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1. Job Dispatching Policies for Queueing Systems with Unknown Service Rates

   https://doi.org/10.1145/3466772.3467047  

   Choudhury, Tuhinangshu; Joshi, Gauri; Wang, Weina; Shakkottai, Sanjay (July 2021, ACM MobiHoc: International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks)

   null (Ed.)

   In multi-server queueing systems where there is no central queue holding all incoming jobs, job dispatching policies are used to assign incoming jobs to the queue at one of the servers. Classic job dispatching policies such as join-the-shortest-queue and shortest expected delay assume that the service rates and queue lengths of the servers are known to the dispatcher. In this work, we tackle the problem of job dispatching without the knowledge of service rates and queue lengths, where the dispatcher can only obtain noisy estimates of the service rates by observing job departures. This problem presents a novel exploration-exploitation trade-off between sending jobs to all the servers to estimate their service rates, and exploiting the currently known fastest servers to minimize the expected queueing delay. We propose a bandit-based exploration policy that learns the service rates from observed job departures. Unlike the standard multi-armed bandit problem where only one out of a finite set of actions is optimal, here the optimal policy requires identifying the optimal fraction of incoming jobs to be sent to each server. We present a regret analysis and simulations to demonstrate the effectiveness of the proposed bandit-based exploration policy. 

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2. A Theory of Auto-Scaling for Resource Reservation in Cloud Services

   https://doi.org/10.1287/stsy.2021.0091  

   Psychas, Konstantinos; Ghaderi, Javad (February 2022, Stochastic Systems)

   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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3. Near-Optimal Stochastic Bin-Packing in Large Service Systems with Time-Varying Item Sizes

   https://doi.org/10.1145/3626779  

   Hong, Yige; Xie, Qiaomin; Wang, Weina (December 2023, Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   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. 

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4. Optimal Scheduling in the Multiserver-job Model under Heavy Traffic

   https://doi.org/10.1145/3570612  

   Grosof, Isaac; Scully, Ziv; Harchol-Balter, Mor; Scheller-Wolf, Alan (December 2022, Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   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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5. Strongly Tail-Optimal Scheduling in the Light-Tailed M/G/1

   https://doi.org/10.1145/3656011  

   Yu, George; Scully, Ziv (May 2024, Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   We study the problem of scheduling jobs in a queueing system, specifically an M/G/1 with light-tailed job sizes, to asymptotically optimize the response time tail. This means scheduling to make P[T > t], the chance a job's response time exceeds t, decay as quickly as possible in the t \to \infty limit. For some time, the best known policy was First-Come First-Served (FCFS), which has an asymptotically exponential tail: P[T > t] ~ C e^-γ t . FCFS achieves the optimal decay rate γ, but its tail constant C is suboptimal. Only recently have policies that improve upon FCFS's tail constant been discovered. But it is unknown what the optimal tail constant is, let alone what policy might achieve it. In this paper, we derive a closed-form expression for the optimal tail constant C, and we introduce γ-Boost, a new policy that achieves this optimal tail constant. Roughly speaking, γ-Boost operates similarly to FCFS, but it pretends that small jobs arrive earlier than their true arrival times. This significantly reduces the response time of small jobs without unduly delaying large jobs, improving upon FCFS's tail constant by up to 50% with only moderate job size variability, with even larger improvements for higher variability. While these results are for systems with full job size information, we also introduce and analyze a version of γ-Boost that works in settings with partial job size information, showing it too achieves significant gains over FCFS. Finally, we show via simulation that γ-Boost has excellent practical performance. 

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