Mylosz, Jennifer
[Author]
;
Daduna, Hans
[Contributor]
Local Stabilization of Non-Ergodic Jackson Networks with Unreliable Nodes ; Lokale Stabilisierbarkeit nicht-ergodischer Jackson-Netzwerke mit unzuverlässigen Knoten
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Media type:
Doctoral Thesis;
E-Book;
Electronic Thesis
Title:
Local Stabilization of Non-Ergodic Jackson Networks with Unreliable Nodes ; Lokale Stabilisierbarkeit nicht-ergodischer Jackson-Netzwerke mit unzuverlässigen Knoten
Contributor:
Mylosz, Jennifer
[Author]
imprint:
Staats- und Universitätsbibliothek Hamburg Carl von Ossietzky, 2013-01-01
Footnote:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Description:
This thesis contributes to a better understanding of the behavior of queueing networks that cannot approach a classical equilibrium state. We consider Jackson networks with unreliable nodes which randomly break down and are under repair for a random time. Our networks are described by Markov processes the states of which incorporate the availability status and the queue-lengths vector. For Jackson networks with unreliable nodes, it is known that, under ergodicity conditions, the Markovian availability-queue-lengths process has a stationary product-form distribution. Ergodicity conditions can be expressed as local rate conditions: The total arrival rate at each node has to be strictly less than its maximal service rate. If for some nodes the ergodicity condition is violated, the network process is not ergodic and there cannot exist a stationary distribution. Nevertheless, we are able to obtain the complete asymptotics for non-ergodic Jackson networks with unreliable nodes and show that the state distribution of the stable subnetworks, i.e., the set of nodes where the local rate condition is fulfilled, converges to a Jackson-type product-form distribution. The characterization of the asymptotic behavior of non-ergodic Jackson networks with unreliable nodes strongly relies on a detailed investigation of another class of generalized Jackson networks, which is of interest for its own. In these networks some stations may have an additional buffer with an infinite supply of lower priority jobs (customers) served at that station whenever the station runs out of standard customers. Networks incorporating such buffers are called Jackson networks with infinite supply. We analyze the stationary and limiting behavior of these networks with reliable nodes as well as with unreliable nodes. Our results offer a new way to measure and assess the performance of non-ergodic Jackson networks with unreliable nodes where steady-state methods cannot be applied because no steady state exists. Using the obtained limiting distributions we ...