Abstract In the rapidly expanding field of parallel processing, job schedulers are the “operating systems” of modern big data architectures and supercomputing systems. Job schedulers allocate computing resources and control the execution of processes on those resources. Historically, job schedulers were the domain of supercomputers, and job schedulers were designed to run massive, long-running computations over days and weeks. More recently, big data workloads have created a need for a new class of computations consisting of many short computations taking seconds or minutes that process enormous quantities of data. For both supercomputers and big data systems, the efficiency of the job scheduler represents a fundamental limit on the efficiency of the system. Detailed measurement and modeling of the performance of schedulers are critical for maximizing the performance of a large-scale computing system. This paper presents a detailed feature analysis of 15 supercomputing and big data schedulers. For big data workloads, the scheduler latency is the most important performance characteristic of the scheduler. A theoretical model of the latency of these schedulers is developed and used to design experiments targeted at measuring scheduler latency. Detailed benchmarking of four of the most popular schedulers (Slurm, Son of Grid Engine, Mesos, and Hadoop YARN) is conducted. The theoretical model is compared with data and demonstrates that scheduler performance can be characterized by two key parameters: the marginal latency of the scheduler t s and a nonlinear exponent α s . For all four schedulers, the utilization of the computing system decreases to 90 for all four of the schedulers that were tested.
The publications that are covered in the previous paragraphs are all comparisons of actual schedulers as well as the application of queue management and scheduling algorithms on actual workload traces and simulated workload traces based on actual workload characteristics. However, another branch of job scheduler research has approached this topic from a mathematical and statistical operations research vector. Statistical distributions are applied to various aspects of workload characteristics and resource characteristics. First, a taxonomy of workloads, resources platforms, and mapping and scheduling heuristics is presented in @cite_63 . Workload modeling is extensively treated in @cite_20 , while @cite_46 covers a very large set of scheduling algorithms. An extensive study and comparison of mapping and scheduling algorithms was reported in @cite_1 , with refinements in @cite_9 . Further refinements of the underlying statistical models and parameter set generation was published in @cite_56 and @cite_11 .
@cite_9 @cite_1 @cite_56 @cite_63 @cite_46 @cite_20 @cite_11
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The main aim of this note is to show that a polynomial-time algorithm for the scheduling problem 1|r j ; p j = p| ∑ Uj given by Carlier in (1981) is incorrect. In this problem we are given n jobs with release times and deadlines. All jobs have the same processing time p. The objective is to find a non-preemptive schedule that maximizes the number of jobs completed by their deadlines. The feasibility version of this problem, where we ask whether all jobs can meet their deadlines, has been studied thoroughly. Polynomial-time algorithms for this version were first found, independently, by Simons (1978) and Carlier (1981). A faster algorithm, with running time O(n log n), was subsequently given by (1981). The elegant feasibility algorithm of Carlier (1981) is based on dynamic programming and it processes jobs from left to right on the time-axis. For each time t, it constructs a partial schedule with jobs that complete at or before time t. Carlier also attempted to apply the same technique to design a polynomial-time algorithm for the maximization version, 1|r j ; p j = p| ∑ Uj , and claimed an O(n3 log n)-time algorithm. His result is now widely cited in the literature. We show, however, that this algorithm is not correct, by giving an instance on which it produces a sub-optimal schedule. Our counter-example can be, in fact, extended to support a broader claim, namely that even the general approach from Carlier (1981) cannot yield a polynomial-time algorithm. By this general approach we mean a class of algorithms that processes the input from left to right and make decisions based on the deadline ordering, and not their exact values. The question remains as to how efficiently can we solve the scheduling problem 1|r j ; p j = p| ∑ Uj . Baptiste (1999) gave an O(n7)-time algorithm for the more general version of this problem where jobs have weights. We show how to modify his algorithm to obtain a faster, O(n5)-time algorithm for the non-weighted case. These last two results are discussed only briefly in this note. The complete proofs can be found in the full version of this paper, see (2004). We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the most workload-intensive input