Non-clairvoyant Scheduling Research Articles

Competitive kill-and-restart and preemptive strategies for non-clairvoyant scheduling

AbstractWe study kill-and-restart and preemptive strategies for the fundamental scheduling problem of minimizing the sum of weighted completion times on a single machine in the non-clairvoyant setting. First, we show a lower bound of 3 for any deterministic non-clairvoyant kill-and-restart strategy. Then, we give for any $$b > 1$$ b > 1 a tight analysis for the natural b-scaling kill-and-restart strategy as well as for a randomized variant of it. In particular, we show a competitive ratio of $$(1+3\sqrt{3})\approx 6.197$$ ( 1 + 3 3 ) ≈ 6.197 for the deterministic and of $$\approx 3.032$$ ≈ 3.032 for the randomized strategy, by making use of the largest eigenvalue of a Toeplitz matrix. In addition, we show that the preemptive Weighted Shortest Elapsed Time First (WSETF) rule is 2-competitive when jobs are released online, matching the lower bound for the unit weight case with trivial release dates for any non-clairvoyant algorithm. Using this result as well as the competitiveness of round-robin for multiple machines, we prove performance guarantees smaller than 10 for adaptions of the b-scaling strategy to online release dates and unweighted jobs on identical parallel machines.

Non-Clairvoyant Scheduling of Distributed Machine Learning with Inter-job and Intra-job Parallelism on Heterogeneous GPUs

Non-Clairvoyant Scheduling of Distributed Machine Learning with Inter-job and Intra-job Parallelism on Heterogeneous GPUs

Non-clairvoyant Scheduling with Predictions

In the single-machine non-clairvoyant scheduling problem, the goal is to minimize the total completion time of jobs whose processing times are unknown a priori . We revisit this well-studied problem and consider the question of how to effectively use (possibly erroneous) predictions of the processing times. We study this question from ground zero by first asking what constitutes a good prediction; we then propose a new measure to gauge prediction quality and design scheduling algorithms with strong guarantees under this measure. Our approach to derive a prediction error measure based on natural desiderata could find applications for other online problems.

PROSE: Multi-round fair coflow scheduling without prior knowledge

Coflow scheduling plays a crucial role in enhancing network-level performance in datacenter applications. Existing works on coflow scheduling predominantly concentrate on clairvoyant schedulers, which assume prior knowledge of coflow sizes before transmission. However, this assumption is often unrealistic in practical scenarios like pipelined computation. Consequently, research on non-clairvoyant schedulers has garnered increasing attention. Most studies on non-clairvoyant schedulers focus on either improving efficiency or promoting fairness, with limited emphasis on striking a balance between the two objectives. Additionally, for non-cooperative environments like multi-tenant datacenter networks, it is essential to ensure strategy-proofness in coflow scheduling. Without adequate measures, tenants may manipulate their reported requirements to gain an unfair advantage in resource allocation. Ideally, in non-cooperative environments, a coflow scheduler should achieve efficiency, fairness, and strategy-proofness, all without prior knowledge of coflow sizes. However, few existing efforts have managed to simultaneously achieve these objectives.To fill this gap, we develop PROSE, a non-clairvoyant scheduler for non-cooperative environments. PROSE divides the scheduling time into multiple rounds and employs a two-stage scheduling mechanism based on these rounds. In the first stage, PROSE estimates the sizes of the coflows with unknown sizes by transmitting the probe flows, using a policy that combines coflow competition with batch processing. Once the information about coflow sizes is obtained, PROSE prioritizes coflows among tenants for bandwidth allocation in the second stage, aiming to accelerate coflow completion within each round. Furthermore, PROSE ensures optimal isolation guarantee by fairly limiting the total data transfer for each tenant and dynamically adjusts the scheduling order of coflows in a round-robin manner across multiple rounds. PROSE prevents tenants from attempting to consume excessive network resources through manipulative actions that deceive the scheduler. Trace-driven simulations demonstrate that PROSE outperforms the fair scheduler, achieving up to a 2.37× reduction in average coflow completion time, indicating substantial efficiency improvements.

