Resource scheduling with variable requirements over time

The problem of scheduling resources for tasks with variable requirements over time can be stated as follows. We are given two sequences of vectors A = A1,…, An and R = R1,…, Rm. Sequence A represents resource availability during n time intervals, where each vector Ai has q elements. Sequence R represents resource requirements of a task during m intervals, where each vector Ri has q elements. We wish to find the earliest time interval i, termed latency, such that for 1 ≤ k ≤ m, 1 ≤ j ≤ q: $A_{i+k-1}^j\ge R_k^j$ , where $A_{i+k-1}^j$ and $R_j^k$ are the jth elements of vectors Ai+k−1 and Rk, respectively. One application of this problem is I/O scheduling for multimedia presentations.