Related papers: On rate of convergence for infinite server Erlang-…
Polynomial convergence rate to stationarity is shown for extended Erlang -- Sevastyanov's model.
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…
An elementary and rigorous justification of Dynkin's identity with an extended infinitesimal operator based on the idea of a complete probability formula is given for queueing systems with a single server and discontinuous intensities of…
We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…
We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit…
We introduce a comprehensive framework for analyzing convergence rates for infinite dimensional linear programming problems (LPs) within the context of the moment-sum-of-squares hierarchy. Our primary focus is on extending the existing…
Explicit rate of convergence in variance (or more general entropies) is obtained for a class of Piecewise Deterministic Markov Processes such as the TCP process, relying on functional inequalities. A method to establish Poincar\'e (and more…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…
Convergence rates results for Tikhonov regularization of nonlinear ill-posed operator equations in abstract function spaces require the handling of both smoothness conditions imposed on the solution and structural conditions expressing the…
We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Shannon entropy convergence rates. In the case when they…
A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers also can be of multiple types. Each customer has an independent exponentially…
Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.
A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent…
We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…
The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers of busy servers and served customers, as…
We consider a model inspired by compatibility constraints that arise between tasks and servers in data centers, cloud computing systems and content delivery networks. The constraints are represented by a bipartite graph or network that…
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 large-scale parallel-server system, where each server independently adjusts its processing speed in a decentralized manner. The objective is to minimize the overall cost, which comprises the average cost of maintaining the…
Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…