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Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

Zeifman A., Razumchik R., Satin Y., Kiseleva K., Korotysheva A., Korolev V.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 1

141--154

In this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics (the idle probability and the mean number of customers in the system) of the systems considered with a given approximation error.

Sharp bounds for the bias of trimmed means of progressively censored order statistics

Bieniek M.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 1

99--112

We provide sharp upper and lower bounds on the bias of trimmed means of progressively censored type II order statistics from general distributions in various scale units. The results are illustrated with numerical examples. We also discuss this problem for distributions with decreasing density or failure rate, as well as for generalized order statistics.