Optimal scheduling of parallel queues using stochastic flow models

Kebarighotbi, Ali; Cassandras, Christos G.

doi:10.1007/s10626-011-0105-z

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…It stimulates numerous extensions in the literature [23,26,27,36,48]. Many works aim to study similar properties to the cµ-rule under various queueing systems and assumptions.…”

Section: Related Researchmentioning

confidence: 99%

A $c/μ$-Rule for Service Resource Allocation in Group-Server Queues

Xia,

Zhang,

et al. 2018

Preprint

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This paper addresses a dynamic on/off server scheduling problem in a queueing system with Poisson arrivals and K groups of exponential servers. Servers within each group are homogeneous and between groups are heterogeneous. A scheduling policy prescribes the number of working servers in each group at every state n (number of customers in the system). Our goal is to find the optimal policy to minimize the long-run average cost, which consists of an increasing convex holding cost for customers and a linear operating cost for working servers. We prove that the optimal policy has monotone structures and quasi bang-bang control forms. Specifically, we find that the optimal policy is indexed by the value of c − µG(n), where c is the operating cost rate, µ is the service rate, and G(n) is called perturbation realization factor. Under a reasonable condition of scale economies, we prove that the optimal policy obeys a so-called c/µ-rule. That is, the servers with

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“…It stimulates numerous extensions in the literature [23,26,27,36,48]. Many works aim to study similar properties to the cµ-rule under various queueing systems and assumptions.…”

Section: Related Researchmentioning

confidence: 99%

A $c/μ$-Rule for Service Resource Allocation in Group-Server Queues

Xia,

Zhang,

et al. 2018

Preprint

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“…For concurrent access, we consider a queuing system for tasks submission. For such type of systems, the number of task arrivals in a given interval of time is a random variable with a Poisson distribution [5,12]. In this section, we describe the estimation method for the necessary resources to schedule a set of aperiodic tasks in parallel with periodic tasks.…”

Section: Aperiodic Task Scheduling With Deadline Constraintsmentioning

confidence: 99%

Deadline scheduling for aperiodic tasks in inter-Cloud environments: a new approach to resource management

et al. 2014

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Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Journal of supercomputing.La publicació final està disponible a Springer a través de http://dx.doi.org/10.1007/s11227- 014-1285-8 This is a copy of the author 's final draft version of an article published in the journal Journal of supercomputing. Abstract In the big data era, the speed of analytical processing is influenced by the storage and retrieval capabilities to handle large amounts of data. While the distributed crunching applications themselves can yield useful information, the analysts face difficult challenges: they need to predict how much data to process and where, such that to get an optimum data crunching cost, while also respect deadlines and service level agreements within a limited budget. In today's data centers, data processing on demand and data transfers requests coming from distributed applications are usually expressed as aperiodic tasks. In this paper, we challenge the problem of tasks scheduling with deadline constraints of aperiodic tasks within inter-Cloud environments. In massively multithreaded computing systems that deal with data-intensive applications, Hadoop and BaTs tasks arrive periodically, which challenges traditional scheduling approaches previously proposed for supercomputing. Here, we consider the deadline as the main constraint, and propose a method to estimate the number of resources needed to schedule a set of aperiodic tasks, considering both execution and data transfers costs. Starting from classical scheduling techniques, and considering asynchronous tasks handling, we analyze the possibility of decoupling task arriving from task creation, scheduling and execution, sets of actions that can be put into a peer-to-peer relation over a network or over a client-server architecture in the Cloud. Based on a mathematical model, and using different simulation scenarios, we prove the following statements: (1) multiple source of independent aperiodic tasks can be considered similar to a single one; (2) with respect to the global deadline, the tasks migration between different regional centers is the appropriate solution when the number of estimated resources exceed a data center capacity; and (3) in a heterogeneous data center, we need a higher number of resources for the same request in order to respect the deadline constraints. We believe such results will benefit researchers and practitioners alike, who are interested in optimizing the resource management in data centers according to novel challenges coming from next-generation big data applications.

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“…∂ θ j . However, by (16) we know that β (t) = B(t) and is independent of the control parameters. Thus, we get…”

Section: Event-time Derivativesmentioning

confidence: 99%

“…In addition, a fundamental property of IPA in SFMs (as in DES) is that the derivative estimates obtained are independent of the probability laws of the stochastic rate processes and require minimal information from the observed sample path. This approach has proved useful in optimizing various performance metrics in serial networks [23], systems with feedback control mechanisms [27], scheduling problems [15], [16], and some multiclass models [5], [24].…”

Section: Introductionmentioning

confidence: 99%

Timeout control in distributed systems using perturbation analysis: Multiple communication links

Kebarighotbi

Cassandras

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Timeout control is a simple mechanism used when direct feedback is either impossible, unreliable, or too costly, as is often the case in distributed systems. Its effectiveness is determined by a timeout threshold parameter and our goal is to quantify the effect of this parameter on the system behavior. In this paper, we extend previous results to the case where there are N transmitting nodes making use of a common communication link bandwidth. After deriving the stochastic hybrid model for this problem, we apply Infinitesimal Perturbation Analysis to find the derivative estimates of aggregate average goodput of the system. We also derive the derivative estimate of the goodput of a transmitter with respect to its own timeout threshold which can be used for local and hence, distributed optimization.

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Optimal scheduling of parallel queues using stochastic flow models

Cited by 6 publications

References 17 publications

A $c/μ$-Rule for Service Resource Allocation in Group-Server Queues

A $c/μ$-Rule for Service Resource Allocation in Group-Server Queues

Deadline scheduling for aperiodic tasks in inter-Cloud environments: a new approach to resource management

Timeout control in distributed systems using perturbation analysis: Multiple communication links

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