birth-death process,
nonstationary continuous-time Markov chains,
bounds on the rate of convergence and stability,
approximations.
UDC:
519.217, 517.937, 519.283, 616-036.22
Subject:
Linear differential equations and continuous-time Markov chains and models.
Main publications:
Zeifman A.I., “Some Estimates of the Rate of Convergence for Birth and Death Processes”, Journal of Applied Probability, 28 (1991), 268–277
Zeifman A.I., “Upper and Lower Bounds on the Rate of Convergence for Nonhomogeneous Birth and Death Processes”, Stochastic Processes and Their Applications, 59 (1995), 157–173
Granovsky B., Zeifman A., “Nonstationary Queues: Estimation of the rate of convergence”, Queueing Systems, 46 (2004), 363–388
Zeifman A., Leorato S., Orsingher E., Satin Ya., Shilova G., “Some universal limits for nonhomogeneous birth and death processes”, Queueing Systems, 52 (2006), 139–151
Zeifman A.I., Bening V.E., Sokolov I.A., Markovskie tsepi i modeli s nepreryvnym vremenem, ELEKS-KM, Moskva, 2008
I. A. Usov, Y. A. Satin, A. I. Zeifman, “On the rate of convergence and limiting characteristics for one quasi-birth–death process”, Inform. Primen., 17:3 (2023), 49–57
2022
2.
A. I. Zeifman, V. Yu. Korolev, R. V. Razumchik, Ya. A. Satin, I. A. Kovalev, “Limiting characteristics of queueing systems with vanishing perturbations”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 83–88; Dokl. Math., 106:2 (2022), 375–379
I. A. Kovalev, Y. A. Satin, A. V. Sinitcina, A. I. Zeifman, “On an approach for estimating the rate of convergence for nonstationary Markov models of queueing systems”, Inform. Primen., 16:3 (2022), 75–82
I. A. Kovalev, Y. A. Satin, A. I. Zeifman, “Convergence rate and stability estimates for a class of nonstationary Markov models of queues with impatient customers”, Sistemy i Sredstva Inform., 32:4 (2022), 21–31
6.
I. A. Usov, I. A. Kovalev, A. I. Zeifman, “Truncation bounds for inhomogeneous Markov chains with continuous time and catastrophes”, Sistemy i Sredstva Inform., 32:1 (2022), 34–45
2021
7.
A. I. Zeifman, Ya. A. Satin, I. A. Kovalev, “On one nonstationary service model with catastrophes and heavy tails”, Inform. Primen., 15:2 (2021), 20–25
Ya. A. Satin, A. I. Zeifman, G. N. Shilova, “On approaches to constructing limiting regimes for some queuing models”, Inform. Primen., 14:2 (2020), 3–9
2019
9.
A. I. Zeifman, Ya. A. Satin, K. M. Kiseleva, “On the bounds of the rate of convergence for some queueing models with incompletely defined intensities”, Inform. Primen., 13:3 (2019), 14–19
2018
10.
V. Yu. Korolev, A. K. Gorshenin, A. I. Zeifman, “New mixture representations of the generalized Mittag-Leffler distribution and their applications”, Inform. Primen., 12:4 (2018), 75–85
A. I. Zeifman, A. V. Korotysheva, Ya. A. Satin, K. M. Kiseleva, R. V. Razumchik, V. Yu. Korolev, S. Ya. Shorgin, “Truncation bounds for a class of inhomogeneous birth and death queueing models with additional transitions”, Sistemy i Sredstva Inform., 27:3 (2017), 37–51
V. Yu. Korolev, A. I. Zeifman, A. Yu. Korchagin, “Asymmetric Linnik distributions as limit laws for random sums of independent random variables with finite variances”, Inform. Primen., 10:4 (2016), 21–33
V. Yu. Korolev, A. Yu. Korchagin, A. I. Zeifman, “The Poisson theorem for Bernoulli trials with a random probability of success and a discrete analog of the Weibull distribution”, Inform. Primen., 10:4 (2016), 11–20
A. I. Zeifman, A. V. Korotysheva, V. Yu. Korolev, Ya. A. Satin, “Truncation bounds for approximations of inhomogeneous continuous-time Markov chains”, Teor. Veroyatnost. i Primenen., 61:3 (2016), 563–569; Theory Probab. Appl., 61:3 (2017), 513–520
R. V. Razumchik, A. I. Zeifman, A. V. Korotysheva, Ya. A. Satin, “Energy efficiency estimation of the computational cluster using a queueing system with threshold control and time-dependent service and arrival rates”, Sistemy i Sredstva Inform., 25:4 (2015), 19–30
2014
16.
