SRPT for Multiserver Systems

Grosof, Isaac; Scully, Ziv

doi:10.1145/3305218.3305223

Cited by 20 publications

(35 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To our knowledge, the first analytic results on the M/G/k/SRPT were given by Grosof et al (2018). They proved analytic bounds on the mean response time of the M/G/k/SRPT.…”

mentioning

confidence: 87%

Open Problem—M/G/k/SRPT Under Medium Load

Grosof

2019

Stochastic Systems

Self Cite

View full text Add to dashboard Cite

Please scroll down for article-it is on subsequent pages With 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org

show abstract

“…To our knowledge, the first analytic results on the M/G/k/SRPT were given by Grosof et al (2018). They proved analytic bounds on the mean response time of the M/G/k/SRPT.…”

mentioning

confidence: 87%

Open Problem—M/G/k/SRPT Under Medium Load

Grosof

2019

Stochastic Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…Given the optimality of the Shortest-Remaining-Processing-Time (SRPT) policy in the degenerate case where k = 1 [48], one might hope that SRPT is also optimal in the multiserver case where k ≥ 2. Specifically, one might consider a policy called SRPT-k [19] which always runs the k jobs with the shortest remaining processing times. Unfortunately, [35] shows that SRPT-k can be arbitrarily far from optimal.…”

Section: Why Stochastic Analysis?mentioning

confidence: 99%

“…Much of the prior work has been limited to scheduling jobs on a single server [11]. While there has certainly been work on scheduling in stochastic multiserver systems (e.g [1,6,19,23,24,29]), this literature assumes that a job occupies at most one server at a time (that is, all jobs are inelastic). One notable model that considers jobs that run on multiple servers is the queueing model motivated from MapReduce [32,42,50].…”

Section: Prior Workmentioning

confidence: 99%

Optimal Resource Allocation for Elastic and Inelastic Jobs

Berg

Moseley

Wang

et al. 2020

Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures

Self Cite

View full text Add to dashboard Cite

Modern data centers are tasked with processing heterogeneous workloads consisting of various classes of jobs. These classes differ in their arrival rates, size distributions, and job parallelizability. With respect to parallelizability, some jobs are elastic, meaning they can parallelize linearly across any number of servers. Other jobs are inelastic, meaning they can only run on a single server. Although job classes can differ drastically, they are typically forced to share a single cluster. When sharing a cluster among heterogeneous jobs, one must decide how to allocate servers to each job at every moment in time. In this paper, we design and analyze allocation policies which aim to minimize the mean response time across jobs, where a job's response time is the time from when it arrives until it completes. We model this problem in a stochastic setting where each job may be elastic or inelastic. Job sizes are drawn from exponential distributions, but are unknown to the system. We show that, in the common case where elastic jobs are larger on average than inelastic jobs, the optimal allocation policy is Inelastic-First, giving inelastic jobs preemptive priority over elastic jobs. We obtain this result by introducing a novel sample path argument. We also show that there exist cases where Elastic-First (giving priority to elastic jobs) performs better than Inelastic-First. We provide the first analysis of mean response time under both Elastic-First and Inelastic-First by leveraging techniques for solving high-dimensional Markov chains.

show abstract

“…Gieroba and Kruk [25] investigated some pathwise minimality properties associated with the SRPT protocol in resource sharing networks. Grosof et al [27] provided bounds for the mean response time in the M/G/k queue under the SRPT and showed asymptotic optimality of this mean response time in the heavy-traffic limit. Recently, Dong and Ibrahim [22] investigated the multiserver M/G/k+G queue with impatient customers under the SRPT protocol and showed that, in the many-sever overloaded regime, its performance is asymptotically equivalent in steady state to a preemptive two-class priority queue.…”

Section: Introductionmentioning

confidence: 99%

Instability of SRPT, SERPT and SJF multiclass queueing networks

Kruk

Chojecki

2022

Queueing Syst

View full text Add to dashboard Cite

We provide two examples of strictly subcritical multiclass queueing networks which are unstable under the shortest remaining processing time (SRPT) service protocol. Both of them are reentrant lines with two servers and eight customer classes. The customer service times in our first system are deterministic, yielding an example of an unstable shortest remaining expected processing time (SERPT) network. In the second one, the service times in one customer class are randomized. Both our examples show also system instability under the shortest job first (SJF) discipline. A simulation study of robustness of our results with respect to changes in the customer interarrival and service times is also provided. Our results indicate that size-based service policies may not use the available resources efficiently in a multiserver network setting and in fact cause instability effects. This is in sharp contrast with their satisfactory performance for single-server queues.

show abstract

SRPT for Multiserver Systems

Cited by 20 publications

References 10 publications

Open Problem—M/G/k/SRPT Under Medium Load

Open Problem—M/G/k/SRPT Under Medium Load

Optimal Resource Allocation for Elastic and Inelastic Jobs

Instability of SRPT, SERPT and SJF multiclass queueing networks

Contact Info

Product

Resources

About