Near-Optimal Scheduling Mechanisms for Deadline-Sensitive Jobs in Large Computing Clusters

Abstract

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 C) and s is the slackness on the job completion time, that is, 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 true value and other properties of the job (deadline, work volume, and the parallelism bound) is a dominant strategy for all users. To that end, we extend known results for single-value settings to 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.

Algorithms for scheduling deadline-sensitive malleable tasks

“…This gap between providers offer and tenants goal has received significant attention aiming to allow tenants to describe more precisely the characteristics of their jobs [1], [2] and to design appropriate mechanisms to make every tenant truthfully report the characteristics of their tasks (e.g., value) to the cloud. In the meantime, such technical progress also raises new algorithmic challenges on how to optimally schedule a type of malleable batch jobs arising in cloud computing to maximize the social welfare (i.e., the total value of tasks completed by their deadlines) [3], [4], [5], [6], [7], [8].…”

“…In this paper, we reconsider the fundamental model of [3], [4] in which a set of n malleable batch tasks has to be scheduled on C identical machines. All the jobs are available from the start and each of them is specified by a workload, a parallelism bound, a deadline and a value.…”

“…For the fundamental model in [3], [4] under the objective of maximizing social welfare (i.e., the sum of values of tasks completed before their deadline), Jain et al have proposed an (1 − C 2C−k )(1 − )-approximation algorithm via deterministic rounding of linear program in [3] and a greedy algorithm GreedyRTL via dual fitting technique that achieves an approximation ratio of C−k C · s−1 s in [4]. Here, k is the maximal parallelism bound of tasks, and s (≥ 1) is the slackness which intuitively characterizes the resource allocation flexibility (e.g., s = 1 means that the maximal amount of machines have to be allocated to the task at every time slot until its deadline to ensure full completion).…”

“…Both algorithmic design techniques in [3], [4] are based on the theory of linear programming; they formulate the original problem as an integer program (IP) and relax the IP to a relaxed linear program (LP). In [3], the technique needs to solve the LP for a fractional optimal solution and manage to round the fractional solution of the LP to an integer solution of the IP that corresponds to an approximate solution to the original problem.…”

“…Due to the theoretical constraints of these techniques based on LP in [3], [4], it is difficult to make more progress in designing better or other types of algorithms for scheduling malleable tasks with deadlines. Indeed, the design of the algorithm in [3] has to rely on the formulation of the original problem as a relaxed LP.…”