We consider a distributed server system consisting of a large number of servers, each with limited capacity on multiple resources (CPU, memory, etc.). Jobs with different rewards arrive over time and require certain amounts of resources for the duration of their service. When a job arrives, the system must decide whether to admit it or reject it, and if admitted, in which server to schedule it. The objective is to maximize the expected total reward received by the system. This problem is motivated by control of cloud computing clusters, in which jobs are requests for virtual machines (VMs) or containers that reserve resources for various services, and rewards represent service priority of requests or price paid per time unit of service. We study this problem in an asymptotic regime where the number of servers and jobs’ arrival rates scale by a factor L, as L becomes large. We propose a resource reservation policy that asymptotically achieves at least 1/2, and under certain monotone property on jobs’ rewards and resources, at least [Formula: see text] of the optimal expected reward. The policy automatically scales the number of VM slots for each job type as the demand changes and decides in which servers the slots should be created in advance, without the knowledge of traffic rates.
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This content will become publicly available on December 7, 2024
Near-Optimal Stochastic Bin-Packing in Large Service Systems with Time-Varying Item Sizes
In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule jobs with time-varying resource requirements is limited. Motivated by this gap, we propose a new setting of the stochastic bin-packing problem in service systems that allows for time-varying job resource requirements, also referred to as 'item sizes' in traditional bin-packing terms. In this setting, a job or 'item' must be dispatched to a server or 'bin' upon arrival. Its resource requirement may vary over time while in service, following a Markovian assumption. Once the job's service is complete, it departs from the system. Our goal is to minimize the expected number of active servers, or 'non-empty bins', in steady state.
Under our problem formulation, we develop a job dispatch policy, named Join-Reqesting-Server (JRS). Broadly, JRS lets each server independently evaluate its current job configuration and decide whether to accept additional jobs, balancing the competing objectives of maximizing throughput and minimizing the risk of resource capacity overruns. The JRS dispatcher then utilizes these individual evaluations to decide which server to dispatch each arriving job to. The theoretical performance guarantee of JRS is in the asymptotic regime where the job arrival rate scales large linearly with respect to a scaling factor r. We show that JRS achieves an additive optimality gap of O(√r) in the objective value, where the optimal objective value is Θ(r). When specialized to constant job resource requirements, our result improves upon the state-of-the-art o(r) optimality gap. Our technical approach highlights a novel policy conversion framework that reduces the policy design problem into a single-server problem.
more » « less- NSF-PAR ID:
- 10486824
- Publisher / Repository:
- Association for Computing Machinery
- Date Published:
- Journal Name:
- Proceedings of the ACM on Measurement and Analysis of Computing Systems
- Volume:
- 7
- Issue:
- 3
- ISSN:
- 2476-1249
- Page Range / eLocation ID:
- 1 to 46
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Funding: A. Bassamboo received financial support from the National Science Foundation [Grant CMMI 2006350]. C. (A.) Wu received financial support from the Hong Kong General Research Fund [Early Career Scheme, Project 26206419].
Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.1190 .
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