Hans Daduna
Research interests and projects
Last revision March 2, 2017
My research interest are in the field of stochastic processes and their
applications, especially in computer science and operations research.
Most of my work is on stochastic networks (networks of queues), their
asymptotic behaviour, steady state distributions, busy period analysis
for single servers and subnetworks, sojourn time distribution for individual
customers, and computational algorithms for performance evaluation of
networks.
A survey of some of these topics can be found in
Stochastic networks with product form equilibrium, in: Shanbhag, D.N.;
Rao, C.R. (eds.): Handboof of Statistics, Vol. 19, Chapter 11 (p. 309
 364) Elsevier Sciences B.V., 2001
Parallel to this work on stochastic networks in the classical
continuous time framework is research with the aim to develop a
product form calculus for stochastic networks in discrete time.
A survey of parts of this research is the book
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
More recent are research projects on queueing systems and networks in a random environment,
stochastic orders and dependence
ordering for Markov processes and stochastic networks,
reliability of queueing networks
(Performability), the integration of queueing and inventory
management, and on optimization of stochastic
networks and of locally interacting multidimensional
Markov processes.
Complete list of
publications.
Research projects:

Queueing systems in a random environment

Integrated models for production and inventories. Supply chains

Local stabilization of large unstable networks

Discrete time queueing networks

Nonproduct form models and processes
associated with product form networks

Optimal control of systems with random influences:
Operations Research models

Performability:
Reliability and Performance Analysis of Stochastic Networks

Stochastic orders, monotonicty and correlation in stochastic networks

Passage time and sojourn time analysis for individual customers in stochastic
networks

Markov processes with lattice ordered state space: Theory of order and
dependence, with applications
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 twoway 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 onedimensional time marginals).
Recent applications, where nodes are influenced by their environment are mobile and adhoc 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:

Loss systems in a random environment  steady state analysis
(with Ruslan Krenzler)
Queueing Systems 80, 127  153, 2015 (DOI) 10.1007/s1113401494266,
also available as
Preprint No.201204, Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2012,
pdffile.

Jackson networks in nonautonomous random environments
(with Sonja Otten and Ruslan Krenzler)
Advances in Applied Probability 48, 315  331, 2016

Networks of queues in a random environment: Survey of product form results
In: Wolfinger, Bernd E. ; Heidtmann, KlausD. (eds): Proc. MMBnet 2015,
Berichte des Fachbereichs Informatik der
Universität Hamburg, 302, pages 117, 2015

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 7387

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.201305, Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2013
pdffile.
Integrated models for production and inventories. Supply chains
Queueing theory and inventory theory are fields of Operations Research with different methodologies
to optimize e.g. production processes and inventory control. In classical Operations Research queueing
theory and inventory theory are often considered as disjoint areas of research. On the other side, the
emergence of complex supply chains calls for integrated queueinginventory models, which are the focus
of our present research.
We consider a supply chain consisting of production systems (servers) at several locations, each
with a local inventory, and a supplier network of workstations, which manufactures items of possibly
different kinds (raw material), to replenish the local inventories.
Recent applications, where
Collaboration with NhaNghi de la Cruz (Hamburg University), Ruslan Krenzler (Hamburg University),
Rafal Kulik (Wroclaw University), Pawel Lorek (Wroclaw University),
Christian Malchin (Hamburg University), Sonja Otten (Hamburg University),
Cornelia Sauer (Hamburg University), Maike Schwarz (Hamburg University),
Ryszard Szekli (Wroclaw University), Kersten Tippner (Hamburg University)
Some recent articles concerning
Integrated models for production and inventories. Supply chains:

Monotonicity of Base Stock Policies
(with NhaNghi de la Cruz)
Operations Research Letters 44, 186  190, 2016,

Models for integrated productioninventory systems: Steady state and cost analysis
(with Sonja Otten and Ruslan Krenzler)
Int. Journal of Production Research, 54 (20), 6174  6191, 2016,
DOI:10.1080/00207543.2015.10826692015,

Queueing systems with inventory management with random lead times
and with backordering
(with M. Schwarz )
Mathematical Methods of Operations Research 64, 383414, 2006
also available as:
Preprint No.200503, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2005,
psfile.

