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1. Zero Queueing for Multi-Server Jobs

   https://doi.org/10.1145/3447385  

   Wang, Weina ; Xie, Qiaomin ; Harchol-Balter, Mor ( February 2021 , Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   null (Ed.)

   Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit'' into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems. 

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2. 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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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. Managing Queues with Different Resource Requirements

   https://doi.org/10.1287/opre.2022.2284  

   Zychlinski, Noa ; Chan, Carri W. ; Dong, Jing ( July 2022 , Operations Research)

   Queueing models that are used to capture various service settings typically assume that customers require a single unit of resource (server) to be processed. However, there are many service settings where such an assumption may fail to capture the heterogeneity in resource requirements of different customers. We propose a multiserver queueing model with multiple customer classes in which customers from different classes may require different amounts of resources to be served. We study the optimal scheduling policy for such systems. To balance holding costs, service rates, resource requirement, and priority-induced idleness, we develop an index-based policy that we refer to as the idle-avoid [Formula: see text] rule. For a two-class two-server model, where policy-induced idleness can have a big impact on system performance, we characterize cases where the idle-avoid [Formula: see text] rule is optimal. In other cases, we establish a uniform performance bound on the amount of suboptimality incurred by the idle-avoid [Formula: see text] rule. For general multiclass multiserver queues, we establish the asymptotic optimality of the idle-avoid [Formula: see text] rule in the many-server regime. For long-time horizons, we show that the idle-avoid [Formula: see text] is throughput optimal. Our theoretical results, along with numerical experiments, provide support for the good and robust performance of the proposed policy. 

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5. 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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