Multiserver-job systems, where jobs require concurrent service at many servers, occur widely in practice. Essentially all of the theoretical work on multiserver-job systems focuses on maximizing utilization, with almost nothing known about mean response time. In simpler settings, such as various known-size single-server-job settings, minimizing mean response time is merely a matter of prioritizing small jobs. However, for the multiserver-job system, prioritizing small jobs is not enough, because we must also ensure servers are not unnecessarily left idle. Thus, minimizing mean response time requires prioritizing small jobs while simultaneously maximizing throughput. Our question is how to achieve these joint objectives. We devise the ServerFilling-SRPT scheduling policy, which is the first policy to minimize mean response time in the multiserver-job model in the heavy traffic limit. In addition to proving this heavy-traffic result, we present empirical evidence that ServerFilling-SRPT outperforms all existing scheduling policies for all loads, with improvements by orders of magnitude at higher loads. Because ServerFilling-SRPT requires knowing job sizes, we also define the ServerFilling-Gittins policy, which is optimal when sizes are unknown or partially known.
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Sojourn Time Minimization of Successful Jobs
Due to a growing interest in deep learning applications [5], compute-intensive and long-running (hours to days) training jobs have become a significant component of datacenter workloads. A large fraction of these jobs is often exploratory, with the goal of determining the best model structure (e.g., the number of layers and channels in a convolutional neural network), hyperparameters (e.g., the learning rate), and data augmentation strategies for the target application. Notably, training jobs are often terminated early if their learning metrics (e.g., training and validation accuracy) are not converging, with only a few completing successfully. For this motivating application, we consider the problem of scheduling a set of jobs that can be terminated at predetermined checkpoints with known probabilities estimated from historical data. We prove that, in order to minimize the time to complete the first K successful jobs on a single server, optimal scheduling does not require preemption (even when preemption overhead is negligible) and provide an optimal policy; advantages of this policy are quantified through simulation. Related Work. While job scheduling has been investigated extensively in many scenarios (see [6] and [2] for a survey of recent result), most policies require that the cost of waiting times of each job be known at scheduling time; in contrast, in our setting the scheduler does not know which job will be the K-th successful job, and sojourn times of subsequent jobs do not contribute to the target metric. For example, [4, 3] minimize makespan (i.e., the time to complete all jobs) for known execution times and waiting time costs; similarly, Gittins index [1] and SR rank [7] minimize expected sojourn time of all jobs, i.e., both successfully completed jobs and jobs terminated early. Unfortunately, scheduling policies not distinguishing between these two types of jobs may favor jobs where the next stage is short and leads to early termination with high probability, which is an undesirable outcome in our applications of interest.
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- Award ID(s):
- 1816887
- NSF-PAR ID:
- 10376773
- Date Published:
- Journal Name:
- ACM SIGMETRICS Performance Evaluation Review
- Volume:
- 50
- Issue:
- 2
- ISSN:
- 0163-5999
- Page Range / eLocation ID:
- 24 to 26
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We consider the optimal scheduling problem in the M/G/1 queue. While this is a thoroughly studied problem when the target is to minimize the mean delay, there are still open questions related to some other objective functions. In this paper, we focus on minimizing mean slowdown among non-anticipating polices, which may utilize the attained service of the jobs but not their remaining service time when making scheduling decisions. By applying the Gittins index approach, we give necessary and sufficient conditions for the jobs’ service time distribution under which the well-known scheduling policies first come first served and foreground background are optimal with respect to the mean slowdown. Furthermore, we characterize the optimal non-anticipating policy in the multi-class case for certain types of service time distributions. In fact, our results cover a more general objective function than just the mean slowdown, since we allow the holding costs for a job to depend on its own service time
S via a generic functionc (S ). When minimizing the mean slowdown, this function reads as$$c(x) = 1/x$$ -
null (Ed.)The Gittins scheduling policy minimizes the mean response in the single-server M/G/1 queue in a wide variety of settings. Most famously, Gittins is optimal when preemption is allowed and service requirements are unknown but drawn from a known distribution. Gittins is also optimal much more generally, adapting to any amount of available information and any preemption restrictions. However, scheduling to minimize mean response time in a multiserver setting, specifically the central-queue M/G/k, is a much more difficult problem. In this work we give the first general analysis of Gittins in the M/G/k. Specifically, we show that under extremely general conditions, Gittins's mean response time in the M/G/k is at most its mean response time in the M/G/1 plus an $O(łog(1/(1 - ρ)))$ additive term, where ρ is the system load. A consequence of this result is that Gittins is heavy-traffic optimal in the M/G/k if the service requirement distribution S satisfies $\mathbfE [S^2(łog S)^+] < \infty$. This is the most general result on minimizing mean response time in the M/G/k to date. To prove our results, we combine properties of the Gittins policy and Palm calculus in a novel way. Notably, our technique overcomes the limitations of tagged job methods that were used in prior scheduling analyses.more » « less
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null (Ed.)While cloud platforms enable users to rent computing resources on demand to execute their jobs, buying fixed resources is still much cheaper than renting if their utilization is high. Thus, optimizing cloud costs requires users to determine how many fixed resources to buy versus rent based on their workload. In this paper, we introduce the concept of a waiting policy for cloud-enabled schedulers, which is the dual of a scheduling policy, and show that the optimal cost depends on it. We define multiple waiting policies and develop simple analytical models to reveal their tradeoff between fixed resource provisioning, cost, and job waiting time. We evaluate the impact of these waiting policies on a year-long production batch workload consisting of 14M jobs run on a 14.3k-core cluster, and show that a compound waiting policy decreases the cost (by 5%) and mean job waiting time (by 7x) compared to a fixed cluster of the current size.more » « less
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Matching markets with historical data are abundant in many applications, e.g., matching candidates to jobs in hiring, workers to tasks in crowdsourcing markets, and jobs to servers in cloud services. In all these applications, a match consumes one or more shared and limited resources and the goal is to best utilize these to maximize a global objective. Additionally, one often has historical data and hence some statistics (usually first-order moments) of the arriving agents (e.g., candidates, workers, and jobs) can be learnt. To model these scenarios, we propose a unifying framework, called Multi- Budgeted Online Assignment with Known Adversarial Distributions. In this model,we have a set of offline servers with different deadlines and a set of online job types. At each time, a job of type j arrives. Assigning this job to a server i yields a profit w(i, j) while consuming a(i,j) -- a vector lying in [0, 1]^K -- quantities of distinct resources. The goal is to design an (online) assignment policy that maximizes the total expected profit without violating the (hard) budget constraint. We propose and theoretically analyze two linear programming (LP) based algorithms which are almost optimal among all LP-based approaches. We also propose several heuristics adapted from our algorithms and compare them to other LP-agnostic algorithms using both synthetic as well as real-time cloud scheduling and public safety datasets. Experimental results show that our proposed algorithms are effective and significantly out-perform the baselines. Moreover, we show empirically the trade-off between fairness and efficiency of our algorithms which does well even on fairness metrics without explicitly optimizing for it.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3561074.3561083