A. I. Zeifman, A. V. Korotysheva, K. M. Kiseleva, V. Yu. Korolev, S. Ya. Shorgin, “On the bounds of the rate of convergence and stability for some queueing models”, Inform. Primen., 8:3 (2014), 19–27
17.
A. I. Zeifman, V. Yu. Korolev, A. V. Korotysheva, S. Ya. Shorgin, “General bounds for nonstationary continuous-time Markov chains”, Inform. Primen., 8:1 (2014), 106–117
V. Yu. Korolev, L. M. Zaks, A. I. Zeifman, “On convergence of random walks generated by compound Cox processes to Levy processes”, Inform. Primen., 7:2 (2013), 84–91
2012
19.
V. Yu. Korolev, V. E. Bening, L. M. Zaks, A. I. Zeifman, “Generalized Laplace distribution as a limit law for random sums and statistics constructed from samples with randomsizes”, Inform. Primen., 6:4 (2012), 34–39
A. I. Zeifman, A. V. Korotysheva, Ya. A. Satin, S. Ya. Shorgin, “Bounds in null ergodic case for some queueing systems”, Inform. Primen., 6:4 (2012), 27–33
Ya. A. Satin, A. I. Zeifman, A. V. Korotysheva, “Convergence rate and truncations for one class of Markov queueing systems”, Teor. Veroyatnost. i Primenen., 57:3 (2012), 611–621; Theory Probab. Appl., 57:3 (2013), 529–539
A. I. Zeifman, A. V. Korotysheva, T. L. Panfilova, S. Ya. Shorgin, “Stability bounds for some queueing systems with catastrophes”, Inform. Primen., 5:3 (2011), 27–33
A. I. Zeifman, A. V. Korotysheva, Ya. A. Satin, S. Ya. Shorgin, “On stability for nonstationary queueing systemswith catastrophes”, Inform. Primen., 4:3 (2010), 9–15
A. I. Zeifman, Ya. A. Satin, A. V. Korotysheva, N. A. Tereshina, “On the limiting characteristics for $M(t)/M(t)/S$ queue with catastrophes”, Inform. Primen., 3:3 (2009), 16–22
E. van Doorn, A. I. Zeifman, T. L. Panfilova, “Bounds and Asymptotics for the Rate of Convergence of Birth-Death Processes”, Teor. Veroyatnost. i Primenen., 54:1 (2009), 18–38; Theory Probab. Appl., 54:1 (2010), 97–113
A. I. Zeifman, A. V. Chegodaev, V. S. Shorgin, “Some bounds for closed to absorbing Markov models”, Inform. Primen., 2:2 (2008), 35–40
2007
30.
A. I. Zeifman, Ya. A. Satin, “Mean characteristics of Markov queueing systems”, Avtomat. i Telemekh., 2007, no. 9, 122–133; Autom. Remote Control, 68:9 (2007), 1583–1593
A. I. Zeifman, “On Sharp Estimates of the Rate of Convergence for Some Systems of Differential Equations”, Mat. Zametki, 75:2 (2004), 303–306; Math. Notes, 75:2 (2004), 273–277
32.
B. L. Granovskii, A. I. Zeifman, “On the lower bound of the spectrum of some mean-field models”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 164–171; Theory Probab. Appl., 49:1 (2005), 148–155
A. I. Zeifman, “Some properties of a system with losses in the case of variable rates”, Avtomat. i Telemekh., 1989, no. 1, 107–113; Autom. Remote Control, 50:1 (1989), 82–87
A. I. Zeifman, “Positivity of the Cauchy matrix of a linear periodic system”, Differ. Uravn., 25:9 (1989), 1618–1619
36.
A. I. Zeifman, “Quasi-ergodicity and stability of some nonhomogeneous Markov processes”, Sibirsk. Mat. Zh., 30:2 (1989), 85–89; Siberian Math. J., 30:2 (1989), 236–239
1988
37.
A. I. Zeifman, “Truncation error in a birth and death system”, Zh. Vychisl. Mat. Mat. Fiz., 28:12 (1988), 1906–1907; U.S.S.R. Comput. Math. Math. Phys., 28:6 (1988), 210–211
A. I. Zeifman, “General birth and death processes and elementary stochastic models of epidemics”, Avtomat. i Telemekh., 1985, no. 6, 128–135; Autom. Remote Control, 46 (1985), 789–795
1982
39.
A. I. Zeifman, “Asymptotic behaviour of some stochastic models of species coexistence”, Avtomat. i Telemekh., 1982, no. 12, 120–123; Autom. Remote Control, 43:12 (1982), 1600–1603