Uniform Machine Scheduling with Predictions

The revival in learning theory has provided us with improved capabilities for accurate predictions. This work contributes to an emerging research agenda of online scheduling with predictions by studying the makespan minimization in uniformly related machine non-clairvoyant scheduling with job size predictions. Our task is to design online algorithms that effectively use predictions and have performance guarantees with varying prediction quality. We first propose a simple algorithm-independent prediction error measurement to quantify prediction quality. To effectively use the predicted job sizes, we design an offline improved 2-relaxed decision procedure approximating the optimal schedule. With this decision procedure, we propose an online O(min{log eta, log m})-competitive algorithm that assumes a known prediction error. Finally, we extend this algorithm to construct a robust O(min{log eta, log m})-competitive algorithm that does not assume a known error. Both algorithms require only moderate predictions to improve the well-known Omega(log m) lower bound, showing the potential of using predictions in managing uncertainty.

Managing Energy Plus Performance in Data Centers and Battery-Based Devices Using an Online Non-Clairvoyant Speed-Bounded Multiprocessor Scheduling

An efficient scheduling reduces the time required to process the jobs, and energy management decreases the service cost as well as increases the lifetime of a battery. A balanced trade-off between the energy consumed and processing time gives an ideal objective for scheduling jobs in data centers and battery based devices. An online multiprocessor scheduling multiprocessor with bounded speed (MBS) is proposed in this paper. The objective of MBS is to minimize the importance-based flow time plus energy (IbFt+E), wherein the jobs arrive over time and the job’s sizes are known only at completion time. Every processor can execute at a different speed, to reduce the energy consumption. MBS is using the tradition power function and bounded speed model. The functioning of MBS is evaluated by utilizing potential function analysis against an offline adversary. For processors m ≥ 2, MBS is O(1)-competitive. The working of a set of jobs is simulated to compare MBS with the best known non-clairvoyant scheduling. The comparative analysis shows that the MBS outperforms other algorithms. The competitiveness of MBS is the least to date.

Energy-Aware Online Non-Clairvoyant Scheduling Using Speed Scaling with Arbitrary Power Function

Efficient job scheduling reduces energy consumption and enhances the performance of machines in data centers and battery-based computing devices. Practically important online non-clairvoyant job scheduling is studied less extensively than other algorithms. In this paper, an online non-clairvoyant scheduling algorithm Highest Scaled Importance First (HSIF) is proposed, where HSIF selects an active job with the highest scaled importance. The objective considered is to minimize the scaled importance based flow time plus energy. The processor’s speed is proportional to the total scaled importance of all active jobs. The performance of HSIF is evaluated by using the potential analysis against an optimal offline adversary and simulating the execution of a set of jobs by using traditional power function. HSIF is 2-competitive under the arbitrary power function and dynamic speed scaling. The competitive ratio obtained by HSIF is the least to date among non-clairvoyant scheduling. The simulation analysis reflects that the performance of HSIF is best among the online non-clairvoyant job scheduling algorithms.

Non-clairvoyant scheduling with conflicts for unit-size jobs

We consider the problem of scheduling unit-size jobs with conflicts in a non-clairvoyant setting. In this problem, all jobs are released at the same time but the conflict graph is unknown to the scheduling algorithm beforehand. Instead, the conflicts between the jobs are revealed online by an adversary during the jobs' execution. There is an unlimited number of processors so that all jobs could be executed simultaneously. However, two jobs with a conflict cannot be both completed in the same time step; when their conflict is revealed, one of them must be aborted and re-executed later. The objective is to minimize the total number of time steps required to complete all jobs, or the makespan. We present an online non-clairvoyant algorithm and analyze its performance for three types of conflict graphs. For bipartite graphs, we show that it is O(log⁡n)-competitive, where n denotes the total number of jobs. For unit-interval graphs, we show that it is O(log⁡χ)-competitive, where χ denotes the chromatic number of the graph. For bounded-degree graphs, we show that it is O(Δ)-competitive, where Δ denotes the maximum degree of any node in the graph. For bipartite and bounded-degree graphs, we also provide matching lower bounds and show that the obtained competitive ratios are asymptotically tight.

