International Journal of Supply and Operations Management

International Journal of Supply and Operations Management

A Queueing Theory Model Based on Bivariate Birth/Birth-Death Stochastic Processes to Analyze Manufacturing Systems under Limited Maintenance Resources

Articles in Press

Document Type : Research Paper

Authors
Hasan Rasay 1
Jalal Taji 2
Amir-mohammad Golmohammadi 3
Mohammad Biglari Kami 1
1 Department of Industrial Engineering, Kermanshah University of Technology, Kermanshah, Iran
2 Department of Industrial Engineering, Faculty of Engineering, University of Bojnord, Bojnord, Iran
3 Department of Industrial Engineering, Faculty of Engineering, Arak University, Arak, Iran
10.22034/ijsom.2026.110975.3529
Abstract
Objective: This paper analyzes maintenance scheduling in systems comprising multiple identical parallel production units using queueing theory. Most queueing-based studies of such systems assume two states for each unit: operational (healthy) and failed. We model each unit with several operational states in addition to a failed state, with the system state represented by a bivariate state vector.
Methods: Given the state of the units, different maintenance actions are conducted by a crew capable of addressing a limited number of units concurrently. Based on birth-death process and queueing theory with a limited population and number of servers, the transition rate diagram (TRD) and equilibrium equations are derived. The system TRD combines two TRDs: (i) degradation without maintenance effects and (ii) maintenance actions. Using Little’s laws and the TRD, essential performance metrics and steady-state probabilities are computed.
Results: The developed model provides steady-state probabilities for different system states and enables the calculation of key performance measures related to production-unit degradation, failure, and maintenance. Numerical examples demonstrate the proposed framework and quantify system performance under the considered maintenance conditions.
Conclusion: The proposed approach provides a framework for analyzing maintenance scheduling in systems with identical parallel production units, considering multiple operational states, degradation, and limited maintenance capacity.
Keywords
multi-unit production systems
maintenance
queueing theory
birth-death process
operational state
transition rate
Subjects
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International Journal of Supply and Operations Management

Articles in Press, Accepted Manuscript
Available Online from 07 October 2026