Product form models for queueing networks with an inventory
(with M. Schwarz and C. Sauer)
Stochastic Models 23, 627  663, 2007;
also available as extended version:
Exponential queueing networks with an attached inventory
under (r,Q) or (r,S)policy
(with M. Schwarz and C. Sauer)
Preprint No.200309, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2003, submitted
psfile.
 M/M/1 Queueing systems with inventory
(with Maike K. Schwarz, Cornelia Sauer, Rafal Kulik, Ryszard Szekli)
Queueing Systems and Their Applications 54, 55  78, 2006
also available as:
Preprint No.200307, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2003
psfile.
Local stabilization of large unstable networks
The investigation in this project is motivated by the following observation:
In large and complex networks, unstable subnetworks often occur due to
local overload or due to nonavailability of nodes or links, but nevertheless,
there coexist regions where other subnetworks stabilize locally.
Due to the local instability the describing Markovian network processes
are generically nonergodic. Nevertheless it can be seen that locally, i.e.,
for some subset of nodes the local processes, which are not Markovian
of their own, converge to a well defined stochastic limit.
Additionally, we investigate the impact of unreliability of nodes on the
stabilization of networks or subnetworks.
Recent applications, where nodes or links may be not available for some
time, are mobile and adhoc networks or sensor networks.
The emergence of wireless adhoc networks, which are built of varying sets of
mobile users
with wireless communication capabilities without relying on a preexisting
infrastructure, introduces
problems concerning availability of transmission nodes in the vicinity of a
user. On the other hand, in such networks, overload emerges from too many
users entering a region and applying for transmission.
Collaboration with Jennifer Mylosz (University of Hamburg) and
Bernd Heidergott (Vrije Universiteit Amsterdam).
Some recent articles concerning
Local stabilization of large unstable networks:

Nonergodic Jackson networks with infinite supply 
local stabilization and local equilibrium analysis
(with Jennifer Sommer and Bernd Heidergott)
Journal of Applied Probability 53(4), 1125  1142, 2016

On the behavior of stable subnetworks in nonergodic
networks with unreliable nodes (with Jennifer Mylosz)
Computer Networks 53 (8), 12491263, 2009
 On the behavior of stable subnetworks in nonergodic networks:
A quasistationary approach in a twonode system (with Jennifer Mylosz)
in: Wolfinger, B. E. and Heidtmann, K.D. (eds.):
Leistungs, Zuverlässigkeits und
Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten
Systemen, 6. GI/NTGWorkshop MMBnet 2011
Berichte des Fachbereichs Informatik der
Universität Hamburg No. 298, 99106, Hamburg 2011.
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 (InterRegional 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
200506 under
DA 774/1
Some recent articles concerning Discrete time queueing networks:

Some results for steadystate 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

The cycle time distribution in a cycle of Bernoulli servers in discrete
time
Mathematical Methods in Operations Research 44, 295  332, 1996

Discrete time queueing networks: Recent developments
Tutorial Lecture Notes,
in :
Tutorials Performance 96 (Lecture Notes),
163  204, IFIP, LRCEPFL, Lausanne, 1996

Networks of queues in discrete time
Lecture Notes, Hamburg 1997

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, PotentialTheoryCognition.
Christian Freksa, Matthias Jantzen, Rüdiger Valk (eds.), 287
296, Springer Berlin 1997

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
 Controlled Markov fields with finite state space on graphs
( with Ruslan K. Chornei and Pavel S. Knopov)
Stochastic Models 21, 847874, 2005
also available: Preprint No.200008, Schwerpunkt Mathematische Statistik
und Stochastische Prozesse,
University of Hamburg 2000,
psfile
 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

Asymptotic throughput in discretetime cyclic networks with
queuelengthdependent service rates
(with Subrahmanian Ramakrishnan and Victor Pestien)
Stochastic Models, 19, 483  506, 2003
Preliminary version:
Preprint No.200104, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2001,
psfile.

Discrete time tandem networks of queues  Effects of different
regulation schemes for simultaneous events
(with Bernadette Desert)
Performance Evaluation 47, 73  104, 2002
 On the structure of roundtrip time
distributions in discrete time networks
(with Christian Malchin)
Preprint No.200403, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2004, submitted
psfile.

