On-Off Systems with Strategic Customers

2025-03-29

AI Summary

This paper investigates equilibrium behavior of strategic customers and optimal service scheduling in a single-server multi-queue on–off switching system. Customers decide whether to join based on real-time queue on/off states, and the system’s revenue depends on rewards from successfully served customers. The study distinguishes two switching mechanisms: exogenous (with pre-specified on/off durations) and endogenous (where durations are dynamically determined by the service policy). For the exogenous case—first modeling strategic customer behavior in an on–off setting—the paper derives a closed-form Nash equilibrium and formulates a linear program to compute optimal durations. For the endogenous case, it proves that at most one queue requires extended service time and proposes a structurally transparent, O(n)-time closed-form algorithm for optimal scheduling. The results substantially improve both total system revenue and operational stability.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Security and Privacy: Large-scale security measurements

Abstract

Motivated by applications such as urban traffic control and make-to-order systems, we study a fluid model of a single-server, on-off system that can accommodate multiple queues. The server visits each queue in order: when a queue is served, it is"on", and when the server is serving another queue or transitioning between queues, it is"off". Customers arrive over time, observe the state of the system, and decide whether to join. We consider two regimes for the formation of the on and off durations. In the exogenous setting, each queue's on and off durations are predetermined. We explicitly characterize the equilibrium outcome in closed form and give a compact linear program to compute the optimal on-off durations that maximizes total reward collected from serving customers. In the endogenous setting, the durations depend on customers' joining decisions under an exhaustive service policy where the server never leaves a non-empty queue. We show that an optimal policy in this case extends service beyond the first clearance for at most one queue. Using this property, we introduce a closed-form procedure that computes an optimal policy in no more than 2n steps for a system with n queues.

Problem

• Study fluid model of single-server on-off system with multiple queues
• Analyze equilibrium and optimal on-off durations for exogenous settings
• Determine optimal policy for endogenous settings with exhaustive service

Innovation

• Fluid model for single-server on-off systems
• Closed-form equilibrium and linear program
• Optimal policy extends service selectively