traffic traces (arrival processes). Stability preserves the job inflow–outflow balance at each queue on the traffic traces. Two key families of service policies are shown to maximize throughput, under the mild condition that traffic traces have long-term average workload rates. In the first family of cone policies, the service mode is chosen based on the system backlog state belonging to a corresponding cone. Two distinct policy classes of that nature are investigated, MaxProduct and FastEmpty. In the second family of batch policies (BatchAdapt), jobs are collectively scheduled over adaptively chosen horizons, according to an asymptotically optimal, robust schedule. The issues of nonpreemptive job processing and non-negligible switching times between service modes are addressed. The analysis is extended to cover feed-forward networks of such processing systems nodes. The approach taken unifies and generalizes prior studies, by developing a general trace-based modeling framework (sample-path approach) for addressing the queueing stability problem. It treats the queueing structure as a deterministic dynamical system and analyzes directly its evolution trajectories. It does not require any probabilistic superstructure, which is typically used in previous approaches. Probability can be superposed later to address finer performance questions (e.g., delay). The throughput maximization problem is seen to be primarily of structural nature. The developed methodology appears to have broader applicability to other queueing systems. We consider a market-based resource allocation model for batch jobs in cloud computing clusters. In our model, we incorporate the importance of the due date of a job rather than the number of servers allocated to it at any given time. Each batch job is characterized by the work volume of total computing units (e.g., CPU hours) along with a bound on maximum degree of parallelism. Users specify, along with these job characteristics, their desired due date and a value for finishing the job by its deadline. Given this specification, the primary goal is to determine the scheduling of cloud computing instances under capacity constraints in order to maximize the social welfare (i.e., sum of values gained by allocated users). Our main result is a new ( C (C-k) ⋅ s (s-1))-approximation algorithm for this objective, where C denotes cloud capacity, k is the maximal bound on parallelized execution (in practical settings, k l C) and s is the slackness on the job completion time i.e., the minimal ratio between a specified deadline and the earliest finish time of a job. Our algorithm is based on utilizing dual fitting arguments over a strengthened linear program to the problem. Based on the new approximation algorithm, we construct truthful allocation and pricing mechanisms, in which reporting the job true value and properties (deadline, work volume and the parallelism bound) is a dominant strategy for all users. To that end, we provide a general framework for transforming allocation algorithms into truthful mechanisms in domains of single-value and multi-properties. We then show that the basic mechanism can be extended under proper Bayesian assumptions to the objective of maximizing revenues, which is important for public clouds. We empirically evaluate the benefits of our approach through simulations on data-center job traces, and show that the revenues obtained under our mechanism are comparable with an ideal fixed-price mechanism, which sets an on-demand price using oracle knowledge of users' valuations. Finally, we discuss how our model can be extended to accommodate uncertainties in job work volumes, which is a practical challenge in cloud settings. Scheduling workflows in cloud service environment has attracted great enthusiasm, and various approaches have been reported up to now. However, these approaches often ignored the uncertainties in the scheduling environment. Ignoring these uncertain factors often leads to the violation of workflow deadlines and increases service renting costs of executing workflows. This study devotes to improving the performance for cloud service platforms by minimizing uncertainty propagation in scheduling workflow applications that have both uncertain task execution time and data transfer time. To be specific, a novel scheduling architecture is designed to control the count of workflow tasks directly waiting on each service instance (e.g., virtual machine). Based on this architecture, we develop an unceRtainty-aware Online Scheduling Algorithm (ROSA) to schedule dynamic and multiple workflows with deadlines. The proposed ROSA skillfully integrates both the proactive and reactive strategies. Then, on the basis of real-world workflow traces, five groups of simulation experiments are carried out to compare ROSA with five typical algorithms. The comparison results reveal that ROSA performs better than the five compared algorithms with respect to costs (up to 56 ), deviation (up to 70 ), resource utilization (up to 37 ) and fairness (up to 37).