Asymptotic throughput in discretetime cyclic networks with
queuelengthdependent service rates
(with Subrahmanian Ramakrishnan and Victor Pestien)
Stochastic Models, 19, 483  506, 2003
Preliminary version:
Preprint No.200104, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2001,
psfile.
 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.200506, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2005
psfile.
 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.200602, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2006
psfile.
 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

Bottleneck analysis of discrete time networks: Sojourn times (with Christian Malchin)
Preprint No.200703, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2007, submitted
psfile.

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, 2008
Stochastic orders, monotonicty and correlation in stochastic networks
This is a joint project with
Ryszard Szekli.
(Wroclaw University).
The project is funded by the AlexandervonHumboldtStiftung,
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 :

Dependencies in Markovian networks (with R.Szekli)
Adv.Appl.Prob. 27, 226  254 1995

A queueing theoretical proof of increasing property for Polyafrequency
functions (with R.Szekli)
Statistics and Probabilty Letters 26, 233  242, 1996

On the correlation of sojourn times in open networks of exponential multiserver
queues (with R. Szekli)
Queueing Systems and Their Applications 34, 169181, 2000

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.200005, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2000
psfile.

Dependence structure of sojourn times via partition separated ordering
(with Ryszard Szekli)
Operations Research Letters
31, 462  472, 2003
Preliminary version:
Preprint No.200203, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2002,
psfile
.

Dependence ordering for Markov processes on partially ordered spaces
(with Ryszard Szekli)
Journal of Applied Probability 43, 793814, 2006
also available as:
Report No. 16 2004/2005, fall, Institut MittagLeffler,
2005,
psfile or pdffile.

Impact of routing on correlation strength in stationary queueing
network processes (with Ryszard Szekli)
Journal of Applied Probability 45 (3), 846878 2008

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, 115, Springer Berlin 2012
Passage time and sojourn time analysis for individual customers in stochastic
networks
The sojourn times or passage times of customers in stochastic networks
represent (e.g.) the endtoenddelay in telecommunication networks, the
lead times in production systems, waiting and service times in computer
systems, life times in population models,... . From a theoretical point
of view the stochastic behaviour of these times is up to now not well understood.
Being interested in equilibrium results as a first distributional characterisation
of sojourn times I investigate the steady state passage time distribution
and the joint distribution of a customer's sojourn times at the successive
nodes of a path when traversing the network.
Parts of the research are funded by the AlexandervonHumboldtStiftung,
DAAD (Germany), and KBN (Poland).
Collaboration with Rolf Schassberger (Technical University of
Braunschweig), Stephan Meyer (Hamburg), Christian Malchin (Hamburg),
Onno Boxma (Technical University of Eindhoven),
Ryszard Szekli.
Some recent articles concerning Passage time and sojourn time analysis for individual customers in stochastic
networks :

The cyclic queue and the tandem queue (with Onno Boxma)
Queueing Systems 77, 275  295, 2014; DOI 10.1007/s1113401393808,
also available as
Preprint No.201301, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2013
pdffile.
 Weak convergence limits for closed cyclic networks of queues
with multiple bottleneck nodes
(with Ole Stenzel)
Journal of Applied Probability 49 (1), 6083, 2012; also available as
Preprint No.200905, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2009
psfile.
 Weak convergence limits for sojourn times in cyclic queues
under heavy traffic (with Christian Malchin and Ryszard
Szekli)
Journal of Applied Probability 45, 1 14, 2008; also available as
Preprint No.200704, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2007
psfile.
 An invariance property of conditional sojourn time
distributions in cyclic networks of queues
(with Christian Malchin)
Operations Research Letters 33, 18, 2004
Preliminary version:
Preprint No.200306, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2003,
psfile.

Dependence structure of sojourn times via partition separated ordering
(with Ryszard Szekli)
Operations Research Letters
31, 462  472, 2003
Preliminary version:
Preprint No.200203, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2002,
psfile
.

