A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation of the stationary probability distribution is not available in general, the performance is approximated by a perturbed random walk, whose transition rates o...

This paper focuses on the problem of stability in homogeneous systems with dilation. First, we propose an ‘homogeneous eigenvalue’ for homogeneous systems. Next, we analyze the stability of homogeneous systems using homgeneous eigenvalues, and we show that the use of positive real homogeneous eigenvalues implies instability. Finally, we show the effectiveness of the proposed method through an e...

I survey classification results for countable homogeneous or ‘partially homogeneous’ ordered structures. This includes some account of Schmerl’s classification of the countable homogeneous partial orders, outlining an extension of this to the coloured case, and also treating results on linear orders, and their generalizations, trees and cycle-free partial orders. 2000 Mathematics Subject Classi...

In our preceding paper we have introduced the notion of an s-homogeneous triple. this use technique to study connected algebras with two relations. For such algebras, describe all possible pairs (A,M), where A is s-Veronese ring and M (s,1)-Veronese bimodule dual algebra. each a pair classify corresponding or give necessary sufficient conditions for algebra under consideration correspond given ...