Spectral Analysis and Eigenvalue Decomposition of Quasi-Birth-Death  Processes in Priority Queueing Systems

Hambeer Singh

Spectral Analysis and Eigenvalue Decomposition of Quasi-Birth-Death Processes in Priority Queueing Systems

Authors

Hambeer Singh

Keywords:

Eigenvalue Decomposition, Markov Chains, Matrix-Analytic Methods, Priority Queueing, Quasi-Birth-Death Processes

Abstract

The present study offers an extensive spectral analysis of Quasi-Birth-Death (QBD)processes to priority-based queueing systems. In particular, we analyze a single-server, twoclass preemptive-resume priority queue through a structured continuous-time Markov chainframework. The system is mathematically represented by a block-tridiagonal infinitesimalgenerator matrix capturing arrivals, departures, and intra-level transitions. The central approach is solving the matrix quadratic equation

References

Bean, N. G., Bright, L., Latouche, G., Pearce, C. E. M., Pollett, P. K., & Taylor, P. G. (1997). The quasi-stationary behavior of quasi-birth-and-death processes. Annals of Applied Probability. https://doi.org/10.1214/aoap/1034625256

Downloads

Published

2024-08-25

How to Cite

Hambeer Singh. (2024). Spectral Analysis and Eigenvalue Decomposition of Quasi-Birth-Death Processes in Priority Queueing Systems. Journal of Computational Analysis and Applications (JoCAAA), 33(08), 7473–7504. Retrieved from https://eudoxuspress.com/index.php/pub/article/view/4718