Optimal Real-Time Scheduling on Two-Type Heterogeneous Multicore Platforms

Abstract

Motivated by the cutting-edge two-type heterogeneous multicore chips, such as ARM's big.LITTLE, that offer a practical support for migration, this paper studies the global (or fully-migrative) approach to two-type heterogeneous multicore scheduling. Our goal is to design an optimal fully-migrative scheduling framework. To achieve this goal in an efficient and simple manner, we break the scheduling problem into two subproblems: workload assignment and schedule generation. We propose a per-cluster workload assignment algorithm, called Hetero-Split, that determines the fractions of workload of each task to be assigned to both clusters without losing feasibility with the complexity of O(n log n), where n is the number of tasks. Furthermore, it provides a couple of important properties (e.g., a dual property) that help to generate an optimal schedule efficiently. We also derive scheduling guidelines to design optimal schedulers for two-type heterogeneous multicore platforms, called Hetero-Fair. By tightly coupling the solutions of Hetero-Split and Hetero-Fair, we develop the first optimal two-type heterogeneous multicore scheduling algorithm, called Hetero-Wrap, that has the same complexity (O(n)) as in the identical multicore case. Finally, concerning a practical point of view, we derive the first bounds on the numbers of intra-and inter-cluster migrations under two-type heterogeneous multicore scheduling, respectively.

Energy-efficient real-time scheduling for two-type heterogeneous multiprocessors

“…However, with the advent of ARM two-type heterogeneous multicores architecture, such as the big.LITTLE architecture [9], that supports task migrations among different core types, a global scheduling algorithm is possible. In [10], [11], the first energy-aware global scheduling framework for this special architecture is presented, where an algorithm called Hetero-Split is proposed to solve a workload assignment and a Hetero-Wrap algorithm to solve a schedule generation problem. Their framework is similar to ours, except that we adopt a fluid model to represent a scheduling dynamic, our assigned operating frequency is time-varying and the CPU idle energy consumption is also considered.…”

“…where (4h)-(4i) enforce upper and lower bounds on discretization time steps. Proof: Follows from the fact that if a solution exists to (1), then the Hetero-Wrap scheduling algorithm [11] can find a valid schedule with at most m r − 1 migrations within the cluster. [11,Lemma 2].…”

“…To avoid a parallel execution on any two clusters, we can adopt the Hetero-Wrap algorithm proposed in [11] to solve a task ordering problem of a two-type heterogeneous multiprocessor platform. The algorithm takes the workload partitioning solution to STEP 1 as its inputs and returns (σ r ik , η r ik ) ∈ [0, 1] 2 , ∀i, k, r, which is a task-to-processor interval assignment on each cluster.…”

“…Algorithm 1 Hetero-Wrap Algorithm [11] Proof: A unique basic solution can be identified by any n + m linearly independent active constraints. Since there are n nonnegative constraints and m < n, a basic solution will have at most m non-zero values.…”

“…Proof: The existence of a valid schedule is proven in [11,Thm 3]. It follows from Facts 4-6 and Lemma 7 that one can compute a solution with at most one intercluster partitioning task.…”