Queues with inspection cost: To see or not to see?

2025-03-17

AI Summary

This paper investigates the strategic joining decisions of customers in an M/M/1 queue when observing the queue length incurs a private inspection cost: customers may join blindly, balk blindly, or pay to observe the state before deciding. We formulate this as a Bayesian game—first introducing explicit inspection costs into the queueing games framework to rigorously characterize the trade-off between information value and waiting cost. Through analytical derivation, we obtain a closed-form solution for the Nash equilibrium, prove its uniqueness, and establish necessary and sufficient conditions for existence, revealing a structured threshold policy. Results show that reducing inspection costs improves social welfare, albeit with diminishing returns; conversely, increasing the reward for joining enhances individual incentives but may induce excessive entry, degrading system efficiency. This work provides foundational theoretical support for information design and mechanism optimization in observable queueing systems.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Problem

• Optimal decision-making in queues with inspection costs.
• Impact of inspection cost on social welfare maximization.
• Comparison of lowering inspection cost vs increasing joining reward.

Innovation

• Introduces queue inspection cost model
• Develops closed-form equilibrium probability expressions
• Compares inspection cost and reward impacts