Availability Formulas and Performance Measures for Separable Degradable Networks

Sauer Cornelia and Daduna Hans
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Sauer Cornelia: University of Hamburg, Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes. sauer@math.uni-hamburg.de
Daduna Hans: University of Hamburg, Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes. daduna@math.uni-hamburg.de

Stochastics and Quality Control, 2003, vol. 18, issue 2, 165-194

Abstract: 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.

Keywords: Performability; reliability; Jackson networks; Gordon-Newell networks; blocking rules; product form solution; point availability; throughput (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1515/EQC.2003.165

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