resources available for executing the program code; in response to determining that the active pool contains a virtual machine instance that is assigned to the user and has at least the first amount of computing resources available for executing the program code, creating a container having at least the first amount of computing resources on the virtual machine instance and assigning the container to handle the request to execute the program code on the virtual compute system; and causing the program code of the user to be executed in the container created on the virtual machine instance.