A method for requesting, from a computational resource manager, computational resources for executing a computer program, having a plurality of program portions, in a computing system, the method including: storing information specifying target quantities of computational resources associated with respective ones of the program portions, where each program portion uses granted computational resources granted by the computational resource manager enabling that program portion to be executed in the computing system; and computing requests, the requests being for computational resources for executing the computer program in the computing system, for submission to the computational resource manager as a plurality of sets of requests, where each set of requests, except for an initial set of requests, would become processed by the computational resource manager only if the previously submitted one or more sets of the plurality of sets of requests were granted by the computational resource manager for use by the plurality of program portions, the computing including: forming the initial set of requests, wherein the initial set of requests includes a minimum request for each program portion, where each minimum request requests a minimum quantity of computational resources needed to execute the corresponding portion of the program, and forming one or more additional sets of requests for processing by the computational resource manager after the initial set of requests, characterized in that each program portion of the plurality of program portions is associated with a respective fulfillment ratio of its quantity of previously requested computational resources divided by its associated target quantity of computational resources, wherein the program portions of the plurality of program portions are ranked according to their fulfillment ratios, and wherein at least one set of requests of the additional sets of requests includes a request for one or more computational resource units for at least one program portion of the plurality of program portions that is the least-fulfilled program portion of the ranked program portions, and wherein the request for one or more computational resource units requests an additional quantity of one or more computational resource units for the least-fulfilled program portion that increases the current fulfillment ratio for the least-fulfilled program portion to a value less than one but greater than the current fulfillment ratio for a program portion that is the second least-fulfilled program portion of the ranked program portions. storing information specifying target quantities of computational resources associated with respective ones of the program portions, where each program portion uses granted computational resources granted by the computational resource manager enabling that program portion to be executed in the computing system; and computing requests, the requests being for computational resources for executing the computer program in the computing system, for submission to the computational resource manager as a plurality of sets of requests, where each set of requests, except for an initial set of requests, would become processed by the computational resource manager only if the previously submitted one or more sets of the plurality of sets of requests were granted by the computational resource manager for use by the plurality of program portions, the computing including: forming the initial set of requests, wherein the initial set of requests includes a minimum request for each program portion, where each minimum request requests a minimum quantity of computational resources needed to execute the corresponding portion of the program, and forming one or more additional sets of requests for processing by the computational resource manager after the initial set of requests, forming the initial set of requests, wherein the initial set of requests includes a minimum request for each program portion, where each minimum request requests a minimum quantity of computational resources needed to execute the corresponding portion of the program, and forming one or more additional sets of requests for processing by the computational resource manager after the initial set of requests, characterized in that each program portion of the plurality of program portions is associated with a respective fulfillment ratio of its quantity of previously requested computational resources divided by its associated target quantity of computational resources, wherein the program portions of the plurality of program portions are ranked according to their fulfillment ratios, and wherein at least one set of requests of the additional sets of requests includes a request for one or more computational resource units for at least one program portion of the plurality of program portions that is the least-fulfilled program portion of the ranked program portions, and wherein the request for one or more computational resource units requests an additional quantity of one or more computational resource units for the least-fulfilled program portion that increases the current fulfillment ratio for the least-fulfilled program portion to a value less than one but greater than the current fulfillment ratio for a program portion that is the second least-fulfilled program portion of the ranked program portions.