Conditional job observer property for multitype closed
queueing networks
Journal of Applied Probability 39 (2002) p. 865881

On the correlation of sojourn times in open networks of exponential multiserver
queues (with R. Szekli)
Queueing Systems and Their Applications 34, 169181, 2000

Individual customer's behaviour in networks with statedependent
arrival rates (with S. Meyer)
Queueing Systems and Their Applications 32 (1999) p. 351362

Sojourn time distributions in nonproductform queueing networks
in : Dshalalow,J.(ed.):Frontiers of queueing: Models and Applications
in Science and Engineering, Chapter 8, CRC Press, Boca Raton, 1996

Delay time distributions and adjusted transfer rates for Jackson networks
(mit R.Schassberger)
AEUArchiv fuer Elektronik und Uebertragungstechnik 47 (Special Issue
on Teletraffic Theory and Engineering in Memory of Felix Pollaczek) 342348
1993

On network flow equations and splitting formulas for sojourn times in in
queueing networks
J.Appl.Math.and Stoch.Analysis 4, 111116 1991

Sojourn times in queueing networks ( with O.J.Boxma )
in: Takagi,H.(ed): Stochastic analysis of computer and communication
systems, 401450 NorthHolland, Amsterdam 1990

Sojourn times in queueing networks with multiserver nodes (with R.Schassberger)
J. Appl. Prob. 24, 511521 1987
Optimal control of systems with random influences:
Operations Research models
This is a joint project with Pavel S. Knopov (V. M. Glushkov
Institute of Cybernetics, Academy of Science of the Ukraina). The
project is funded by the DFG (Germany).
(1) We consider stochastic models from the field of Operations Research
(queueing systems, inventory sytems, repair and renewal sytems) subject to an external (open loop) control by a
decision maker. The aim is to find simple optimal or nearly optimal control policies which minimize the long range
costs (maximize the long range reward). The common feature of the models is the contiuous state space of the
describing system processes; so the variable (observation) where the
control decision is based on is continuous.
(2) Stochastic networks are random fields on graphs, when
considered at a fixed time instant. Incoprorating the spacetime
variabilty of such systems leads to time dependent random fields. If
the systems are controlled by decision makers which act at the nodes
and make their decisions on the basis of local information only, and
if the spacetime behavior of the system carries Markov structures in
time and space, we obtain controlled Markov processes with locally
interacting components. Our interest is in finding optimal strategies
inside the class of local strategies and in proving conditions which
guarantee that these locally
optimal strategies are even globally optimal.
Collaboration with Ludmila P. Tur (Kiew) and Ruslan K. Chornei (Kiew).
Some recent articles concerning Optimal control of systems with
random influences: Operations Research models :

Optimal admission control for M/D/1/K queueing systems (with Pavel S. Knopov )
Mathematical Methods of Operations Research 50 (1999), p. 91100

Optimal strategies for an inventory systems with cost
functions of general form
(with Pavel S. Knopov and Ludmila P. Tur )
Cybernetics and System Analysis 35, 602  618, 1999
(Translation from Kibernetica i Sistemyi Analiz 4' 99, 106123, 1999)

Local control of interacting Markov fields on graphs with compact state space
(with Ruslan K. Chornei and Pavel S. Knopov)
Kibernetica i Sistemyi Analiz 2001, No. 3 p. 62  77,
also available as
Preprint No.200009, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2002, submitted 
psfile.

Stochastic games for distributed players on graphs
(with Ruslan K. Chornei and Pavel S. Knopov)
Mathematical Methods of Operations Research 60, 279298, 2004
Preliminary version: Preprint No.200206,
Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2002,
psfile.
 Controlled semiMarkov fields with graphstructured
compact state space
(with Ruslan K. Chornei and Pavel S. Knopov)
Theory of Probability and
Mathematical Statistics 69, 3953, 2004
translation from: Teor. Ymovirnost. Matem. Statist. 69, 4247, 2003,
(in Ukrainian)
also available as Preprint No.200208, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2002,
psfile.
 Controlled Markov fields with finite state space on graphs
( with Ruslan K. Chornei and Pavel S. Knopov)
Stochastic Models 21, 847874, 2005
also available: Preprint No.200008, Schwerpunkt Mathematische Statistik
und Stochastische Prozesse,
University of Hamburg 2000,
psfile
 Control of Spatially Structured Random Processes and
Random
fields with Applications
( with Ruslan K. Chornei and Pavel S. Knopov)
Springer, New York, 2006
Performability:
Reliability and Performance Analysis of Stochastic Networks
This is a joint project with Cornelia Sauer.
We consider stochastic networks (networks of queues) where nodes
or the servers at the nodes are degradable, i.e., the nodes may be
subject to breakdown or perturbations, which decrease their capacity.
Following this, repair mechanisms and repair strategies are introduced.
Our aim is to find network models where the performance behaviour of
the network and
the breakdown and repair
mechanism are incorporated into a unified Markovian system description, which
nevertheless admits an explicit steady state.
Collaboration with Jennifer Mylosz (University of Hamburg).
Some recent articles concerning Performability:
Reliability and Performance Analysis of Stochastic Networks :

Modeling networks with unreliable servers (with Cornelia Sauer)
Proceedings of the 2. MMBArbeitsgespräch
Leistungs, Zuverlässigkeits und
Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten
Systemen,
Berichte des Fachbereichs Informatik der
Universität Hamburg No. 242, 83  90, Hamburg 2002.
 Separable networks with unreliable servers
(with Cornelia Sauer)
in Charzinski, J; Lehnert, R.; TranGia, P. (eds.):
Providing Quality of Service in Heterogeneous Environments
(Proceedings of the 18 ITC, Berlin), Teletraffic Science and
Engineering Vol 5b, 821  830, Elsevier 2003.
Extended version: BCMP networks with unreliable servers
(with Cornelia Sauer)
Preprint No.200301, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2003,
psfile.

Availability formulas and performance measures for separable
degradable networks
(with C. Sauer)
Economic Quality Control, 18, 165  194, 2003

Degradable networks with general up and down time distributions.
(with C. Sauer)
in: Buchholz, P.; Lehnert, R.; Pioro, M. (eds.): MMB & PGTS 2004,
Proceedings of the 12th GI/ITG Conference on Measuring, Modelling and
Evaluation of Computer and Communications Systems and 3rd
PolishGerman Teletraffic Symposium, 185  194, 2004
Extended Version:
Preprint No.200404, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2004
psfile.
 Dependence ordering for queueing networks with breakdown and
repair
(with Cornelia Sauer, Rafal Kulik, Ryszard Szekli)
Probability in the Engineering and Informational
Sciences 20, 575594, 2006
also available as:
Isotone differences ordering for unreliable Markovian queueing networks,
Preprint No.200504, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2005, submitted
psfile.
 Discrete time queueing networks with product form steady
state: Availability and performance analysis in an
integrated model
(with Christian Malchin)
Preprint No.200602, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2006, submitted
psfile.

On the behavior of stable subnetworks in nonergodic
networks with unreliable nodes (with Jennifer Mylosz)
Computer Networks 53 (8), 12491263, 2009
Nonproduct form models and processes
associated with product form networks
This is a joint project with
Ryszard Szekli.
(Wroclaw University). The project is funded by DAAD (Germany) and
KBN (Poland) in 200304.
We start from a class of stochastic networks (networks of queues) and their
describing stochastic processes which exhibit a product form
stationary distribution. Extending this class of networks by attaching
inventories to the service nodes of the network and considering the
nodes to be unreliable due to external random influences, we arrive
at nonstandard models, which in some cases exhibit a new form of
product structure for the equilibrium and in other cases deviate from
the product form class completely. Our aim is to compute in both
cases steady states for the (supplemented) network
processes and to derive performance quantities of the systems in an
explicite form.
Further topics are stochastic orderings in these class of systems and
the structure of dependencies over time and space of the processes, as
well as the asymptotic behaviour of the processes.
In cases where no explicit quantitative measures are available we
prove easy to apply bounds by comparing different systems.
Cooperation with Rafal Kulik, Pawel Lorek, Christian Malchin,
Cornelia Sauer, Maike Schwarz, Ryszard Szekli, Kersten Tippner.
Some recent articles concerning Nonproduct form models and processes
associated with product form networks :

Modeling networks with unreliable servers (with Cornelia Sauer)
Proceedings of the 2. MMBArbeitsgespräch
Leistungs, Zuverlässigkeits und
Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten
Systemen,
Berichte des Fachbereichs Informatik der
Universität Hamburg No. 242, 83  90, Hamburg 2002.

