Queueing systems in a random environment

The investigation in this project is motivated by the observation that many complex networks are typically subject to influences from an external environment. The impact of the evolving environment on the network is typically by changing service capacities (upgrading and/or degrading, breakdown, repair) or by changing the paths of the travelling customers when the environment changes its state. On the other side, customers departing from the network may enforce the environment to jump immediately. This means that the environment is nonautonomous and therefore results in a rather complex two-way interaction, especially if the environment is not itself Markov. We are especially interested in separable models, i.e., although there is the important bidirectional interaction of the network's nodes with the environment, asymptotically and in steady state the environment and the network (or a single node) behave stochastically as if they are independent (with respect to one-dimensional time marginals).
Recent applications, where nodes are influenced by their environment are mobile and ad–hoc networks or sensor networks. Here the environment of a typical node is composed of the geographical surroundings and the behaviour of the node's neighboured nodes. In this example the behaviour of the referenced node influences the behaviour of the environment.
Collaboration with Ruslan Krenzler (Hamburg University), Sonja Otten (Hamburg University), Ryszard Szekli (Wroclaw University.

Some recent articles concerning Queueing systems in a random environment:

1. Loss systems in a random environment – steady state analysis (with Ruslan Krenzler)
   Queueing Systems 80, 127 – 153, 2015 (DOI) 10.1007/s11134–014–9426–6, also available as
   Preprint No.2012–04, Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2012, pdf–file.
2. Jackson networks in non-autonomous random environments (with Sonja Otten and Ruslan Krenzler)
   Advances in Applied Probability 48, 315 – 331, 2016
3. Networks of queues in a random environment: Survey of product form results
   In: Wolfinger, Bernd E. ; Heidtmann, Klaus-D. (eds): Proc. MMBnet 2015, Berichte des Fachbereichs Informatik der Universität Hamburg, 302, pages 1––17, 2015
4. Modeling and Performance Analysis of a Node in Fault Tolerant Wireless Sensor Networks (with Ruslan Krenzler)
   in: Fischbach, K., Krieger, U. (eds.) Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance, Lecture Notes in Computer Science Volume 8376, Springer 2014, pp 73–87
5. Correlation formulas for Markovian network processes in a random environment (with Ryszard Szekli)
   Advances in Applied Probability 48 (1), 176 – 198, 2016; doi:10.1017/apr.2015.12; also available as
   Preprint No.2013–05, Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2013 pdf–file.