Multi-server threshold queues with hysteresis

Ibe, Oliver C.; Keilson, Julian

doi:10.1016/0166-5316(94)e0043-i

Cited by 52 publications

(41 citation statements)

References 10 publications

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“…Threshold-based service policies have been applied and proven to be optimal to queueing systems to control service rate and the number of servers taking a single queue as policies [11]. The queue is controlled by a sequence of forward thresholds and a sequence of reverse thresholds.…”

Section: Threshold Queuementioning

confidence: 99%

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Performance Evaluation of Gang Scheduling Policies with Migration in a Grid System

Ro¹,

Cao²

2010

International Journal of Contents

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Section: Threshold Queuementioning

confidence: 99%

“…Place N 1 and N 2 imply the capacity of each site. Transition GS 11 and GS 21 are migrations mechanism we adopt to transfer a job from one local queue to another queue to ensure all tasks of a gang will get execution simultaneously. This method will be explained in Section 3.2.…”

Section: Model Descriptionmentioning

confidence: 99%

Performance Evaluation of Gang Scheduling Policies with Migration in a Grid System

Ro¹,

Cao²

2010

International Journal of Contents

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“…In [11], see also Section 4.2, closed form expressions are obtained for the steady-state distributions for the M/M/c with c heterogeneous servers. Using Green's function, Ibe and Keilson [7] studied the M/M/c queue with homogeneous servers and the M/M/2 queue with heterogeneous servers. The M/M/c with heterogeneous servers is also studied in [12] where the steady-state probabilities are obtained using a stochastic complement analysis for uncoupling Markov Chains.…”

Section: Introductionmentioning

confidence: 99%

The PH/PH/1 Multi-threshold Queue

Baër

Boucherie

Ommeren

2014

Analytical and Stochastic Modeling Techniques and Applications

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We consider a P H/P H/1 queue in which a threshold policy determines the stage of the system. The arrival and service processes follow a Phase-Type (P H) distribution depending on the stage of the system. Each stage has both a lower and an upper threshold at which the stage of the system changes, and a new stage is chosen according to a prescribed distribution. This P H/P H/1 multi-threshold queue is modelled as a Level Dependent Quasi-Birth-and-Death process. An efficient algorithm is presented to obtain the stationary queue length vectors using Matrix Analytic methods.

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“…An approximate solution for solving a degenerate form of this problem (where all thresholds are set to zero) is presented in [7], [9]; an approximate solution for a system that employs (non-zero) thresholds is presented in [22] (but without hysteresis). In [8], the authors solve a multi-server thresholdbased queueing system with hysteresis, using the Green's function method [6], [10], [11]. In [17] we give a solution of several forms of the single class, multi-server threshold-based queueing system with hysteresis using stochastic complementation [18].…”

Section: Introductionmentioning

confidence: 99%

Multiclass Multiserver Threshold-Based Systems: A Study of Noninstantaneous Server Activation

Chou

Golubchik

Lui

2007

IEEE Trans. Parallel Distrib. Syst.

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In this paper, we consider performance evaluation of a system which shares K servers (or resources) among N heterogeneous classes of workloads, where server allocation and de-allocation for class i is dictated by a class specific threshold-based policy with hysteresis control. In particular, the server activation time for class i is non-instantaneous. There are many systems and applications where a multi-class threshold-based queueing system can be of great use. One important utility of using threshold-based approaches is in situations where applications may incur server usage costs. In these cases, one needs to consider not only the performance aspects but also the resulting cost/performance ratio. The motivation for using hysteresis control is to reduce the unnecessary cost of server setup (or activation) and server removal (or deactivation) whenever there are momentary fluctuations in workload. Moreover, servers in such systems and applications are often needed by multiple classes of workloads, and hence, it is desirable to find good approaches to sharing server resources among the different classes of workloads, preferably without statically partitioning the server pool among these classes. An important and distinguishing characteristic of our work is that we consider the modeling and analysis of a multi-class system with non-instantaneous server activation, which is of use in studying many important applications. The main contributions of this work are (a) in developing an efficient approximation method for solving such models, (b) in verifying the convergence of our iterative method, and (c) in evaluating the resulting accuracy of the technique for computing performance measures of interest, which can subsequently be used in making system design choices.

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Multi-server threshold queues with hysteresis

Cited by 52 publications

References 10 publications

Performance Evaluation of Gang Scheduling Policies with Migration in a Grid System

Performance Evaluation of Gang Scheduling Policies with Migration in a Grid System

The PH/PH/1 Multi-threshold Queue

Multiclass Multiserver Threshold-Based Systems: A Study of Noninstantaneous Server Activation

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