A 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; receive a request to execute a program code associated with a user on the virtual compute system, the request including information indicating the program code and the user associated with the program code, and a first amount of a computing resource available on the virtual compute system to be used to execute the program code, wherein the first amount is determined based on a user-specified amount indicated in the request or other configuration information associated with the request, the program code, or the user to execute the program code on the virtual compute system; select a virtual machine instance from the plurality of virtual machine instances to be used to execute the program code, the selected virtual machine instance having at least the first amount of the computing resource; create a container in the selected virtual machine instance, the container having the first amount of the computing resource; cause the program code associated with the user to be loaded onto the container and executed in the container; monitor a usage of the computing resource by the program code during one or more executions of the program code in the container created in the selected virtual machine instance; determine, based on the usage of the computing resource by the program code, that the first amount allocated for executing the program code should be adjusted following the usage of the computing resource being compared to a threshold value; create, in response to determining that the first amount should be adjusted, an additional container in the selected virtual machine instance such that the additional container has a second amount of the computing resource that is different from the first amount, wherein the second amount is determined based on the usage of the computing resource by the program code, and wherein the container having the first amount of the computing resources is drained; and cause the program code to be executed in the additional container having the second amount of the computing resource. maintain a plurality of virtual machine instances on one or more physical computing devices; receive a request to execute a program code associated with a user on the virtual compute system, the request including information indicating the program code and the user associated with the program code, and a first amount of a computing resource available on the virtual compute system to be used to execute the program code, wherein the first amount is determined based on a user-specified amount indicated in the request or other configuration information associated with the request, the program code, or the user to execute the program code on the virtual compute system; select a virtual machine instance from the plurality of virtual machine instances to be used to execute the program code, the selected virtual machine instance having at least the first amount of the computing resource; create a container in the selected virtual machine instance, the container having the first amount of the computing resource; cause the program code associated with the user to be loaded onto the container and executed in the container; monitor a usage of the computing resource by the program code during one or more executions of the program code in the container created in the selected virtual machine instance; determine, based on the usage of the computing resource by the program code, that the first amount allocated for executing the program code should be adjusted following the usage of the computing resource being compared to a threshold value; create, in response to determining that the first amount should be adjusted, an additional container in the selected virtual machine instance such that the additional container has a second amount of the computing resource that is different from the first amount, wherein the second amount is determined based on the usage of the computing resource by the program code, and wherein the container having the first amount of the computing resources is drained; and cause the program code to be executed in the additional container having the second amount of the computing resource.