Apparatus and accompanying methods for optimally using available computer resources, illustratively processing time, and which can be advantageously used for selecting task(s) instances to be precomputed during idle time as well as during other periods of processing activity. Specifically, at an onset of each idle-time interval, processing time is allocated to precompute during the remainder of that interval a future task instance, from among a group of such instances then available for precomputation, that will provide the highest fixed or incremental utility. For those task instances which exhibit constant or varying value with time, task selection is based on maximum probability of future occurrence, or net expected value (NEV), respectively, of each such instance. NEV is evaluated as a product of the task instance probability multiplied by a rate of change in the value (EVC flux) to be provided by that task with continued computation time, respectively. This product is assessed, for task instances that exhibit linearly changing value with time, at the onset of each idle-time interval, or, for task instances that exhibit non-linearly changing value, at the onset of each time slice occurring during such an interval. Processing time can be also allocated, at non-idle times, to precomputing a future task instance in lieu of continuing a presently executing task instance, if the future task instance then exhibits a time-discounted NEV that is larger than the EVC flux presently being provided by the currently executing task instance.