A first benchmark of performance when analyzing dynamic stochastic systems is the stability of the underlying stochastic processes (the positive-recurrent property for Markov processes). When modeling wireless systems in particular, one is often confronted to deal with multidimensional birth and death process with state dependent transitions, (the state dependency occurs because of opportunistic scheduling and/or interferences between base stations and users). The stability regions of such processes is in general very difficult to obtain and has been mathematically handled only for quite specific cases. To establish a link between the asymptotic stability of deterministic differential equations and the stability of the original Markov processes has turned out to be one of the most promising approach to answer these questions.
Publications:
• Stability of multidimensional birth and death processes with 0-homogeneous state dependent transitions
Publications:
• Stability of multidimensional birth and death processes with 0-homogeneous state dependent transitions
with S. Shneer,
submitted. [arxiv]
•Rate stability and output rates in queueing networks with shared resources
with R.D. van der Mei, W. van der Weij,
Performance Evaluation, 67(1), 28-42, 2010. [publi_site].
•Stability of parallel queueing systems with coupled service rates
with S. Borst and L. Leskelä,
Discrete Event Dynamic Systems, 18(4), 447-472 2008, [arxiv_new_version].