Exponential Conic Optimization for Multi-Regime Service System Design under Congestion and Tail-Risk Control
Víctor Blanco, Miguel Martínez-Antón, Justo Puerto
TL;DR
This work addresses the design of single-facility service systems operating under multiple regimes with SLA and tail-risk considerations. It develops a mixed-integer exponential-cone optimization that exploits the hyperexponential end-to-end delay structure arising from regime-based routing among parallel $M/M/1$ queues, and supports selective SLA coverage, conflict-graph constraints, and CVaR tail control. Key contributions include explicit regime-dependent performance modeling, endogenous protected demand sets, exact conic representations, and a decomposition algorithm with a polynomial-time solution for conflict-free, uniform-confidence cases. The NYC EMS case study demonstrates substantial improvements in efficiency, congestion control, fairness, and robustness, illustrating the framework’s practical value for congestion-aware service system design.
Abstract
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.