Stochastic orders, monotonicty and correlation in stochastic networks

This is a joint project with Ryszard Szekli. (Wroclaw University). The project is funded by the Alexander-von-Humboldt-Stiftung, DAAD (Germany), and KBN (Poland). We consider stochastic networks exhibiting in steady state a product form equilibrium, i.e., the nodes of the networks behave asymptotically at a fixed time instant as if they are spatially independent. In the transient phase of such systems and in steady state when considering joint distributions of the network processes over time strong correlations in space and time occur. The aim of the project is to characterize these correlation and to obtain bounds for the transient probabilities of the networks.
Collaboration with Lars Peter Saul.

Some recent articles concerning Stochastic orders, monotonicty and correlation in stochastic networks :

1. Dependencies in Markovian networks (with R.Szekli)
   Adv.Appl.Prob. 27, 226–254 1995
2. A queueing theoretical proof of increasing property for Polya–frequency functions (with R.Szekli)
   Statistics and Probabilty Letters 26, 233–242, 1996
3. On the correlation of sojourn times in open networks of exponential multiserver queues (with R. Szekli)
   Queueing Systems and Their Applications 34, 169–181, 2000
4. On the correlation structure of closed queueing networks (with Ryszard Szekli)
   Stochastic Models, 20, 1–30, 2004
   Preliminary version: Monotonicity and dependence properties of sojourn and cycle times in closed networks
   Preprint No.2000–05, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2000.
5. Dependence structure of sojourn times via partition separated ordering (with Ryszard Szekli)
   Operations Research Letters 31, 462–472, 2003
   Preliminary version: Preprint No.2002–03, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2002.
6. Dependence ordering for Markov processes on partially ordered spaces (with Ryszard Szekli)
   Journal of Applied Probability 43, 793–814, 2006
   also available as: Report No. 16 2004/2005, fall, Institut Mittag-Leffler, 2005.
7. Impact of routing on correlation strength in stationary queueing network processes (with Ryszard Szekli)
   Journal of Applied Probability 45 (3), 846–878 2008
8. Availability in large networks: Global characteristics from local unreliability properties (with Lars Peter Saul)
   to appear in: Schmitt, J. (ed.): Proceedings of the 16th International GI/ITG Conference on Measurement, Modelling and Evaluation of Computing Systems and Dependability and Fault Tolerance, Lecture Notes in Computer Science 7201, 1–15, Springer Berlin 2012