caa a22 4500 378847759 CHVBK 20180305123315.0 cr unu---uuuuu 161128e200310 xx s 000 0 eng 10.1515/EQC.2003.165 doi (NATIONALLICENCE)gruyter-10.1515/EQC.2003.165 Availability Formulas and Performance Measures for Separable Degradable Networks [Elektronische Daten] [Cornelia Sauer, Hans Daduna] We derive explicit formulas for availability and performance measures in complex degradable stochastic networks. The networks consist of interacting service systems (queues) where servers are unreliable and may break down. The breakdown and repair mechanisms are of rather general structure, and may show complex dependencies among the nodes of the networks. The degradable network models investigated incorporate the breakdowns of the servers and their repairs as well as the behavior of the service mechanisms and the customers' routing into the overall Markovian system description. The service rates may depend on the local loads of the service centers, and furthermore working and repair periods are globally determined by state dependent intensities. Three different rules are applied to handle the customers' routing connected with nodes in repair status. These rules originate from communication and production theory where they are used to resolve blocking situations. Modeling unreliable networks in this way leads to steady state distributions of product form for the supplemented Markovian state processes. From these first quantities we are able to derive point availabilities for single nodes and for groups of nodes as well as the standard performance measures for service networks. © Heldermann Verlag Performability nationallicence reliability nationallicence Jackson networks nationallicence Gordon-Newell networks nationallicence blocking rules nationallicence product form solution nationallicence point availability nationallicence throughput nationallicence Sauer Cornelia University of Hamburg, Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes. sauer@math.uni-hamburg.de aut Daduna Hans University of Hamburg, Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes. daduna@math.uni-hamburg.de aut Economic Quality Control Walter de Gruyter GmbH & Co. KG 18/2(2003-10), 165-194 0940-5151 18:2<165 2003 18 EQC https://doi.org/10.1515/EQC.2003.165 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/EQC.2003.165 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sauer Cornelia University of Hamburg, Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes. sauer@math.uni-hamburg.de aut NATIONALLICENCE 700 1- Daduna Hans University of Hamburg, Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes. daduna@math.uni-hamburg.de aut NATIONALLICENCE 773 0- Economic Quality Control Walter de Gruyter GmbH & Co. KG 18/2(2003-10), 165-194 0940-5151 18:2<165 2003 18 EQC CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter