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1. Bringing Inter-Thread Cache Benefits to Federated Scheduling

   https://doi.org/10.1109/RTAS48715.2020.00005  

   Tessler, Corey ; Modekurthy, Venkata P. ; Fisher, Nathan ; Saifullah, Abusayeed ( April 2020 , Proceedings of the IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS))

   Multiprocessor scheduling of hard real-time tasks modeled by directed acyclic graphs (DAGs) exploits the inherent parallelism presented by the model. For DAG tasks, a node represents a request to execute an object on one of the available processors. In one DAG task, there may be multiple execution requests for one object, each represented by a distinct node. These distinct execution requests offer an opportunity to reduce their combined cache overhead through coordinated scheduling of objects as threads within a parallel task. The goal of this work is to realize this opportunity by incorporating the cache-aware BUNDLE-scheduling algorithm into federated scheduling of sporadic DAG task sets.This is the first work to incorporate instruction cache sharing into federated scheduling. The result is a modification of the DAG model named the DAG with objects and threads (DAG-OT). Under the DAG-OT model, descriptions of nodes explicitly include their underlying executable object and number of threads. When possible, nodes assigned the same executable object are collapsed into a single node; joining their threads when BUNDLE-scheduled. Compared to the DAG model, the DAG-OT model with cache-aware scheduling reduces the number of cores allocated to individual tasks by approximately 20 percent in the synthetic evaluation and up to 50 percent on a novel parallel computing platform implementation. By reducing the number of allocated cores, the DAG-OT model is able to schedule a subset of previously infeasible task sets. 

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2. On Max-Min Fairness of Completion Times for Multi-Task Job Scheduling

   Shafiee, Mehrnoosh ; Ghaderi, Javad ( July 2020 , 2020 IFIP Networking Conference (Networking))

   We study the max-min fairness of multi-task jobs in distributed computing platforms. We consider a setting where each job consists of a set of parallel tasks that need to be processed on different servers, and the job is completed once all its tasks finish processing. Each job is associated with a utility which is a decreasing function of its completion time, and captures how sensitive it is to latency. The objective is to schedule tasks in a way that achieves max-min fairness for jobs' utilities, i.e., an optimal schedule in which any attempt to improve the utility of a job necessarily results in hurting the utility of some other job with smaller or equal utility. We first show a strong result regarding NP-hardness of finding the max-min fair vector of job utilities. The implication of this result is that achieving max-min fairness in many other distributed scheduling problems (e.g., coflow scheduling) is NP-hard. We then proceed to define two notions of approximation solutions: one based on finding a certain number of elements of the max-min fair vector, and the other based on a single-objective optimization whose solution gives the max-min fair vector. We develop scheduling algorithms that provide guarantees under these approximation notions, using dynamic programming and random perturbation of tasks' processing times. We verify the performance of our algorithms through extensive simulations, using a real traffic trace from a large Google cluster. 

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3. On Max-Min Fairness of Completion Times for Multi-Task Job Scheduling

   Shafiee, Mehrnoosh ; Ghaderi, Javad ( July 2020 , IFIP Networking Conference)

   We study the max-min fairness of multi-task jobs in distributed computing platforms. We consider a setting where each job consists of a set of parallel tasks that need to be processed on different servers, and the job is completed once all its tasks finish processing. Each job is associated with a utility which is a decreasing function of its completion time, and captures how sensitive it is to latency. The objective is to schedule tasks in a way that achieves max-min fairness for jobs’ utilities, i.e., an optimal schedule in which any attempt to improve the utility of a job necessarily results in hurting the utility of some other job with smaller or equal utility.We first show a strong result regarding NP-hardness of finding the max-min fair vector of job utilities. The implication of this result is that achieving max-min fairness in many other distributed scheduling problems (e.g., coflow scheduling) is NP-hard. We then proceed to define two notions of approximation solutions: one based on finding a certain number of elements of the max-min fair vector, and the other based on a single-objective optimization whose solution gives the max-min fair vector. We develop scheduling algorithms that provide guarantees under these approximation notions, using dynamic programming and random perturbation of tasks’ processing times. We verify the performance of our algorithms through extensive simulations, using a real traffic trace from a large Google cluster. 

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4. RT-Gang: Real-Time Gang Scheduling Framework for Safety-Critical Systems

   Ali, Waqar ; Yun, Heechul. ( January 2019 , Proceedings - IEEE Real-Time and Embedded Technology and Applications Symposium)

   In this paper, we present RT-Gang: a novel realtime gang scheduling framework that enforces a one-gang-at-atime policy. We find that, in a multicore platform, co-scheduling multiple parallel real-time tasks would require highly pessimistic worst-case execution time (WCET) and schedulability analysis—even when there are enough cores—due to contention in shared hardware resources such as cache and DRAM controller. In RT-Gang, all threads of a parallel real-time task form a real-time gang and the scheduler globally enforces the one-gangat-a-time scheduling policy to guarantee tight and accurate task WCET. To minimize under-utilization, we integrate a state-of-the-art memory bandwidth throttling framework to allow safe execution of best-effort tasks. Specifically, any idle cores, if exist, are used to schedule best-effort tasks but their maximum memory bandwidth usages are strictly throttled to tightly bound interference to real-time gang tasks. We implement RT-Gang in the Linux kernel and evaluate it on two representative embedded multicore platforms using both synthetic and real-world DNN workloads. The results show that RT-Gang dramatically improves system predictability and the overhead is negligible. 

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5. Scheduling Parallel-Task Jobs Subject to Packing and Placement Constraints

   https://doi.org/10.1287/opre.2021.2198  

   Shafiee, Mehrnoosh ; Ghaderi, Javad ( January 2022 , Operations Research)

   Motivated by modern parallel computing applications, we consider the problem of scheduling parallel-task jobs with heterogeneous resource requirements in a cluster of machines. Each job consists of a set of tasks that can be processed in parallel; however, the job is considered completed only when all its tasks finish their processing, which we refer to as the synchronization constraint. Furthermore, assignment of tasks to machines is subject to placement constraints, that is, each task can be processed only on a subset of machines, and processing times can also be machine dependent. Once a task is scheduled on a machine, it requires a certain amount of resource from that machine for the duration of its processing. A machine can process (pack) multiple tasks at the same time; however, the cumulative resource requirement of the tasks should not exceed the machine’s capacity. Our objective is to minimize the weighted average of the jobs’ completion times. The problem, subject to synchronization, packing, and placement constraints, is NP-hard, and prior theoretical results only concern much simpler models. For the case that migration of tasks among the placement-feasible machines is allowed, we propose a preemptive algorithm with an approximation ratio of [Formula: see text]. In the special case that only one machine can process each task, we design an algorithm with an improved approximation ratio of four. Finally, in the case that migrations (and preemptions) are not allowed, we design an algorithm with an approximation ratio of 24. Our algorithms use a combination of linear program relaxation and greedy packing techniques. We present extensive simulation results, using a real traffic trace, that demonstrate that our algorithms yield significant gains over the prior approaches. 

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