Facilitating load-dependent queueing analysis through factorization

Casale, Giuliano; Harrison, Peter G.; Ong, Wai Hong

doi:10.1016/j.peva.2021.102241

Cited by 3 publications

(8 citation statements)

References 69 publications

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“…( 29)], which obtains a closed-form solution for single-class LLD models with single-server and multi-server stations. All such results are generalized by the following expression obtained in [4], which applies to arbitrary LLD models.…”

Section: Single Class Lld Modelsmentioning

confidence: 99%

“…This is made possible by a finite difference relation connecting the single class normalizing constant h θ (N ) with its multiclass counterpart H θ (N ). In particular, [4] derives novel integral expressions, such as formulations on the unit simplex and novel expressions leveraging the Norlund-Rice integral form for finite differences. Notably, the latter requires one to consider integrands that are themselves singleclass normalizing constants, but with complex service demands.…”

Section: Single Class Lld Modelsmentioning

confidence: 99%

“…Notably, the latter requires one to consider integrands that are themselves singleclass normalizing constants, but with complex service demands. As such, specialized results are obtained in [4] to evaluate normalizing constants with complex demands as well as their complex derivatives.…”

Section: Single Class Lld Modelsmentioning

confidence: 99%

“…In this abstract, we report the key results derived in [4], which revisits the problem. The paper determines in particular novel exact and approximate solutions for product-form…”

Section: Introductionmentioning

confidence: 96%

“…LLD closed queueing networks, both in the single-class and multiclass cases. For a full derivation of the results, as well as several additional contributions, we point the reader to [4].…”

Section: Introductionmentioning

confidence: 99%

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Facilitating Load-Dependent Queueing Analysis Through Factorization (Extended Abstract)

Casale

Harrison

Ong

2022

SIGMETRICS Perform. Eval. Rev.

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We construct novel exact and approximate solutions for meanvalue analysis and probabilistic evaluation of closed queueing network models with limited load-dependent (LLD) nodes. In this setting, load-dependent functions are assumed to become constant after a finite queue-length threshold. For single-class models, we provide an explicit formula for the normalizing constant that applies to models with arbitrary LLD functions, whilst retaining constant complexity with respect to the total population size. From this result, we then derive corresponding closed-form solutions for the multiclass case and show that these yield a novel mean value analysis approach for LLD models. Significantly, this allows us to determine exactly the correction factor between a load-independent solution and a limited load-dependent one, enabling the reuse of state-of-the-art methods for loadindependent models in the analysis of load-dependent networks.

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Section: Single Class Lld Modelsmentioning

confidence: 99%

Section: Single Class Lld Modelsmentioning

confidence: 99%

Section: Single Class Lld Modelsmentioning

confidence: 99%

“…In this abstract, we report the key results derived in [4], which revisits the problem. The paper determines in particular novel exact and approximate solutions for product-form…”

Section: Introductionmentioning

confidence: 96%

“…LLD closed queueing networks, both in the single-class and multiclass cases. For a full derivation of the results, as well as several additional contributions, we point the reader to [4].…”

Section: Introductionmentioning

confidence: 99%

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Facilitating Load-Dependent Queueing Analysis Through Factorization (Extended Abstract)

Casale

Harrison

Ong

2022

SIGMETRICS Perform. Eval. Rev.

Self Cite

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LN: A Meta-solver for Layered Queueing Network Analysis

Casale

Yicheng²,

Niu³

et al. 2022

Quantitative Evaluation of Systems

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LN: A Flexible Algorithmic Framework for Layered Queueing Network Analysis

Casale,

Gao,

Niu

et al. 2024

ACM Trans. Model. Comput. Simul.

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Layered queueing networks (LQNs) are an extension of ordinary queueing networks useful to model simultaneous resource possession and stochastic call graphs in distributed systems. Existing computational algorithms for LQNs have primarily focused on mean-value analysis. However, other solution paradigms, such as normalizing constant analysis and mean-field approximation, can improve the computation of LQN mean and transient performance metrics, state probabilities, and response time distributions. Motivated by this observation, we propose the first LQN meta-solver, called LN, that allows for the dynamic selection of the performance analysis paradigm to be iteratively applied to the submodels arising from layer decomposition. We report experiments where this added flexibility helps us to reduce the LQN solution errors. We also demonstrate that the meta-solver approach eases the integration of LQNs with other formalisms, such as caching models, enabling the analysis of more general classes of layered stochastic networks. Additionally, to support the accurate evaluation of the LQN submodels, we develop novel algorithms for homogeneous queueing networks consisting of an infinite server node and a set of identical queueing stations. In particular, we propose an exact method of moment algorithms, integration techniques for normalizing constants, and a fast non-iterative mean-value analysis technique.

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Facilitating load-dependent queueing analysis through factorization

Cited by 3 publications

References 69 publications

Facilitating Load-Dependent Queueing Analysis Through Factorization (Extended Abstract)

Facilitating Load-Dependent Queueing Analysis Through Factorization (Extended Abstract)

LN: A Meta-solver for Layered Queueing Network Analysis

LN: A Flexible Algorithmic Framework for Layered Queueing Network Analysis

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