We study an optimal choice of the buffer size in the Internet routers. The objective is to determine the minimum value of the buffer size required in order to fully utilize the link capacity. Theâ€¦ (More)

The result by Dvoretzky, Wald, and Wolfowitz on the sufficiency of nonrandomized decision rules for statistical decision problems with nonatomic state distributions holds for arbitrary Borel decisionâ€¦ (More)

Abstract:Under the heavy traffic condition, i.e. under large values of the scaling paramter n, it is sensible to replace the stochastic queueing model with the corresponding fluid model. Afterâ€¦ (More)

The purpose of this paper is to study an optimal stopping problem with constraints for a Markov chain with general state space by using the convex analytic approach. The costs are assumed to beâ€¦ (More)

Dvoretzky, Wald and Wolfowitz proved in 1951 the existence of equivalent and strongly equivalent mappings for a given transition probability when the number of nonatomic measures is finite and theâ€¦ (More)

Optimal control of stochastic bandwidth-sharing networks is typically difficult. In order to facilitate the analysis, deterministic analogues of stochastic bandwidth-sharing networks, the so-calledâ€¦ (More)

For a fixed given deterministic final horizon T > 0, let us consider the following multidimensional SDE: dXt = b(t,Xt)dt+ Ïƒ(t,Xt)dWt, t âˆˆ [0, T ] (1) where b : [0, T ] Ã— Rd â†’ Rd, Ïƒ : [0, T ] Ã— Rd â†’â€¦ (More)