An M/M/s Queue With Servers’ Vacations

Levy, Yonatan; Yechiali, Uri

doi:10.1080/03155986.1976.11731635

Cited by 89 publications

(66 citation statements)

References 5 publications

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“…Only the studies [21], [25], [27], [30], considering single-queue systems, and [12], [15], [16], focusing on a limited class of models with coupled servers, present any exact distributional results. To the best of the authors' knowledge, there are no exact results known for models with independent servers, apart from some mean-value results for global performance measures like cycle times and intervisit times.…”

Section: Applicationsmentioning

confidence: 99%

“…Levy & Yechiali [25] and Kao & Narayanan [21] study the joint distribution of the queue length and the number of busy servers for a Markovian multiple-server queue, where the servers individually go on vacation when there are no waiting customers left. Mitrany & Avi-Itzhak [27] and Neuts & Lucantoni [30] analyze the joint distribution of the queue length and the number of busy servers for a Markovian multiple-server queue, where servers break down at exponential intervals and then get repaired.…”

Section: Applicationsmentioning

confidence: 99%

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Analysis of multiple-server polling systems by means of the power-series algorithm

Mei¹,

Borst²

1997

Communications in Statistics. Stochastic Models

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We consider a polling model with multiple servers, each of which visits the queues according to its own service order table. In general, such a model is not tractable by means of analytical techniques. In this paper, we show how the model can be analyzed by the power-series algorithm (PSA), a tool for the numerical evaluation and optimization of the performance of a broad class of multi-queue models. Various numerical experiments with the PSA are performed, providing new insights into the behavior of multiple-server polling systems.

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Section: Applicationsmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Analysis of multiple-server polling systems by means of the power-series algorithm

Mei¹,

Borst²

1997

Communications in Statistics. Stochastic Models

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“…There are three types of transitions in (H, Z). First, (h, Z) + (h l t,ej,Z -ej>, Zj = 1, (23) representing a departure of Sj from Q,(hj), which does not result from an instantaneous passage; here ej represents the jth nr-dimensional unit vector; hj + 1 is to be understood as (hj mod n) + 1.…”

Section: Approximating the Probabilities Qimentioning

confidence: 99%

Waiting-time approximations for multiple-server polling systems

Borst¹,

Mei

1998

Performance Evaluation

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We consider multiple-server polling systems, in which each of the servers visits the queues according to its own cyclic schedule. Such systems appear to completely defy the derivation of exact waiting-time results, which motivates the search for accurate approximations. In the present paper, we derive waiting-time approximations for asymmetric systems with the exhaustive and gated service discipline. The approximations are tested for a wide range of parameter combinations. 0 1998 Elsevier Science B.V.

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“…Mitrany and Avi-Izhak [11] and Neuts and Lucantoni [13] have studied the M/M/s queueing system with server breakdowns and repairs. In paper of Levi and Yechiali [9] the queue M/M/s with servers' vacations was analyzed. A recent paper of Efrosinin et al [3] deals with an stationary analysis performed on the busy period for the multi-server Markovian queueing system with simultaneous failures of servers.…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis of a Two-Server Heterogeneous Unreliable Queueing System with a Threshold Control Policy

Efrosinin

Sztrik

Farkhadov

et al. 2017

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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Abstract. Heterogeneous servers which can differ in service speed and reliability are getting more popular in modeling of modern communication systems. For a two-server queueing system with unreliable servers the allocation of customers between the servers is performed via a threshold control policy which prescribes to use the fastest server whenever it is free and the slower one only if the number of waiting customers exceeds some threshold level depending on the state of faster server. The main task of the paper consists in reliability analysis of the proposed system including evaluation of the stationary availability and reliability function. The effects of different parameters on introduced reliability characteristics are analyzed numerically.

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An M/M/s Queue With Servers’ Vacations

Cited by 89 publications

References 5 publications

Analysis of multiple-server polling systems by means of the power-series algorithm

Analysis of multiple-server polling systems by means of the power-series algorithm

Waiting-time approximations for multiple-server polling systems

Reliability Analysis of a Two-Server Heterogeneous Unreliable Queueing System with a Threshold Control Policy

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