Cite

Almasi, B., Roszik, J. and Sztrik, J. (2005). Homogeneous finite-source retrial queues with server subject to breakdowns and repairs, Mathematical and Computer Modelling42(5): 673–682.10.1016/j.mcm.2004.02.046Search in Google Scholar

Brugno, A., D’Apice, C., Dudin, A. and Manzo, R. (2017). Analysis of an MAP/PH/1 queue with flexible group service, International Journal of Applied Mathematics and Computer Science27(1): 119–131, DOI: 10.1515/amcs-2017-0009.10.1515/amcs-2017-0009Search in Google Scholar

Crescenzo, A.D., Giorno, V., Kumar, B.K. and Nobile, A. (2018). A time-non-homogeneous double-ended queue with failures and repairs and its continuous approximation, Mathematics6(5): 81.10.3390/math6050081Search in Google Scholar

Doorn, E. V., Zeifman, A. and Panfilova, T. (2010). Bounds and asymptotics for the rate of convergence of birth-death processes, Theory of Probability and Its Applications54(1): 97–113.10.1137/S0040585X97984097Search in Google Scholar

Giorno, V., Nobile, A.G. and Spina, S. (2014). On some time non-homogeneous queueing systems with catastrophes, Applied Mathematics and Computation245: 220–234.10.1016/j.amc.2014.07.076Search in Google Scholar

Granovsky, B. and Zeifman, A. (2004). Nonstationary queues: Estimation of the rate of convergence, Queueing Systems46(3–4): 363–388.10.1023/B:QUES.0000027991.19758.b4Search in Google Scholar

Kalashnikov, V. (1971). Analysis of ergodicity of queueing systems by Lyapunov’s direct method, Automation and Remote Control32(4): 559–566.Search in Google Scholar

Kartashov, N. (1985). Criteria for uniform ergodicity and strong stability of Markov chains with a common phase space, Theory of Probability and Mathematical Statistics30: 71–89.10.1137/1130034Search in Google Scholar

Li, H., Zhao, Q. and Yang, Z. (2007). Reliability modeling of fault tolerant control systems, International Journal of Applied Mathematics and Computer Science17(4): 491–504, DOI: 10.2478/v10006-007-0041-0.10.2478/v10006-007-0041-0Search in Google Scholar

Li, J. and Zhang, L. (2017). MX/M/c queue with catastrophes and state-dependent control at idle time, Frontiers of Mathematics in China12(6): 1427–1439.10.1007/s11464-017-0674-8Search in Google Scholar

Liu, Y. (2012). Perturbation bounds for the stationary distributions of Markov chains, SIAM Journal on Matrix Analysis and Applications33(4): 1057–1074.10.1137/110838753Search in Google Scholar

Malyshev, V. and Menshikov, M. (1982). Ergodicity, continuity and analyticity of countable Markov chains, Transactions of the Moscow Mathematical Society1(148).Search in Google Scholar

Meyn, S. and Tweedie, R. (1993). Stability of Markovian processes. III: Foster–Lyapunov criteria for continuous time processes, Advances in Applied Probability25(3):518–548.Search in Google Scholar

Meyn, S. and Tweedie, R. (2012). Markov Chains and Stochastic Stability, Springer Science & Business Media, Berlin/Heidelberg/New York, NY.Search in Google Scholar

Mitrophanov, A. (2003). Stability and exponential convergence of continuous-time Markov chains, Journal of Applied Probability40(4): 970–979.10.1239/jap/1067436094Search in Google Scholar

Mitrophanov, A. (2004). The spectral gap and perturbation bounds for reversible continuous-time Markov chains, Journal of Applied Probability41(4): 1219–1222.10.1239/jap/1101840568Search in Google Scholar

Mitrophanov, A. (2018). Connection between the rate of convergence to stationarity and stability to perturbations for stochastic and deterministic systems, Proceedings of the 38th International Conference ‘Dynamics Days Europe’, DDE 2018, Loughborough, UK, pp. 3–7.Search in Google Scholar

Moiseev, A. and Nazarov, A. (2016). Queueing network MAP − (GI/∞)K with high-rate arrivals, European Journal of Operational Research254(1): 161–168.Search in Google Scholar

Nelson, R., Towsley, D. and Tantawi, A. (1988). Performance analysis of parallel processing systems, IEEE Transactions on Software Engineering14(4): 532–540.10.1109/32.4676Search in Google Scholar

