Related papers: On convergence rate for Erlang--Sevastyanov type m…
Polynomial convergence rates in total variation are established in Erlang-Sevastyanov's type problem with an infinite number of servers and a general distribution of service under assumptions on the intensity of serving.
The upper bound for the convergence rate of the distribution of the state of a queuing system with infinitely many servers is obtained, in the case when the intensity of the incoming flow and the intensity of the service depend on the state…
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…
The exponential rate of convergence for some Markov operators is established. The operators correspond to continuous iterated function systems which are a very useful tool in some cell cycle models.
Recurrence and ergodic properties are established for a single--server queueing system with variable intensities of arrivals and service. Convergence to stationarity is also interpreted in terms of reliability theory.
Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary…
We study convergence in variation of probability solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary solutions. We obtain sufficient conditions for the exponential convergence of solutions to the stationary solution in…
A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…
We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our…
The past few decades have seen robust research on questions regarding the existence, form, and properties of stationary distributions of stochastically modeled reaction networks. When a stochastic model admits a stationary distribution an…
This paper is devoted to analyzing the observer convergence rate for a class of linear control systems in a Hilbert space. To characterize the polynomial stability of the observer error system, we apply the spectral theory of linear…
This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of inputs but not for all inputs. We show that solutions…
We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…
We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…
This paper studies the rate of convergence of the power-of-two-choices, a celebrated randomized load balancing algorithm for many-server queueing systems, to its mean field limit. The convergence to the mean-field limit has been proved in…
Using elementary methods, we prove that for a countable Markov chain $P$ of ergodic degree $d > 0$ the rate of convergence towards the stationary distribution is subgeometric of order $n^{-d}$, provided the initial distribution satisfies…
We prove the convergence at an exponential rate towards the invariant probability measure for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster…
The exponential upper bounds for the convergence rate of the distribution of restorable element with partially energized standby redundancy are founded, in the case when all working and repair times are bounded by exponential random…
Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the…
We consider a Markovian single-server retrial queueing system with a constant retrial rate. Conditions of null ergodicity and exponential ergodicity for the correspondent process, as well as bounds on the rate of convergence are obtained.