Condition-Based Maintenance for Queues with Degrading Servers

Iqra Ejaz, Michelle Alvarado, Natarajan Gautam, Nagi Gebraeel, Mark Lawley

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The integration of condition monitoring with queueing systems to support decision making is not well explored. This paper 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, and so on). 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 benchmarked 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. 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. Note to Practitioners-We propose condition-based maintenance for queues with degrading servers. The proposed model has been verified in simulation using degradation data of tools in a manufacturing facility. In order to implement, one must first model the underlying degradation process using the data from condition monitoring. We can get service and repair time distributions using data from the plant floor. Then, we need reasonable estimates of costs. These include costs of holding, quality, repair, and failure. They can be relative, prioritized or zero. The long-run average cost per unit time can then be evaluated. Then, the model provides the degradation state of the server at which maintenance is the most cost efficient. The degradation data can be used to continually obtain the optimal state of degradation at which the server can be taken offline with minimal costs.

Original languageEnglish (US)
Article number8645721
Pages (from-to)1750-1762
Number of pages13
JournalIEEE Transactions on Automation Science and Engineering
Issue number4
StatePublished - Oct 2019
Externally publishedYes


  • Condition-based maintenance
  • Markovian degradation
  • cost optimization
  • single-server queues

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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