Sequential quadratic programming-based economic optimisation of an MAP /PH/1 queueing system with negative arrivals and unreliable repairers
Abstract
This paper studies an MAP/PH/1 queueing system with negative arrivals, unreliable repairers addressing the challenges posed by repair failures through the analysis of two models. In model 1, a failed repair leads to the removal of all positive arrivals from the system, while in model 2, a standby server is activated to ensure service continuity. The study compares the key performance measures (derived using matrix-analytic method) and economic functions of both models. We have also determined the optimum values of the profit functions for both models using sequential quadratic programming (SQP). The results indicate that model 2 leads to lower loss of positive arrivals and demonstrates greater economic efficiency compared to model 1.
Fields of Study & Subjects
Advanced Queuing Theory Analysis
Reliability and Maintenance Optimization
Age of Information Optimization
Publication details
- Journal / source
- International Journal of Mathematical Modelling and Numerical Optimisation
- Volume
- 16
- Issue
- 1
- Pages
- 1–29
- Publication date
- 1 January 2026
- Language
- EN