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The aim is to evaluate the performance of a single-server queueing system with specific arrival and service characteristics.

June 20, 2026MathematicsOpen Access

Performance Evaluation of a Single-Server Queueing System with Correlated Arrivals, Two-Tier Service Structure, Random Breakdowns and Phase-Type Repairs

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The aim is to evaluate the performance of a single-server queueing system with specific arrival and service characteristics.
Analyzed a queueing system with Markovian arrivals and phase-type distributions for service times.
Applied matrix-analytic methods for steady-state analysis, yielding stability conditions and performance measures.
Conducted numerical experiments to validate analytical findings.
Identified stability condition and stationary probability vectors for the system.
Analyzed busy periods and key performance metrics, showing effective service structure.
Demonstrated practical applicability through numerical experiments aligned with analytical results.

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Analytical model examines the performance of a single-server queueing system with correlated arrivals, impacting service efficiency and repairs.

Gurulakshmi et al. (2026) studied this question.

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Analytical model examines the performance of a single-server queueing system with correlated arrivals, impacting service efficiency and repairs.