Discrete time queueing networks

The aim of this project is to develop a product form calculus for such networks similar to the BCMP and Kelly networks in continuous time. This will provide us with a versatile class of discrete time network models where the equilibrium behaviour can be explicitly computed. Having this at hand, the main performance characteristics can be derived as well.
Collaboration with Ruslan K. Chornei (Inter-Regional Academy of Personnel Management, Kiew, Ukraina), Bernadette Desert (Hamburg), Marten Holst (Hamburg), Pavel S. Knopov (Kiew, National Academy of Sciences of the Ukraina), Christian Malchin (University of Hamburg) Victor Pestien (University of Miami), Subramanian Ramakrishnan (University of Miami), and Kersten Tippner (Hamburg).

Part of this research programm is the project Stochastic networks in discrete time: Analysis of performance and availability, funded by the DFG (German Reseach Foundation) in 2005–06 under DA 774/1

Some recent articles concerning Discrete time queueing networks:

1. Some results for steady-state and sojourn time distributions in open and closed linear networks of Bernoulli servers with state– dependent service and arrival rates
   Performance Evaluation 30 (1997), 3 –18
2. The cycle time distribution in a cycle of Bernoulli servers in discrete time
   Mathematical Methods in Operations Research 44, 295 – 332, 1996
3. Discrete time queueing networks: Recent developments Tutorial Lecture Notes,
   in : Tutorials Performance 96 (Lecture Notes), 163 – 204, IFIP, LRC––EPFL, Lausanne, 1996
4. Networks of queues in discrete time
   Lecture Notes, Hamburg 1997
5. Discrete time analysis of a state dependent tandem with different customer types
   In Lecture Notes in Computer Science 1337, Springer Heidelberg 2001:
   Foundations of Computer Science, Potential–Theory–Cognition. Christian Freksa, Matthias Jantzen, Rüdiger Valk (eds.), 287 –296, Springer Berlin 1997
6. The joint distribution of sojourn times for a customer traversing a series of queues : The discrete time case
   Queueing Systems and Their Applications 27, 297 –323, 1998
7. Controlled Markov fields with finite state space on graphs ( with Ruslan K. Chornei and Pavel S. Knopov)
   Stochastic Models 21, 847–874, 2005
   also available: Preprint No.2000–08, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2000
8. Queueing Networks with Discrete Time Scale
   Explicit Expressions for the Steady State Behavior of Discrete Time Stochastic Networks
   Lecture Notes in Computer Science 2046, Springer Heidelberg 2001
9. Asymptotic throughput in discrete-time cyclic networks with queue-length-dependent service rates (with Subrahmanian Ramakrishnan and Victor Pestien)
   Stochastic Models, 19, 483 – 506, 2003
   Preliminary version: Preprint No.2001–04, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2001.
10. Discrete time tandem networks of queues – Effects of different regulation schemes for simultaneous events
    (with Bernadette Desert)
    Performance Evaluation 47, 73 – 104, 2002
11. On the structure of roundtrip time distributions in discrete time networks (with Christian Malchin)
    Preprint No.2004–03, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2004, submitted.
12. Asymptotic throughput in discrete-time cyclic networks with queue-length-dependent service rates
    (with Subrahmanian Ramakrishnan and Victor Pestien)
    Stochastic Models, 19, 483 – 506, 2003
    Preliminary version: Preprint No.2001–04, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2001.
13. Availability and performance analysis in a discrete time tandem network with product form steady state (with Christian Malchin)
    in: German, R.; Heindl, A. (eds.): Proceedings of the GI/ITG Conference on Measuring, Modelling and Evaluation of Computer and Communications Systems , 2006, 381 –398, 2006
    Extended Version: Preprint No.2005–06, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2005.
14. Discrete time queueing networks with product form steady state: Availability and performance analysis in an integrated model (with Christian Malchin)
    Queueing Systems and Their Applications 65, 385 – 421, 2010 2010; also available as
    Preprint No.2006–02, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2006 ps–file.
15. Discrete time queueing networks with product form steady state
    in: Boucherie, R. J. and van Dijk, N. (eds) Queueing Networks: A Fundamental Approach, 269 – 312, Springer, New York, 2010
16. Bottleneck analysis of discrete time networks: Sojourn times (with Christian Malchin)
    Preprint No.2007–03, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2007, submitted ps–file.
17. Customer oriented performance measures for packet transmission in a ring network with blocking (with Marten Holst)
    in: (eds.): Proceedings of the GI/ITG Conference on Measuring, Modelling and Evaluation of Computer and Communications Systems , 2008, 223 –236, 2000