Steady state approximations of limited processor sharing queues in heavy traffic

Zhang, Jiheng; Zwart, Bert

doi:10.1007/s11134-008-9095-4

Cited by 58 publications

(51 citation statements)

References 21 publications

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“…Most analyses of the M/G/PS-MPL queue do not allow for load-dependent service rates. For example, Itzhak and Halfin [3] derive a 2-moment approximation for the mean response time for the M/G/PS-MPL queue where the service rate is fixed, while Zhang and Zwart [28] derive a heavy-traffic diffusion approximation for M/G/PS-MPL (which they refer to as the Limited Processor Sharing queue) with a fixed service rate. There is one analysis of the M/G/PS-MPL that does involve state-dependent service rates, see Rege & Sengupta [21].…”

Section: Prior Workmentioning

confidence: 99%

Self-adaptive admission control policies for resource-sharing systems

Gupta

2009

Proceedings of the Eleventh International Joint Conference on Measurement and Modeling of Computer Systems

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We consider the problem of admission control in resource sharing systems, such as web servers and transaction processing systems, when the job size distribution has high variability, with the aim of minimizing the mean response time. It is well known that in such resource sharing systems, as the number of tasks concurrently sharing the resource is increased, the server throughput initially increases, due to more efficient utilization of resources, but starts falling beyond a certain point, due to resource contention and thrashing. Most admission control mechanisms solve this problem by imposing a fixed upper bound on the number of concurrent transactions allowed into the system, called the MultiProgramming-Limit (MPL), and making the arrivals which find the server full queue up. Almost always, the MPL is chosen to be the point that maximizes server efficiency.In this paper we abstract such resource sharing systems as a Processor Sharing (PS) server with state-dependent service rate and a First-Come-First-Served (FCFS) queue, and we analyze the performance of this model from a queueing theoretic perspective. We start by showing that, counter to the common wisdom, the peak efficiency point is not always optimal for minimizing the mean response time. Instead, significant performance gains can be obtained by running the system at less than the peak efficiency. We provide a simple expression for the static MPL that achieves nearoptimal mean response time for general distributions.Next we present two traffic-oblivious dynamic admission control policies that adjust the MPL based on the instantaneous queue length while also taking into account the variability of the job size distribution. The structure of our admission control policies is a mixture of fluid control when the number of jobs in the system is high, with a stochastic component when the system is near-empty. We show via simulations that our dynamic policies are much more robust to unknown traffic intensities and burstiness in the arrival process than imposing a static MPL.

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Section: Prior Workmentioning

confidence: 99%

Self-adaptive admission control policies for resource-sharing systems

Gupta

2009

Proceedings of the Eleventh International Joint Conference on Measurement and Modeling of Computer Systems

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“…The state-of-the-art deals with two causes of varying execution speeds: state-dependent and exogenous/environmental variability. The former [Gupta and Harchol-Balter, 2009;Rege and Sengupta, 1985;Zhang and Zwart, 2008] models the execution speed based on the current state of the system, i.e., the combination of the number of jobs and the multiprogramming levels. The latter [Mahabhashyam and Gautam, 2005;Casale and Tribastone, 2013;Zhang and Zwart, 2012;Dorsman et al, 2013] models the transition of execution speeds as Markov-modulated speed for single queue and multiple queues.…”

