Zeitschrift für Operations-Research

, Volume 27, Issue 1, pp 239–256 | Cite as

On passage times in Jackson networks: Two-stations walk and overtake-free paths

  • H. Daduna
Papers Series A: Theory


We compute the distribution of the time for a two-stations walk in an open Jackson network (which includes the twofold service at one station), and give a simple derivation of the distribution of the sojourn times for overtake-free paths in these networks.


Queue Length Passage Time Sojourn Time Arrival Intensity Queueing Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Wir bestimmen die Verteilung der Durchlaufzeit durch zwei aufeinander folgende Knoten in einem offenen Jackson-Netzwerk und die Verteilung der Zeit für einen zweifachen Durchlauf durch einen Knoten.

Ferner berechnen wir die Verweilzeitverteilung für überholfreie Pfade.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Daduna, H.: Passage Times for Overtake-Free Paths in Gordon-Newell Networks. Adv. Appl. Prob.14, 1982, 672–686.MathSciNetMATHGoogle Scholar
  2. Kelly, F.P.: Reversibility and Stochastic Networks. New York 1979.Google Scholar
  3. Melamed, B.: On Markov Jump Processes Imbedded at Jump Epochs and Their Queueing-Theoretic Applications. Mathem. of Operations Res.7, 1982a, 111–128.MathSciNetCrossRefMATHGoogle Scholar
  4. —: Sojourn Times in Queueing Networks. Mathem. of Operations Res.7, 1982b, 223–244.MathSciNetCrossRefMATHGoogle Scholar
  5. Reich, E.: Waiting Times when Queues are in Tandem. Ann. Math. Stat.28, 1957, 768–773.MathSciNetCrossRefMATHGoogle Scholar
  6. —: Note on Queues in Tandem. Ann. Math. Stat.34, 1963, 338–341.MathSciNetCrossRefMATHGoogle Scholar
  7. SchaΒberger, R., andH. Daduna: The Time for a Round-Trip in a Cycle of Exponential Queues. J. Assoc. Comp. Mach.30, 1983, 146–150.MathSciNetCrossRefMATHGoogle Scholar
  8. Sevcik, K.C., andI. Mitrani: The Distribution of Queueing Network States at Input and Output Instants. J. Assoc. Comp. Mach.28, 1981, 358–371.MathSciNetCrossRefMATHGoogle Scholar
  9. Walrand, J., andP. Varaiya: Sojourn Times and the Overtaking Condition in Jacksonian Networks. Adv. Appl. Prob.12, 1980, 1000–1018.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Physica-Verlag 1983

Authors and Affiliations

  • H. Daduna
    • 1
  1. 1.Technische Universität.BerlinBerlin 12

Personalised recommendations