Non-clairvoyant scheduling of independent parallel tasks on single and multiple multicore processors

We investigate the problem of non-clairvoyant scheduling of independent parallel tasks on single and multiple multicore processors. For a single multicore processor, we derive an asymptotic worst-case performance bound for a non-clairvoyant offline scheduling algorithm called largest task first (LTF). The result improves our previous result on a single parallel computing system. For multiple multicore processors, we derive an asymptotic worst-case performance bound for the LTF algorithm. To the best of our knowledge, there has been little result on scheduling parallel tasks on multiple parallel computing systems. For multiple multicore processors, we also derive an asymptotic average-case performance bound for a non-clairvoyant online scheduling algorithm called random task first (RTF). The result extends our earlier result on a single parallel computing system. Extensive simulation results are also demonstrated.

Non-clairvoyant online scheduling of synchronized jobs on virtual clusters

Although virtualization technology is recently applied to next-generation distributed high-performance computing systems, theoretical aspects of scheduling jobs on these virtualized environments are not sufficiently studied, especially in online and non-clairvoyant cases. Virtualization of computing resources results in interference and virtualization overheads that negatively impact the load balancing objectives on commonly used cluster of multi-core physical machines. We present a technique for non-clairvoyant online scheduling of globally synchronized jobs, each of which spawns tasks to execute compute-intensive works. Our technique considers both load balancing of physical cores and per job synchronization cost minimization. We show that in the presence of arbitrary virtualization overheads, interference effects and synchronization cost, the problem can be reduced to an online unrelated parallel machine scheduling, which is solved using routing of virtual circuits. We present a new opportunity cost model to reduce the problem to the routing of virtual circuits and prove the effectiveness of our scheduling technique using mathematical analysis and simulative experiments.

Power‐aware speed scaling in multiprocessor systems

A huge consumption of energy in the data centres has become a motivation for improvement in computing capability and energy conservation. The dynamic speed scaling and job scheduling are efficient methods to improve the energy efficiency of processors. In this study, an online non-clairvoyant scheduling algorithm arrival time-algorithm (At-ALG) is proposed with an objective to scale the speed of processors and schedule the jobs in a multiprocessor system to minimise the total magnitude-based/weighted flow time plus energy consumed. The traditional power function Power = Spee d ω is adopted, where ω > 1 is a constant. At-ALG is analysed, against an offline adversary, using the potential function analysis. The magnitude/weight/priority of jobs in At-ALG are generated using their processed time (waiting time plus executed time) and speed of any processor depends on the number of active jobs plus sum of processed time of active jobs. At-ALG is O ( 1 ) -competitive with no resource augmentation.

Energy efficient non-clairvoyant scheduling for unbounded-speed multi-core machines

With the increasing consumption of energy in data centers, the demand for energy efficient multiprocessor job scheduling is growing dramatically. Besides flow time, energy conservation has become a significant issue and drawn enormous interest. In this paper, an online non-clairvoyant scheduling algorithm Significance-based Multiprocessor Round Robin (SbMRR) is proposed. SbMRR utilizes the unbounded speed model, where the range of the speed of any processor is from zero to infinity. To validate the effectiveness of the algorithm, mathematical and simulation-based analysis are conducted which demonstrates that SbMRR provides the minimum sum of significance-based flow time and energy consumed. SbMRR is O(α)-competitive, more precisely ((α + 1)⁄((1–1⁄αβ)))-competitive, where β ≥ 4 a constant. The competitive ratio of SbMRR is least to date. SbMRR provides the minimum sum of energy consumed and significance-based flow-time.

Energy‐aware online non‐clairvoyant multiprocessor scheduling: multiprocessor priority round robin

In the current epoch, the energy consumption is a great concern in the online non-clairvoyant job scheduling. The online non-clairvoyant scheduling is studied less extensively than the online clairvoyant scheduling. The authors study non-clairvoyant scheduling problem of minimising the total prioritised flow time plus energy, where the jobs with arbitrary sizes and priorities arrive online. The authors consider unbounded speed model in multiprocessor settings, where the speed of m individual processors can vary from zero to infinity, i.e. [0, ∞) , to save the energy and to optimise the prioritised flow time plus energy. The authors consider the traditional power function P s = s α , where s is the speed of a processor and α > 1, a constant. In this study, the authors introduce an online non-clairvoyant scheduling multiprocessor priority round robin (MPRR), which is O ( α ) -competitive; more precisely ( 2 α 2 / ( α − ( 1 / 2 ) ) ) -competitive, i.e. the competitive ratio is 5.33 for α = 2 and 7.3 for α = 3. In this study, the algorithm is studied using the potential analysis against an optimal offline adversary.

