Exponential Conic Optimization for Multi-Regime Service System Design under Congestion and Tail-Risk Control

TL;DR

This paper introduces an exponential conic optimization framework for designing multi-regime service systems that effectively balance cost, congestion, fairness, and tail-risk, even under complex probabilistic constraints.

Contribution

It develops a novel mixed-integer exponential conic optimization model incorporating SLA chance constraints and tail-risk measures, with efficient solution methods for complex, NP-hard problems.

Findings

Significant improvements over existing systems in computational experiments.

Effective trade-offs between efficiency, congestion, fairness, and robustness demonstrated.

Practical tool for congestion-aware service system design developed.

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.