Abstract
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.
Zusammenfassung
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.
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References
Daduna, H.: Passage Times for Overtake-Free Paths in Gordon-Newell Networks. Adv. Appl. Prob.14, 1982, 672–686.
Kelly, F.P.: Reversibility and Stochastic Networks. New York 1979.
Melamed, B.: On Markov Jump Processes Imbedded at Jump Epochs and Their Queueing-Theoretic Applications. Mathem. of Operations Res.7, 1982a, 111–128.
—: Sojourn Times in Queueing Networks. Mathem. of Operations Res.7, 1982b, 223–244.
Reich, E.: Waiting Times when Queues are in Tandem. Ann. Math. Stat.28, 1957, 768–773.
—: Note on Queues in Tandem. Ann. Math. Stat.34, 1963, 338–341.
SchaΒberger, R., andH. Daduna: The Time for a Round-Trip in a Cycle of Exponential Queues. J. Assoc. Comp. Mach.30, 1983, 146–150.
Sevcik, K.C., andI. Mitrani: The Distribution of Queueing Network States at Input and Output Instants. J. Assoc. Comp. Mach.28, 1981, 358–371.
Walrand, J., andP. Varaiya: Sojourn Times and the Overtaking Condition in Jacksonian Networks. Adv. Appl. Prob.12, 1980, 1000–1018.
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Daduna, H. On passage times in Jackson networks: Two-stations walk and overtake-free paths. Zeitschrift für Operations Research 27, 239–256 (1983). https://doi.org/10.1007/BF01916920
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DOI: https://doi.org/10.1007/BF01916920