Executed-time Round Robin: EtRR an online non-clairvoyant scheduling on speed bounded processor with energy management

Energy conservation has become a prime objective due to excess use and huge demand of energy in data centers. One solution is to use efficient job scheduling algorithms. The scheduler has to maintain the machine’s state balance to obtain efficient job schedule and avoid unnecessary energy consumption. Although the practical importance of non-clairvoyant scheduling problem is higher than clairvoyant scheduling, in the past few years the non-clairvoyant scheduling problem has been studied lesser than clairvoyant scheduling. In this paper, an online non-clairvoyant scheduling problem is studied to minimize total weighted flow time plus energy and a scheduling algorithm Executed-time Round Robin (EtRR) is proposed. Generally, weights of jobs are system generated and they are assigned to jobs at release/arrival time. In EtRR, the weights are not generated by the system, rather by the scheduler using the executed time of jobs. EtRR is a coupling of weighted generalization of Power Management and Weighted Round Robin (WRR). We adopt the conventional power function P=sα, where s and α>1 are speed of a processor and a constant, respectively. EtRR is O(1)-competitive, it is using a processor with the maximum speed (1+τ/3)T, where the maximum speed of optimal offline adversary is T and 0<τ⩽(3α)-1.

Release Round Robin: R3 an energy-aware non-clairvoyant scheduling on speed bounded processors

In the past few years the online scheduling problem has been studied extensively under clairvoyant settings and a relatively less amount of evolution is observed under non-clairvoyant setting. A non-clairvoyant scheduling problem has its practical significance. We study online non-clairvoyant scheduling problem of minimizing total weighted flow plus energy. Usually weights in weighted flow study are assumed to be system generated and they are allocated to the jobs at their release time. In this paper, weights are not provided by the system, rather they are generated using the release time by the scheduler. The scheduler maintains a balance of the machine's state to obtain an efficient schedule of jobs and avoid energy wastage. This paper provides potential analysis of a weighted generalization of the power management algorithm which is coupled with Weighted Round Robin. We adopt the traditional model of power function P=sα, where s, P and α>1 are speed of processor, power and a constant, respectively. We introduced Release Round Robin (R3) scheduling algorithm with competitive ratio O (3α/τ) when using a processor with the maximum speed (3 + τ) times higher than the maximum speed of the Optimal offline adversary, where 0<τ≤(3α−1).

Efficient Coflow Scheduling Without Prior Knowledge

Inter-coflow scheduling improves application-level communication performance in data-parallel clusters. However, existing efficient schedulers require a priori coflow information and ignore cluster dynamics like pipelining, task failures, and speculative executions, which limit their applicability. Schedulers without prior knowledge compromise on performance to avoid head-of-line blocking. In this paper, we present Aalo that strikes a balance and efficiently schedules coflows without prior knowledge. Aalo employs Discretized Coflow-Aware Least-Attained Service (D-CLAS) to separate coflows into a small number of priority queues based on how much they have already sent across the cluster. By performing prioritization across queues and by scheduling coflows in the FIFO order within each queue, Aalo's non-clairvoyant scheduler reduces coflow completion times while guaranteeing starvation freedom. EC2 deployments and trace-driven simulations show that communication stages complete 1.93X faster on average and 3.59X faster at the 95th percentile using Aalo in comparison to per-flow mechanisms. Aalo's performance is comparable to that of solutions using prior knowledge, and Aalo outperforms them in presence of cluster dynamics.