Degradable networks with general up and down time distributions.
(with C. Sauer)
in: Buchholz, P.; Lehnert, R.; Pioro, M. (eds.): MMB & PGTS 2004,
Proceedings of the 12th GI/ITG Conference on Measuring, Modelling and
Evaluation of Computer and Communications Systems and 3rd
PolishGerman Teletraffic Symposium, 185  194, 2004
Extended Version:
Preprint No.200404, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2004
psfile.
 M/M/1  systems with different inventory management policies
and lost sales
(with Maike K. Schwarz, Cornelia Sauer, Rafal Kulik, Ryszard Szekli)
to appear in: Queueing Systems and Their Applications
also available as:
Preprint No.200307, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2003
psfile.
 An invariance property of conditional sojourn time
distributions in cyclic networks of queues
(with Christian Malchin)
Operations Research Letters 33, 18, 2004
Preliminary version:
Preprint No.200306, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2003,
psfile.

Exponential queueing networks with an attached inventory
under (r,Q) or (r,S)policy
(with M. Schwarz and C. Sauer)
Preprint No.200309, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2003, submitted
psfile.submitted

Availability formulas and performance measures for separable
degradable networks
(with C. Sauer)
Economic Quality Control, 18, 165  194, 2003
 On the structure of roundtrip time
distributions in discrete time networks
(with Christian Malchin)
Preprint No.200403, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2004, submitted
psfile.

Dependence ordering for Markov processes on partially ordered spaces
(with Ryszard Szekli)
Journal of Applied Probability 43, 793814, 2006
also available as:
Report No. 16 2004/2005, fall, Institut MittagLeffler,
2005
psfile or pdffile.

Queueing systems with inventory management with random lead times
and with backordering
(with M. Schwarz )
Mathematical Methods of Operations Research 64, 383414, 2006
also available as:
Preprint No.200503, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2005
psfile.
 Dependence ordering for queueing networks with breakdown and
repair
(with Cornelia Sauer, Rafal Kulik, Ryszard Szekli)
Probability in the Engineering and Informational
Sciences 20, 575594, 2006
also available as:
Isotone differences ordering for unreliable Markovian queueing networks,
Preprint No.200504, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2005, submitted
psfile.

Product form models for queueing networks with an inventory
(with M. Schwarz and C. Sauer)
Stochastic Models 23, 627  663, 2007;
also available as extended version:
Exponential queueing networks with an attached inventory
under (r,Q) or (r,S)policy
(with M. Schwarz and C. Sauer)
Preprint No.200309, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2003, submitted
psfile.
Markov processes with lattice ordered state space: Theory of order and
dependence, with applications
This is a joint project with
Ryszard Szekli.
(Wroclaw University). The project is funded by DAAD (Germany) and
KBN (Poland) in 200506.
The class of monotone Markov processes plays an important role in many
applications, e.g. interacting particle systems, queueing networks,
reliability structures. Moreover a satisfying theory for positive
correlation of Markovian processes has up to now only been developed for
monotone Markov processes.
The theory of dependence and order is develpoped up to now mainly
for linearly ordered state spaces or products of linearly ordered
spaces. In this project we intend to investigate Markov processes with
nonlinearly ordered state spaces, especially with lattice ordered
state space. The planned subtopics of the project encompass:
Dependence ordering for monotone Markov processes,
isotone differences ordering for Markov processes with state spaces of
product form, dependence ordering for Markov processes without
assuming monotonicity, and
applications in reliability ordering for complex systems with internal
dependencies, and dependencies in stochastic networks.
Cooperation with Rafal Kulik, Pavel Lorek, Christian Malchin,
Cornelia Sauer, Ryszard Szekli, Kersten Tippner.
Some recent articles concerning
Markov processes with lattice ordered state space: Theory of order and
dependence, with applications :
 Dependence ordering for queueing networks with breakdown and
repair
(with Cornelia Sauer, Rafal Kulik, Ryszard Szekli)
Probability in the Engineering and Informational
Sciences 20, 575594, 2006
also available as:
Isotone differences ordering for unreliable Markovian queueing networks,
Preprint No.200504, Schwerpunkt Mathematische Statistik und
Stochastische Prozesse, University of Hamburg 2005, submitted
psfile.

Dependence ordering for Markov processes on partially ordered spaces
(with Ryszard Szekli)
Journal of Applied Probability 43, 793814, 2006
also available as:
Report No. 16 2004/2005, fall, Institut MittagLeffler,
2005,
psfile or pdffile.

Impact of routing on correlation strength in stationary queueing
network processes (with Ryszard Szekli)
Journal of Applied Probability 45 (3), 846878, 2008
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