Condition-Based Maintenance for Queues With Degrading Servers
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abstract
The integration of condition monitoring with queueing systems to support decision making is not well explored. This work addresses the impact of condition monitoring of the server on the system level performance experienced by entities in a queueing system. The system consists of a queue with a single server subject to Markovian degradation. The model assumes a Poisson arrival process with service times and repair times according to general distributions. We develop stability conditions and perform steady state analysis to obtain performance measures (average queue length, average degradation, etc.). We propose minimizing an objective function involving four types of costs: repair, catastrophic failure, quality and holding. The queue performance measures derived from steady state analysis are bench-marked and compared to those from a discrete event simulation model. After verifying the queuing model, a sensitivity analysis is performed to determine the relationships between system performance and model parameters. Further, we explore the impact of stochastic service times on degradation and cost coefficients on optimal repair policy. Results indicate that the total cost function is convex and thus subject to an optimal repair policy. The model is sensitive to service time, quality costs, and failure costs for late-stage policy repairs decisions and sensitive to expected repair times and repair costs for early-stage policy repair decisions. The stochastic nature of service times drastically increases the likelihood of catastrophic failure of the server, and substantially increases holding costs. However, quality degrades more for constant service times while repair costs are minimally impacted.
