Exponential Conic Optimization for Multi-Regime Service System Design under Congestion and Tail-Risk Control
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| Format: | Preprint |
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2026
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| author | Blanco, Víctor Martínez-Antón, Miguel Puerto, Justo |
| author_facet | Blanco, Víctor Martínez-Antón, Miguel Puerto, Justo |
| contents | We study the design of single-facility service systems operating under multiple recurring regimes with service-level constraints on response times. Regime-dependent arrival and service rates induce hyperexponential response-time distributions, and the design problem selects regime-specific capacities to balance cost, congestion, fairness, and reliability. We propose a mixed-integer exponential conic optimization framework integrating SLA chance constraints, conflict-graph design restrictions, and CVaR-based tail-risk control. Although NP-hard, the problem admits an efficient decomposition scheme and tractable special cases. Computational experiments and a large-scale urban case study show substantial improvements over the current system, quantifying explicit trade-offs between efficiency, congestion control, fairness, and robustness. The framework provides a practical tool for congestion-aware and tail-control service system design. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_16021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exponential Conic Optimization for Multi-Regime Service System Design under Congestion and Tail-Risk Control Blanco, Víctor Martínez-Antón, Miguel Puerto, Justo Optimization and Control 90B80, 90B85, 90B22, 90C46, 90C25, 90C10, 90C15, 60K25 We study the design of single-facility service systems operating under multiple recurring regimes with service-level constraints on response times. Regime-dependent arrival and service rates induce hyperexponential response-time distributions, and the design problem selects regime-specific capacities to balance cost, congestion, fairness, and reliability. We propose a mixed-integer exponential conic optimization framework integrating SLA chance constraints, conflict-graph design restrictions, and CVaR-based tail-risk control. Although NP-hard, the problem admits an efficient decomposition scheme and tractable special cases. Computational experiments and a large-scale urban case study show substantial improvements over the current system, quantifying explicit trade-offs between efficiency, congestion control, fairness, and robustness. The framework provides a practical tool for congestion-aware and tail-control service system design. |
| title | Exponential Conic Optimization for Multi-Regime Service System Design under Congestion and Tail-Risk Control |
| topic | Optimization and Control 90B80, 90B85, 90B22, 90C46, 90C25, 90C10, 90C15, 60K25 |
| url | https://arxiv.org/abs/2602.16021 |