Energy-efficient multiprocessor scheduling for flow time and makespan

We consider energy-efficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power sα when running at speed s, for α>1. A scheduling algorithm needs to decide at any time both processor allocations and processor speeds for a set of parallel jobs with time-varying parallelism. The objective is to minimize the sum of the total energy consumption and certain performance metric, which in this paper includes total flow time and makespan. For both objectives, we present instantaneous parallelism-clairvoyant (IP-clairvoyant) algorithms that are aware of the instantaneous parallelism of the jobs at any time but not their future characteristics, such as remaining parallelism and work. For total flow time plus energy, we present an O(1)-competitive algorithm, which significantly improves upon the best known non-clairvoyant algorithm. In the case of makespan plus energy, we present an O(ln1−1/α⁡P)-competitive algorithm, where P is the total number of processors. We show that this algorithm is asymptotically optimal by providing a matching lower bound. In addition, we study non-clairvoyant scheduling for total flow time plus energy, and present an algorithm that is O(ln⁡P)-competitive for jobs with arbitrary release time and O(ln1/α⁡P)-competitive for jobs with identical release time. Finally, we prove an Ω(ln1/α⁡P) lower bound on the competitive ratio of any non-clairvoyant algorithm.

The sandpile scheduler

This paper studies a self-organized criticality model called sandpile for dynamically load-balancing tasks arriving in the form of Bag-of-Tasks in large-scale decentralized system. The sandpile is designed as a decentralized agent system characterizing a cellular automaton, which works in a critical state at the edge of chaos. Depending on the state of the cellular automaton, different responses may occur when a new task is assigned to a resource: it may change nothing or generate avalanches that reconfigure the state of the system. The abundance of such avalanches is in power-law relation with their sizes, a scale-invariant behavior that emerges without requiring tuning or control parameters. That means that large—catastrophic—avalanches are very rare but small ones occur very often. Such emergent pattern can be efficiently adapted for non-clairvoyant scheduling, where tasks are load balanced in computing resources trying to maximize the performance but without assuming any knowledge on the tasks features. The algorithm design is experimentally validated showing that the sandpile is able to find near-optimal schedules by reacting differently to different conditions of workloads and architectures.

Non-clairvoyant Weighted Flow Time Scheduling on Different Multi-processor Models

We study non-clairvoyant scheduling to minimize weighted flow time on two different multi-processor models. In the first model, processors are all identical and jobs can possibly be speeded up by running on several processors in parallel. Under the non-clairvoyant model, the online scheduler has no information about the actual job size and degree of speed-up due to parallelism, yet it has to determine dynamically when and how many processors to run the jobs. The literature contains several O(1)-competitive algorithms for this problem under the unit-weight multi-processor setting (Edmonds, Theor. Comput. Sci. 235(1), 109---141, 2000; Edmonds and Pruhs, in Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), 685---692, 2009) as well as the weighted single-processor setting (Bansal and Dhamdhere, ACM Trans. Algorithms 3(4), 2007). This paper shows the first O(1)-competitive algorithm for weighted flow time in the multi-processor setting. In the second model, we consider processors with different functionalities and only processors of the same functionality can work on the same job in parallel. Here a job is modeled as a sequence of non-clairvoyant demands of different functionalities. This model is derived naturally from the classical job shop scheduling; but as far as we know, there is no previous work on scheduling to minimize flow time. In this paper we take a first step to study non-clairvoyant scheduling on this multi-processor model. Motivated by the literature on 2-machine job shop scheduling, we focus on the special case when processors are divided into two types of functionalities, and we show a non-clairvoyant algorithm that is O(1)-competitive for weighted flow time.

Transactional scheduling for read-dominated workloads

The transactional approach to contention management guarantees atomicity by aborting transactions that may violate consistency. A major challenge in this approach is to schedule transactions in a manner that reduces the total time to perform all transactions (the makespan), since transactions are often aborted and restarted. The performance of a transactional scheduler can be evaluated by the ratio between its makespan and the makespan of an optimal, clairvoyant scheduler that knows the list of resource accesses that will be performed by each transaction, as well as its release time and duration.This paper studies transactional scheduling in the context of read-dominated workloads; these common workloads include read-only transactions, i.e., those that only observe data, and late-write transactions, i.e., those that update only towards the end of the transaction.We present the Bimodal transactional scheduler, which is especially tailored to accommodate read-only transactions, without punishing transactions that write most of their duration (early-write transactions). It is evaluated by comparison with an optimal clairvoyant scheduler; we prove that Bimodal demonstrates the best competitive ratio achievable by a non-clairvoyant schedule for workloads consisting of early-write and read-only transactions.We also show that late-write transactions significantly deteriorate the competitive ratio of any non-clairvoyant scheduler, assuming it takes a conservative approach to conflicts.