Resource Allocation under Sequential Resource Access: Theory and Application

Abstract

This paper treats the problem of optimal resource allocation over time in a finite-horizon setting, in which the resource become available only sequentially and in incremental values and the utility function is concave and can freely vary over time. Such resource allocation problems have direct applications in data communication networks (e.g., energy harvesting systems). This problem is studied extensively for special choices of the concave utility function (time-invariant and logarithmic) in which case the optimal resource allocation policies are well-understood. This paper treats this problem in its general form and analytically characterizes the structure of the optimal resource allocation policy, and devises an algorithm for computing the exact solutions analytically. An observation instrumental to devising the provided algorithm is that there exist time instances at which the available resources are exhausted, with no carry-over to future. This algorithm identifies all such instances, which in turn facilitates breaking the original problem into multiple problems with significantly reduced dimensions. Furthermore, some widely-used special cases in which the algorithm takes simpler structures are characterized, and the application to the energy harvesting systems is discussed. Numerical evaluations are provided to assess the key properties of the optimal resource allocation structure and to compare the performance with the generic convex optimization algorithms.