Stability for Two-class Multiserver-job Systems

Grosof, Isaac; Scheller‐Wolf, Alan

doi:10.48550/arxiv.2010.00631

Cited by 4 publications

(10 citation statements)

References 19 publications

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“…To illustrate, in Fig. 5 we show the distribution of the number of CPUs requested by the jobs in Google's recently published trace of its "Borg" computation cluster [15,43]. The distribution is highly variable, with jobs requesting anywhere from 1 to 100,000 normalized CPUs 1 .…”

Section: Motivationmentioning

confidence: 99%

WCFS: A new framework for analyzing multiserver systems

Grosof¹,

Scheller‐Wolf²

2021

Preprint

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Multiserver queueing systems are found at the core of a wide variety of practical systems. Unfortunately, existing tools for analyzing multiserver models have major limitations: Techniques for exact analysis often struggle with high-dimensional models, while techniques for deriving bounds are often too specialized to handle realistic system features, such as variable service rates of jobs. New techniques are needed to handle these complex, important, high-dimensional models.In this paper we introduce the work-conserving finite-skip class of models. This class includes many important models, such as the heterogeneous M/G/k, the limited processor sharing policy for the M/G/1, the threshold parallelism model, and the multiserver-job model under a simple scheduling policy.We prove upper and lower bounds on mean response time for any model in the work-conserving finite-skip class. Our bounds are separated by an additive constant, giving a strong characterization of mean response time at all loads. When specialized to each of the models above, these bounds represent the first bounds on mean response time known for each setting.

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Section: Motivationmentioning

confidence: 99%

WCFS: A new framework for analyzing multiserver systems

Grosof¹,

Scheller‐Wolf²

2021

Preprint

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“…This work was generalized in [34] and [2] to allow for more general arrival processes, still under the assumption that all jobs have the same exponential service duration. Very recently, Grosof et al [13] derived a simple closed-form expression for the stability region for the multi-server job model where jobs have different exponential service time durations. Unfortunately the work [13] is limited to the case of only 2 classes.…”

Section: Related Workmentioning

confidence: 99%

“…Very recently, Grosof et al [13] derived a simple closed-form expression for the stability region for the multi-server job model where jobs have different exponential service time durations. Unfortunately the work [13] is limited to the case of only 2 classes. The characterization of stability in the case of more than 2 job classes is open.…”

Section: Related Workmentioning

confidence: 99%

“…1. Distribution of the number of CPU cores requested by individual Google jobs according to Google's recently published Borg Trace [42,50] as taken from [13]. For privacy reasons, Google publishes only normalized numbers, however it is still clear that the range spans 5 orders of magnitude across different jobs.…”

Section: Introductionmentioning

confidence: 99%

“…Attempts to derive the steady-state distribution have assumed highly simplified systems with only 𝑛 = 2 servers [8,12], where solutions are already highly complex, involving roots to a quartic equation. Even characterizing the stability region of the system is an open problem except for the special cases where all jobs have the same service rates [2,34,38], or where there are only two job classes with different service rates [13].…”

Section: Introductionmentioning

confidence: 99%

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Zero Queueing for Multi-Server Jobs

Wang¹,

Xie²

2020

Preprint

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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-job-per-server 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.1 Importantly, we note that we are assuming that jobs are served in FCFS order, rather than trying to "pack" jobs into servers.FCFS is the default scheduling policy used throughout the cloud-computing industry when running multi-server jobs [27]. Even when there are multiple priority classes of jobs, as in [42], within each class the jobs are served in FCFS order.

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Overlap times in the infinite server queue

Pender

Palomo

2023

Prob. Eng. Inf. Sci.

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Imagine, you enter a grocery store to buy food. How many people do you overlap with in this store? How much time do you overlap with each person in the store? In this paper, we answer these questions by studying the overlap times between customers in the infinite server queue. We compute in closed form the steady-state distribution of the overlap time between a pair of customers and the distribution of the number of customers that an arriving customer will overlap with. Finally, we define a residual process that counts the number of overlapping customers that overlap in the queue for at least $\delta$ time units and compute its distribution.

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Stability for Two-class Multiserver-job Systems

Cited by 4 publications

References 19 publications

WCFS: A new framework for analyzing multiserver systems

WCFS: A new framework for analyzing multiserver systems

Zero Queueing for Multi-Server Jobs

Overlap times in the infinite server queue

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