Bayesian Analysis of a Queueing System with a Long-Tailed Arrival Process

DOI10.1080/03610910701753861zbMath1160.62025OpenAlexW2102989554MaRDI QIDQ3625295

Michael P. Wiper, Pepa Ramírez, Rosa Elvira Lillo

Publication date: 12 May 2009

Published in: Communications in Statistics - Simulation and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610910701753861

zbMATH Keywords

queueing systemsheavy-tailed variables

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Bayesian inference (62F15) Communication networks in operations research (90B18) Network design and communication in computer systems (68M10) Numerical analysis or methods applied to Markov chains (65C40) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (10)

Bayesian inference for double Pareto lognormal queues ⋮ M/PH/1 queueing model with re-servicing ⋮ Fitting procedure for the two-state batch Markov modulated Poisson process ⋮ Using mixture of gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service ⋮ Best Unbiased Estimation and CAN Property in the Stable M/M/1 Queue ⋮ ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback ⋮ ML and UMVU estimation in the M/D/1 queuing system ⋮ Estimation of Measures in M/M/1 Queue ⋮ Estimation of the Parameters of a Two-phase Tandem Queue with a Second Optional Service ⋮ Spare Reliability for Capacitated Computer Networks Under Tolerable Error Rate and Latency Considerations

Cites Work

• Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
• Bayesian analysis of \(Er/M/1\) and \(Er/M/c\) queues
• Bayesian prediction in \(M/M/1\) queues
• Bayesian analysis of mixture models with an unknown number of components\,--\,an alternative to reversible jump methods.
• Internet-Type Queues with Power-Tailed Interarrival Times and Computational Methods for Their Analysis
• An Algorithm to Compute the Waiting Time Distribution for the M/G/1 Queue
• The Double Pareto-Lognormal Distribution—A New Parametric Model for Size Distributions
• Bayesian Estimation and Prediction for Pareto Data
• Computing Laplace Transforms for Numerical Inversion Via Continued Fractions
• The Importance of Power-Tail Distributions for Modeling Queueing Systems
• Dynamic Models for File Sizes and Double Pareto Distributions

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