The joint distribution of sojourn times for a customer traversing an overtake–free series of queues: The discrete time case

Authors:
Hans Daduna
Affiliations:
Institute of Mathematical Stochastics, University of Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany
Venue:
Queueing Systems: Theory and Applications
Year:
1997

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Abstract

We investigate a cycle of Bernoulli servers in discrete time. We show that the joint distribution of a customer’s sojourn times at the nodes during a round trip is of product form and can explicitly be written down. The results are used to prove independence of sojourn times in an open series of Bernoulli servers.