A 2-Approximation Algorithm for Scheduling Parallel and Time-Sensitive Applications to Maximize Total Accrued Utility Value

Abstract

For a time-sensitive application, the usefulness of its end results (also called the application's accrued utility value in the paper) depends on the time when the application is completed and its results are delivered. In this paper, we address the accrued utility value maximization problem for narrow parallel and time-sensitive applications. We first consider the problem in the context of a discrete time domain and present the Spatial-Temporal Interference Based (STIB) scheduling algorithm. We formally prove that the STIB algorithm is a 2-approximation algorithm. Second, we extend our work to a continuous time domain and present a heuristic scheduling algorithm, i.e., the Continuous Spatial-Temporal Interference Based (STIB-C) algorithm to maximize the system's total accrued utility value when the system operates in a continuous time domain. The extensive empirical evaluations reveal that: (1) in a discrete time domain, the systems’ total accrued utility values obtained through the STIB algorithm are consistent with the theoretic bound, i.e., they never go below 50 percent of the optimal value. In fact, on average, the STIB algorithm can achieve over 92.5 percent of the optimal value; (2) compared to other scheduling policies listed in the literature, the developed STIB and STIB-C algorithms have clear advantages in terms of the system's total accrued utility value and the profitable application ratio. In particular, in terms of the system's total accrued utility value, both the STIB and the STIB-C algorithms achieve as much as six times for both the First Come First Come Serve(FCFS) with backfilling algorithm and the Gang Earliest Deadline First (EDF) algorithm, and 4.5 times for the 0-1 Knapsack based scheduling algorithm. In terms of the profitable application ratio, both the STIB and the STIB-C algorithms obtain as much as four times for both the FCFS with backfilling algorithm and the Gang EDF algorithm, and two times for the 0-1 Knapsack based scheduling algorithm.