@book{9fce274ce7bd4359b24a8cf9cb9bd886,

title = "The invariant measure of homogeneous Markov processes in the quarter-plane: Representation in geometric terms",

abstract = "We consider the invariant measure of a homogeneous continuous-time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geometric distribution. Second, we show that a countable linear combination of geometric terms can be an invariant measure only if it consists of pairwise-coupled terms. As a consequence, we obtain a complete characterization of all countable linear combinations of geometric distributions that may yield an invariant measure for a homogeneous continuous-time Markov process in the quarter-plane.",

keywords = "Geometric product form, Invariant Measure, EWI-20980, Continuous-time Markov process, Linear combination, MSC-60J27, IR-78962, Quarter-plane",

author = "Y. Chen and Boucherie, {Richardus J.} and Jasper Goseling",

year = "2011",

month = dec,

language = "Undefined",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1965",

}