2019/10/05 by Rui-Na Fan, Fan, Rui-Na, Quan‐Lin Li +5
Business, Management and Accounting · Engineering · #60J22 #60J28 #68Q85 #90B06 #90B15 #90B22 #90B25 #Advanced Queuing Theory Analysis #D.4.6 #D.4.8 #Distributed #Dynamical Systems (math.DS) #E.2 #E.3 #FOS: Computer and information sciences #FOS: Mathematics #H.2.4 #H.3.5 #Parallel #Performance (cs.PF) #Probability (math.PR) #Quality Function Deployment in Product Design #Reliability and Maintenance Optimization #Social and Information Networks (cs.SI) #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.1910.02276
openalex publication_date 2019/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper discusses a maintenance network with failed items that can be removed, repaired, redistributed, and reused under two batch policies: one for removing the failed items from each base to a maintenance shop and the other for redistributing the repaired items from the maintenance shop to bases. This maintenance network can be considered a virtual closed queueing network, and the Markov system of each node is described as an elegant block-structured Markov process whose stationary probabilities can be computed by the RG-factorizations. The structure of this maintenance network is novel and interesting. To compute the closed queueing network, we set up a new nonlinear matrix equation to determine the relative arrival rates, in which the nonlinearity comes from two different groups of processes: the failure and removal processes and the repair and redistribution processes. This paper also extends a simple queueing system of a node to a more general block-structured Markov process which can be computed by the RG-factorizations. Based on this, the paper establishes a more general product-form solution for the closed queueing network and provides performance analysis of the maintenance network. Our method will open a new avenue for quantitative evaluation of more general maintenance networks.