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Quality Technology & Quantitative Management Volume 7, 2010 - Issue 4
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Original Articles

Approximation of Performance Measures in an M/G/1 Queue with Breakdowns

Karim AbbasL.A.M.O.S., Laboratory of Modelization and Optimization of Systems, University of Bejaia, AlgeriaView further author information
&
Djamil AïssaniL.A.M.O.S., Laboratory of Modelization and Optimization of Systems, University of Bejaia, AlgeriaView further author information
Pages 353-363 | Received 01 Jan 2009, Accepted 01 May 2009, Published online: 09 Feb 2016

References

  • Abate, J., Choudhury, G. L. and Whitt, W. (2000). An introduction to numerical transform inversion and its application to probability models. In: Computational Probability (Edited by W. K. Grassmann), 257–323. Kluwer Academic Publishers.
  • Aissani, D. and Kartashov, N. V. (1983). Ergodicity and stability of Markov chains with respect to operator topologies in space of transition kernels. Doklady Akad. Nauk AN Ukr. SSR, 11 (series A), 3–5.
  • Anisimov, V. V. (1988). Estimates for the deviations of the transition characteristics of non-homogeneous Markov processes. Ukrainian Mathematical Journal, 40, 588–592.
  • Bouallouche-Medjkoune, L. and Aissani, D. (2006).Performance analysis approximation in a queueing system of type M/G/1. Mathematical Methods of Operations Research, 63(2), 341–356.
  • Cho, G. E. and Meyer, C. D. (2001). Comparison of perturbation bounds for the stationary distribution of a Markov chain. Linear Algebra and its Applications, 335, 137–150.
  • Heidergott, B. and Hordijk, A. (2003). Taylor series expansions for stationary Markov chains. Advances in Applied Probability, 23(4), 1046–1070.
  • Heidergott, B., Hordijk, A. and Leder, N. (2010). Series expansions for continuous-time Markov chains. Operations Research. In Press.
  • Heidergott, B., Hordijk, A. and van Uitert, M. (2007). Series expansions for finite-state Markov chains. Probability in Engineering and Informational Sciences, 21, 381–400.
  • Kartashov, N. V. (1996). Strong Stable Markov Chains. VSP, Utrecht, The Netherlands.
  • Kirkland, S. (2002). On a question concerning condition numbers for Markov chain. SIAM Journal on Matrix Analysis and Applications, 23, 1109–1119.
  • Mitrophanov, A. Y. (2005). Sensitivity and convergence of uniformly ergodic Markov chains. Journal of Applied Probability, 42, 1003–1014.
  • Neumann, M. and Xu, J. (2003). Improved bounds for a condition number of Markov chains. Linear Algebra and its Applications, 386, 225–241.
  • Rachev, S. T. (1989). The problem of stability in queueing theory. Queueing Systems, 4, 287–318.
  • Schweitzer, E. (1968). Perturbation theory and finite Markov chains. Journal of Applied Probability, 5, 401–413.

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