This tool is composed of a set of MATLAB functions (i.e., .m files) to compute the R, G and U matrix of QBD type Markov chains as well as its steady state probability vector. It includes implementations of the following contemporary algorithms: Cyclic Reduction (QBD_CR.m), Functional Iterations (QBD_FI.m), Invariant Subspace Approach (QBD_IS.m), Logarithmic Reduction (QBD_LR.m), Newton Iterations (QBD_NI.m), etc. The steady state vector can be computed via the QBD_pi.m function. When using this tool, please refer to the paper Structured Markov chains solver: software tools by Bini, Meini, Steffe and Van Houdt (SMCtools workshop). Additional info on the tool is found in the paper and on these slides. New tool features added since the publication of the paper can be found in this document

References in zbMATH (referenced in 17 articles )

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  1. Finch, Steven; Latouche, Guy; Louchard, Guy; Meini, Beatrice: Traffic lights, clumping and QBDs (2021)
  2. Chen, Yanting; Bai, Xinwei; Boucherie, Richard J.; Goseling, Jasper: Performance measures for the two-node queue with finite buffers (2020)
  3. Horváth, Gábor; Telek, Miklós: Matrix-analytic solution of infinite, finite and level-dependent second-order fluid models (2017)
  4. Alfa, Attahiru S.: Applied discrete-time queues (2016)
  5. Casale, Giuliano; Sansottera, Andrea; Cremonesi, Paolo: Compact Markov-modulated models for multiclass trace fitting (2016)
  6. Horváth, Gábor: Analysis of generalized QBD queues with matrix-geometrically distributed batch arrivals and services (2016)
  7. Katehakis, Michael N.; Smit, Laurens C.; Spieksma, Floske M.: A comparative analysis of the successive lumping and the lattice path counting algorithms (2016)
  8. Maity, Arunava; Gupta, U. C.: A comparative numerical study of the spectral theory approach of Nishimura and the roots method based on the analysis of (\mathrmBDMMAP/\mathrmG/1) queue (2015)
  9. Boute, Robert N.; Disney, Stephen M.; Lambrecht, Marc R.; Van Houdt, Benny: Coordinating lead times and safety stocks under autocorrelated demand (2014)
  10. Vidalis, Michael; Vrisagotis, Vassilios; Varlas, George: Performance evaluation of a two-echelon supply chain with stochastic demand, lost sales, and Coxian-2 phase replenishment times (2014)
  11. Bini, Dario A.; Favati, Paola; Meini, Beatrice: A compressed cyclic reduction for QBD processes with low-rank upper and lower transitions (2013)
  12. Creemers, Stefan; Beliën, Jeroen; Lambrecht, Marc: The optimal allocation of server time slots over different classes of patients (2012)
  13. Telek, Miklós: Some structural properties of Markov and rational arrival processes (2011)
  14. Taylor, P. G.; van Houdt, B.: On the dual relationship between Markov chains of GI/M/1 and M/G/1 type (2010)
  15. Bini, Dario A.; Meini, Beatrice: The cyclic reduction algorithm: From Poisson equation to stochastic processes and beyond. In memoriam of Gene H. Golub (2009)
  16. Creemers, Stefan; Lambrecht, Marc: An advanced queueing model to analyze appointment-driven service systems (2009)
  17. Van Houdt, B.; Van Velthoven, J.; Blondia, C.: QBD Markov chains on binomial-like trees and its application to multilevel feedback queues (2008)