EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 / No 4 (July-August 2021) RAIRO-Oper. Res., 55 4 (2021) 2223-2240 References
Open Access
Issue
RAIRO-Oper. Res.
Volume 55, Number 4, July-August 2021
Page(s) 2223 - 2240
DOI https://doi.org/10.1051/ro/2021101
Published online 29 July 2021
  • S.I. Ammar, Transient behavior of a two-processor heterogeneous system with catastrophes, server failures and repairs. Appl. Math. Model. 38 (2014) 2224–2234. [CrossRef] [Google Scholar]
  • S.I. Ammar, A. Zeifman, Y. Satin, K. Kiseleva and V. Korolev, On limiting characteristics for a non-stationary two-processor heterogeneous system with catastrophes, server failures and repairs. J. Ind. Manage. Optim. 17 (2021) 1057. [Google Scholar]
  • J.L. Daleckii and M.G. Krein, Stability of Solutions of Differential Equations in Banach Space (No. 43). American Mathematical Soc. (2002). [CrossRef] [Google Scholar]
  • A. Di Crescenzo, V. Giorno, B.K. Kumar and A.G. Nobile, A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation. Methodol. Comput. Appl. Probab. 14 (2012) 937–954. [CrossRef] [Google Scholar]
  • A. Di Crescenzo, V. Giorno, B. Krishna Kumar and A. Nobile, A time-non-homogeneous double-ended queue with failures and repairs and its continuous approximation. Mathematics 6 (2018) 1–23. [Google Scholar]
  • B. Heidergott, H. Leahu, A. Löpker and G. Pflug, Perturbation analysis of inhomogeneous finite Markov chains. Adv. Appl. Probab. 48 (2016) 255–273. [CrossRef] [Google Scholar]
  • C. Knessl and C. Tier, Applications of singular perturbation methods in queueing. Advances in Queueing Theory, Methods, and Open Problems. Probability and Stochastics Series (1995) 311–336. [Google Scholar]
  • C. Knessl and Y.P. Yang, An exact solution for an M(t)/M(t)/1 queue with time-dependent arrivals and service. Queue. Syst. 40 (2002) 233–245. [CrossRef] [Google Scholar]
  • B.K. Kumar, A. Krishnamoorthy, S.P. Madheswari and S.S. Basha, Transient analysis of a single server queue with catastrophes, failures and repairs. Queue. Syst. 56 (2007) 133–141. [CrossRef] [Google Scholar]
  • A. Mandelbaum and W.A. Massey, Strong approximations for time-dependent queues. Math. Oper. Res. 20 (1995) 33–64. [CrossRef] [Google Scholar]
  • H. Masuyama and T. Takine, Algorithmic computation of the time-dependent solution of structured Markov chains and its application to queues. Stochastic Models 21 (2005) 885–912. [CrossRef] [Google Scholar]
  • A.Y. Mitrophanov, Stability and exponential convergence of continuous-time Markov chains. J. Appl. Probab. 40 (2003) 970–979. [CrossRef] [Google Scholar]
  • M.I.G.S. Sampath and J. Liu, Transient analysis of an M/M/1 queue with reneging, catastrophes, server failures and repairs. Bull. Iran. Math. Soc. 44 (2018) 585–603. [CrossRef] [Google Scholar]
  • A.M. Tarabia, Transient and steady-state analysis of an M/M/1 queue with balking, catastrophes, server failures and repairs. J. Ind. Manage. Optim. 7 (2011) 811–823. [Google Scholar]
  • A. Zeifman and A. Korotysheva, Perturbation bounds for Mt/Mt/N queue with catastrophes. Stochastic Models 28 (2012) 49–62. [CrossRef] [Google Scholar]
  • A. Zeifman, Y. Satin, V. Korolev and S. Shorgin, On truncations for weakly ergodic inhomogeneous birth and death processes. Int. J. Appl. Math. Comp. Sci. 24 (2014) 503–518. [CrossRef] [Google Scholar]
  • A. Zeifman, Y. Satin, A. Korotysheva, V. Korolev, S. Shorgin and R. Razumchik, Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to origin. Int. J. Appl. Math. Comput. Sci. 25 (2015) 503–518. [CrossRef] [Google Scholar]
  • A.I. Zeifman, V.Y. Korolev, A.V. Korotysheva, Y.A. Satin, Bounds for Inhomogeneous Markovian Queueing Systems with Particularities in Zero. IPI FRC CSC RAS. Moscow (2016). [Google Scholar]
  • A.I. Zeifman, A.V. Korotysheva, V.Y. Korolev and Y.A. Satin, Truncation bounds for approximations of inhomogeneous continuous-time Markov chains. Theory Probab. App. 61 (2017) 513–520. [CrossRef] [Google Scholar]
  • A. Zeifman, Y. Satin, K. Kiseleva, V. Korolev and T. Panfilova, On limiting characteristics for a non-stationary two-processor heterogeneous system. Appl. Math. Comput. 351 (2019) 48–65. [Google Scholar]
  • A. Zeifman, V. Korolev and Y. Satin, Two approaches to the construction of perturbation bounds for continuous-time Markov chains. Mathematics 8 (2020) 253. [CrossRef] [Google Scholar]
  • A. Zeifman, Y. Satin, A. Kryukova, R. Razumchik, K. Kiseleva and G. Shilova, On the three methods for bounding the rate of convergence for some continuous-time Markov chains. Int. J. Appl. Math. Comput. Sci. 30 (2020) 251–266. [Google Scholar]
  • A. Zeifman, Y. Satin, I. Kovalev, R. Razumchik and V. Korolev, Facilitating numerical solutions of inhomogeneous continuous time markov chains using ergodicity bounds obtained with logarithmic norm method. Mathematics 9 (2021) 42. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.