Section: ¾º¿º½ åó ð ò ì ð ê ×ôóò× ì ñ ×mentioning

confidence: 99%

Resource management of replicated service systems provisioned in the cloud

Björkqvist

Birke

Binder

2016

NOMS 2016 - 2016 IEEE/IFIP Network Operations and Management Symposium

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I certify that except where due acknowledgement has been given, the work presented in this thesis is that of the author alone; the work has not been submitted previously, in whole or in part, to qualify for any other academic award; and the content of the thesis is the result of work which has been carried out since the official commencement date of the approved research program. Lugano, 11 February 2015 ×ØÖ Ø Service providers seek scalable and cost-effective cloud solutions for hosting their applications. Despite significant recent advances facilitating the deployment and management of services on cloud platforms, a number of challenges still remain. Service providers are confronted with time-varying requests for the provided applications, inter-dependencies between different components, performance variability of the procured virtual resources, and cost structures that differ from conventional data centers. Moreover, fulfilling service level agreements, such as the throughput and response time percentiles, becomes of paramount importance for ensuring business advantages. Mathias BjörkqvistIn this thesis, we explore service provisioning in clouds from multiple points of view. The aim is to best provide service replicas in the form of VMs to various service applications, such that their tail throughput and tail response times, as well as resource utilization, meet the service level agreements in the most cost effective manner. In particular, we develop models, algorithms and replication strategies that consider multi-tier composed services provisioned in clouds. We also investigate how a service provider can opportunistically take advantage of observed performance variability in the cloud. Finally, we provide means of guaranteeing tail throughput and response times in the face of performance variability of VMs, using Markov chain modeling and large deviation theory. We employ methods from analytical modeling, event-driven simulations and experiments. Overall, this thesis provides not only a multi-faceted approach to exploring several crucial aspects of hosting services in clouds, i.e., cost, tail throughput, and tail response times, but our proposed resource management strategies are also rigorously validated via trace-driven simulation and extensive experiments.

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“…The authors indicate that the expected sojourn time is monotone in c. In PhD thesis [8], a study of fundamental performance questions about queuing models with shared resources such as stability issues of these models, product-form solutions and scheduling is presented. Approximation formulas for various performance quantities for the LPS queue are derived in [9] and based on diffusion limits.…”

Section: Related Workmentioning

confidence: 99%

Analysis of Sojourn Times in QBD Model of a Thread Pool

2013

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Original scientific paperModern Web or database servers are usually designed with a thread pool as a major component for servicing. Controlling of such servers, as well as defining adequate resource management policies, with the aim of minimizing requests' sojourn times presuppose the existence of performance models of thread-pooled systems. In this paper a queuing model of a thread pool is formulated along with a set of underlying assumptions and definitions used. Requests are abstracted in such a way that they are characterized by service time distribution and CPU consumption parameter. The model is defined as a Quasi-Birth-and-Death (QBD) process. Stability conditions for the model are derived and an analytic method based on generating functions for calculation of expected sojourn times is presented. The analytical results thus obtained are evaluated in a developed experimental environment. The environment contains a synthetic workload generator and an instrumented server application based on a standard Java 7 ThreadPoolExecutor thread pool. Sojourn time measurements confirm the theoretical results and also give additional insight into sojourn times related to more realistic workload cases that otherwise would be difficult to analyze formally.Key words: Thread pool, Sojourn time, CPU-bound tasks, Quasi-Birth-and-Death process, Server application Analiza vremena boravka u QBD modelu thread pool-a. Kod suvremenih web poslužitelja ili poslužitelja baza podataka thread pool najčešće predstavlja glavnu komponentu za posluživanje. Operativno upravljanje kao i definiranje odgovarajućih politika upravljanja resursima s ciljem minimiziranja vremena boravka zahtjeva u sistemu, pretpostavlja postojanje modela performansi sistema koji sadrže thread pool. U ovom radu je formuliran model thread poola zajedno s definicijama i pretpostavkama na kojima se taj model temelji. Zahtjevi su karakterizirani apstraktno preko raspodjele vremena posluživanja i parametra upotrebe CPU. Model je definiran kao Quasi-Birth-and-Death (QBD) proces. Izvedeni su uvjeti stabilnosti modela i razraena je metoda proračuna očeki-vanog vremena boravka zahtjeva. Dobiveni analitički rezultati su provjereni u eksperimentalnoj okolini. Ta okolina se sastoji od generatora opterećenja i instrumentalizirane poslužiteljske aplikacije koja sadrži standardni Java 7 ThreadPoolExecutor. Mjerenja vremena boravka potvruju teoretske rezultate i daju nam dodatan uvid u trajanje boravaka koje se odnosi na slučejeve opterećenja koja više odgovaraju praksi, a koje je inače teško ili nemoguće analitički odrediti.

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Steady state approximations of limited processor sharing queues in heavy traffic

Cited by 58 publications

References 21 publications

Self-adaptive admission control policies for resource-sharing systems

Self-adaptive admission control policies for resource-sharing systems

Resource management of replicated service systems provisioned in the cloud

Analysis of Sojourn Times in QBD Model of a Thread Pool

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