Olwal, T.O., Djouani, K., Kogeda, O.P. and van Wyk, B.J. (2012). Joint queue-perturbed and weakly coupled power control for wireless backbone networks, International Journal of Applied Mathematics and Computer Science22(3): 749–764, DOI: 10.2478/v10006-012-0056-z.10.2478/v10006-012-0056-zSearch in Google Scholar

Rudolf, D. and Schweizer, N. (2018). Perturbation theory for Markov chains via Wasserstein distance, Bernoulli24(4A): 2610–2639.10.3150/17-BEJ938Search in Google Scholar

Satin, Y., Zeifman, A. and Kryukova, A. (2019). On the rate of convergence and limiting characteristics for a nonstationary queueing model, Mathematics7(678): 1–11.10.3390/math7080678Search in Google Scholar

Schwarz, J., Selinka, G. and Stolletz, R. (2016). Performance analysis of time-dependent queueing systems: Survey and classification, Omega63: 170–189.10.1016/j.omega.2015.10.013Search in Google Scholar

Trejo, K.K., Clempner, J.B. and Poznyak, A.S. (2019). Proximal constrained optimization approach with time penalization, Engineering Optimization51(7): 1207–1228.10.1080/0305215X.2018.1519072Search in Google Scholar

Vvedenskaya, N., Logachov, A., Suhov, Y. and Yambartsev, A. (2018). A local large deviation principle for inhomogeneous birth-death processes, Problems of Information Transmission54(3): 263–280.10.1134/S0032946018030067Search in Google Scholar

Wieczorek, R. (2010). Markov chain model of phytoplankton dynamics, International Journal of Applied Mathematics and Computer Science20(4): 763–771, DOI: 10.2478/v10006-010-0058-7.10.2478/v10006-010-0058-7Search in Google Scholar

Zeifman, A. (1985). Stability for continuous-time nonhomogeneous Markov chains, in V.V. Kalashnikov and V.M. Zolotarev (Eds), Stability Problems for Stochastic Models, Springer, Berlin/Heidelberg, pp. 401–414.10.1007/BFb0074830Search in Google Scholar

Zeifman, A. (1989). Properties of a system with losses in the case of variable rates, Automation and Remote Control50(1): 82–87.Search in Google Scholar

Zeifman, A., Kiseleva, K., Satin, Y., Kryukova, A. and Korolev, V. (2018a). On a method of bounding the rate of convergence for finite Markovian queues, 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Moscow, Russia, pp. 1–5.10.1109/ICUMT.2018.8631216Search in Google Scholar

Zeifman, A. and Korolev, V. (2014). On perturbation bounds for continuous-time Markov chains, Statistics & Probability Letters88: 66–72.10.1016/j.spl.2014.01.031Search in Google Scholar

Zeifman, A., Korolev, V., Satin, Y. and Kiseleva, K. (2018b). Lower bounds for the rate of convergence for continuous-time inhomogeneous Markov chains with a finite state space, Statistics & Probability Letters137: 84–90.10.1016/j.spl.2018.01.001Search in Google Scholar

Zeifman, A., Korolev, V., Satin, Y., Korotysheva, A. and Bening, V. (2014a). Perturbation bounds and truncations for a class of Markovian queues, Queueing Systems76(2): 205–221.10.1007/s11134-013-9388-0Search in Google Scholar

Zeifman, A., Leorato, S., Orsingher, E., Satin, Y. and Shilova, G. (2006). Some universal limits for nonhomogeneous birth and death processes, Queueing Systems52(2): 139–151.10.1007/s11134-006-4353-9Search in Google Scholar

Zeifman, A., Razumchik, R., Satin, Y., Kiseleva, K., Korotysheva, K. and Korolev, V. (2018c). Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services, International Journal of Applied Mathematics and Computer Science28(1): 141–154, DOI: 10.2478/amcs-2018-0011.10.2478/amcs-2018-0011Search in Google Scholar

Zeifman, A., Satin, Y., Korolev, V. and Shorgin, S. (2014b). On truncations for weakly ergodic inhomogeneous birth and death processes, International Journal of Applied Mathematics and Computer Science24(3): 503–518, DOI: 10.2478/amcs-2014-0037.10.2478/amcs-2014-0037Search in Google Scholar

Zeifman, A., Satin, Y. and Kryukova, A. (2019). Applications of differential inequalities to bounding the rate of convergence for continuous-time Markov chains, AIP Conference Proceedings2116(090009): 1–5.10.1063/1.5114074Search in Google Scholar

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