A comparative numerical study of the spectral theory approach of Nishimura and the roots method based on the analysis of \(\mathrm{BDMMAP}/\mathrm{G}/1\) queue

DOI10.1155/2015/958730zbMath1351.60118OpenAlexW2001720751WikidataQ59111210 ScholiaQ59111210MaRDI QIDQ274838

Arunava Maity, U. C. Gupta

Publication date: 25 April 2016

Published in: International Journal of Stochastic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2015/958730

zbMATH Keywords

numerical methodsbirth-death modulated Markovian arrival processinfinite-buffer queueing system

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Applications of branching processes (60J85) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (5)

The queue GeoX/G/1/N+1 revisited ⋮ Analytically simple and computationally efficient results for the \(GI^X/ Geo /c\) queues ⋮ Queueing systems with correlated arrival flows and their applications to modeling telecommunication networks ⋮ A new and pragmatic approach to the \(GI^X /Geo/c/N\) queues using roots ⋮ Analytically elegant and computationally efficient results in terms of roots for the \(\mathrm{GI}^X/\mathrm{M}/c\) queueing system

Uses Software

• na12
• na10
• SMCSolver

Cites Work

• Unnamed Item
• A simple and complete computational analysis of MAP/R/1 queue using roots
• Numerical computation of polynomial zeros by means of Aberth's method
• Improved cyclic reduction for solving queueing problems
• A spectral approach to compute the mean performance measures of the queue with low-order BMAP input
• A numerically efficient method for the \(MAP/D/1/K\) queue via rational approximations
• A simple eigenvalue method for low-order D-BMAP/G/1 queues
• Computing the Distribution for the Number of Renewals with Bulk Arrivals
• New results on the single server queue with a batch markovian arrival process
• Nonlinear Matrix Equations in Applied Probability—Solution Techniques and Open Problems
• A stable recursion for the steady state vector in markov chains of m/g/1 type
• A versatile Markovian point process
• AMAP/G/1 Queue with an Underlying Birth–Death Process
• MODELING BURST TRAFFIC USING A MAP WITH A TREE STRUCTURE
• On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems
• Spectral analysis of M/G/1 and G/M/1 type Markov chains

This page was built for publication: A comparative numerical study of the spectral theory approach of Nishimura and the roots method based on the analysis of \(\mathrm{BDMMAP}/\mathrm{G}/1\) queue