Logarithmic heavy traffic error bounds in generalized switch and load balancing systems

Hurtado-Lange, Daniela; Varma, Sushil Mahavir; Maguluri, Siva Theja

doi:10.1017/jpr.2021.82

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…The approach has been adopted in studying various switches (e.g. [21,28,29,32,36,37,49]), load-balancing algorithms (e.g. [20,33,52,58,59,61]), and other stochastic models (e.g.…”

Section: Our Contributionsmentioning

confidence: 99%

Heavy-Traffic Optimal Size- and State-Aware Dispatching

Xie,

Grosof,

Scully

2024

Proc. ACM Meas. Anal. Comput. Syst.

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Dispatching systems, where arriving jobs are immediately assigned to one of multiple queues, are ubiquitous in computer systems and service systems. A natural and practically relevant model is one in which each queue serves jobs in FCFS (First-Come First-Served) order. We consider the case where the dispatcher is size-aware, meaning it learns the size (i.e. service time) of each job as it arrives; and state-aware, meaning it always knows the amount of work (i.e. total remaining service time) at each queue. While size- and state-aware dispatching to FCFS queues has been extensively studied, little is known about optimal dispatching for the objective of minimizing mean delay. A major obstacle is that no nontrivial lower bound on mean delay is known, even in heavy traffic (i.e. the limit as load approaches capacity). This makes it difficult to prove that any given policy is optimal, or even heavy-traffic optimal. In this work, we propose the first size- and state-aware dispatching policy that provably minimizes mean delay in heavy traffic. Our policy, called CARD (Controlled Asymmetry Reduces Delay), keeps all but one of the queues short, then routes as few jobs as possible to the one long queue. We prove an upper bound on CARD's mean delay, and we prove the first nontrivial lower bound on the mean delay of any size- and state-aware dispatching policy. Both results apply to any number of servers. Our bounds match in heavy traffic, implying CARD's heavy-traffic optimality. In particular, CARD's heavy-traffic performance improves upon that of LWL (Least Work Left), SITA (Size Interval Task Assignment), and other policies from the literature whose heavy-traffic performance is known.

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“…The approach has been adopted in studying various switches (e.g. [21,28,29,32,36,37,49]), load-balancing algorithms (e.g. [20,33,52,58,59,61]), and other stochastic models (e.g.…”

Section: Our Contributionsmentioning

confidence: 99%

Heavy-Traffic Optimal Size- and State-Aware Dispatching

Xie,

Grosof,

Scully

2024

Proc. ACM Meas. Anal. Comput. Syst.

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“…• input-queued switches [37,59,60,85,132], and • systems where jobs occupy multiple servers [58,137,151]. We have only just begun to understand scheduling in these systems.…”

Section: Scheduling In More Complicated Multiserver Modelsmentioning

confidence: 99%

“…It thus seems likely that we can use a similar technique to analyze other multiserver systems, particularly if their scheduling policy is an appropriate analogue of SRPT or Gittins. An example might be scheduling in input-queued switches [37,59,60,85,132] that use SRPT or Gittins instead of FCFS within each of its queues. Of course, determining exactly what constitutes an "appropriate analogue" of SRPT or Gittins may well be challenging.…”

Section: New Generalization and Variants Of The Gi Ins Policymentioning

confidence: 99%

A New Toolbox for Scheduling Theory

Scully

2022

SIGMETRICS Perform. Eval. Rev.

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Queueing delays are ubiquitous in many domains, including computer systems, service systems, communication networks, supply chains, and transportation. Queueing and scheduling theory provide a rigorous basis for understanding how to reduce delays with scheduling, including evaluating policy performance and guiding policy design. Unfortunately, stateof- the-art theory fails to address many practical concerns. For example, scheduling theory seldom treats nontrivial preemption limitations, and there is very little theory for scheduling in multiserver queues. My thesis presents two new, broadly applicable tools that greatly expand the reach of scheduling theory, using each to solve multiple open problems. The first tool, called "SOAP", is a new unifying theory of scheduling in single-server queues, specifically the M/G/1 model. SOAP characterizes the delay distribution of a broad space of policies, most of which have never been analyzed before. Such policies include the Gittins index policy, which minimizes mean delay in low-information settings, and many policies with preemption limitations. The second tool, called "WINE", is a new queueing identity that complements Little's law. WINE enables a new method of analyzing complex queueing systems by relating them to simpler systems. This results in the first delay bounds for Shortest Remaining Processing Time (SRPT) and the Gittins policy in multiserver queues, specifically the M/G/k model. This abstract gives a brief overview of my thesis, describing what the SOAP and WINE tools do, the key ideas underlying them, and the open problems they help solve.

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Heavy-traffic queue length behavior in a switch under Markovian arrivals

Mou,

Maguluri

2024

Adv. Appl. Probab.

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This paper studies the input-queued switch operating under the MaxWeight algorithm when the arrivals are according to a Markovian process. We exactly characterize the heavy-traffic scaled mean sum queue length in the heavy-traffic limit, and show that it is within a factor of less than 2 from a universal lower bound. Moreover, we obtain lower and upper bounds that are applicable in all traffic regimes and become tight in the heavy-traffic regime. We obtain these results by generalizing the drift method recently developed for the case of independent and identically distributed arrivals to the case of Markovian arrivals. We illustrate this generalization by first obtaining the heavy-traffic mean queue length and its distribution in a single-server queue under Markovian arrivals and then applying it to the case of an input-queued switch. The key idea is to exploit the geometric mixing of finite-state Markov chains, and to work with a time horizon that is chosen so that the error due to mixing depends on the heavy-traffic parameter.

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Logarithmic heavy traffic error bounds in generalized switch and load balancing systems

Cited by 3 publications

References 12 publications

Heavy-Traffic Optimal Size- and State-Aware Dispatching

Heavy-Traffic Optimal Size- and State-Aware Dispatching

A New Toolbox for Scheduling Theory

Heavy-traffic queue length behavior in a switch under Markovian arrivals

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