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 end-to-end-delay 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 Alexander-von-Humboldt-Stiftung, 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 :

1. The cyclic queue and the tandem queue (with Onno Boxma)
   Queueing Systems 77, 275 – 295, 2014; DOI 10.1007/s11134–013–9380–8, also available as
   Preprint No.2013–01, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2013 pdf–file.
2. Weak convergence limits for closed cyclic networks of queues with multiple bottleneck nodes (with Ole Stenzel)
   Journal of Applied Probability 49 (1), 60–83, 2012; also available as
   Preprint No.2009–05, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2009 ps–file.
3. 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.2007–04, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2007.
4. An invariance property of conditional sojourn time distributions in cyclic networks of queues
   (with Christian Malchin)
   Operations Research Letters 33, 1–8, 2004
   Preliminary version: Preprint No.2003–06, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, University of Hamburg 2003.
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. Conditional job observer property for multitype closed queueing networks
   Journal of Applied Probability 39 (2002) p. 865–881
7. 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
8. Individual customer's behaviour in networks with state–dependent arrival rates (with S. Meyer)
   Queueing Systems and Their Applications 32 (1999) p. 351–362
9. Sojourn time distributions in non–product–form queueing networks
   in : Dshalalow,J.(ed.):Frontiers of queueing: Models and Applications in Science and Engineering, Chapter 8, CRC Press, Boca Raton, 1996
10. Delay time distributions and adjusted transfer rates for Jackson networks (mit R.Schassberger)
    AEU–Archiv fuer Elektronik und Uebertragungstechnik 47 (Special Issue on Teletraffic Theory and Engineering in Memory of Felix Pollaczek) 342–348 1993
11. On network flow equations and splitting formulas for sojourn times in in queueing networks
    J.Appl.Math.and Stoch.Analysis 4, 111–116 1991
12. Sojourn times in queueing networks ( with O.J.Boxma )
    in: Takagi,H.(ed): Stochastic analysis of computer and communication systems, 401–450 North–Holland, Amsterdam 1990
13. Sojourn times in queueing networks with multiserver nodes (with R.Schassberger)
    J. Appl. Prob. 24, 511–521 1987