The G-queue with heterogeneous servers: Steady state solution and an application to performance evaluation

Chakka, Ram; Do, Tien Van

doi:10.1016/j.peva.2006.05.001

Cited by 37 publications

(31 citation statements)

References 24 publications

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“…This is also established in [24] in the context of manufacturing cells and systems, and it was confirmed in [30] using simulation results. In [5] a non-trivial application of a queue with heterogeneous servers to the performance evaluation of a wireless communication system is presented. The question of how to allocate the customers between heterogeneous servers in order to minimize the mean number of customers in the system has been studied by many authors.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Efrosinin¹,

Sztrik²

2016

Communications in Computer and Information Science

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Abstract. Heterogeneous servers which can differ in service speed and reliability are becoming more popular in the modelling of modern communication systems. For a two-server queueing system with one nonreliable server and constant retrial discipline we formulate an optimal allocation problem for minimizing a long-run average cost per unit of time. Using a Markov decision process formulation we prove a number of monotone properties for the increments of the dynamic-programming value function. Such properties imply the optimality of a two-level threshold control policy. This policy prescribes the usage of a less productive server if the number of customers in the queue becomes higher than a predefined level which depends on the state of a non-reliable more powerful server. We provide also a heuristic solution for the optimal threshold levels in explicit form as a function of system parameters.

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Section: Introductionmentioning

confidence: 99%

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Efrosinin¹,

Sztrik²

2016

Communications in Computer and Information Science

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“…where the coefficient matrices Q k can be obtained from system parameters, following the methodology in [6,8,14]. Therefore, when L is finite, the probability invariant vector v j is given by [5,6,39] …”

Section: The Qbd-m Processmentioning

confidence: 99%

“…Transitions in a QBD process are possible within the same level or between adjacent levels. It is observed that QBD processes create a useful framework for the performability analysis pertaining to many problems occurring in telecommunications and computer networks [4,8,18,20,23,36,40,42,45,56,57].…”

Section: Introductionmentioning

confidence: 99%

“…The usefulness and applicability of these models has been validated by measurements for example in [8,23].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, we have proposed two new queuing models, the MM K k=1 CP P k /GE/c/L G-queue [10] with homogenous servers (the Sigma queue) and with heterogeneous servers (the HetSigma queue [8]). We have also developed some transformations which, when applied to the steady state balance equations, result in QBD-M type computable form.…”

Section: Introductionmentioning

confidence: 99%

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Generalized QBD Processes, Spectral Expansion and Performance Modeling Applications

Chakka²

2011

Network Performance Engineering

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Abstract. This paper suggests new queuing models, in the Markovian framework, which can tackle the presence of burstiness in the traffic and autocorrelations among the inter-arrival times of packets in the performance evaluation of next generation networks. These models are essentially based on certain generalizations of the Quasi Birth-Death (QBD) processes. Efficient steady state solution of these new queuing models, along with some illustrative applications, is presented. The proposed models and their further evolutions have the potential to be useful tools for the performance evaluation of modern telecommunication networks.

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A state-dependent Markov-modulated mechanism for generating events and stochastic models

Artalejo

Gómez‐Corral

2009

Math. Meth. Appl. Sci.

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In this paper, we introduce a versatile block-structured state-dependent event (BSDE) approach that provides a methodological tool to construct non-homogeneous Markov-modulated stochastic models. Alternatively, the BSDE approach can be used to construct even a part (e.g. the arrival process) of the model. To illustrate the usefulness of the BSDE approach, several arrival patterns as well as queueing and epidemic models are considered. In particular, we deal with a state-dependent quasi-birth-and-death process that gives a constructive generalization of the scalar birth-and-death process and the homogeneous quasi-birth-and-death process.

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The G-queue with heterogeneous servers: Steady state solution and an application to performance evaluation

Cited by 37 publications

References 24 publications

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Generalized QBD Processes, Spectral Expansion and Performance Modeling Applications

A state-dependent Markov-modulated mechanism for generating events and stochastic models

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