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Abstract:In service systems, customers now rely on congestion information before deciding which queue or server to join, from restaurants and theme-park attractions to road networks. We study this setting as human-in-the-loop learning (HILL), where customers both consume and generate time-sensitive congestion information through crowdsourcing platforms. Because congestion reports become stale, efficient system operation requires continued exploration of servers whose current states are uncertain. Yet selfish customers avoid such exploration when it reduces their immediate service utility, even though their observations would benefit future customers. We analyze this tension between individual incentives and system-wide learning in queueing systems with endogenous congestion. We first show that myopic server choices can induce an infinite price of anarchy (PoA): decentralized customers may cause arbitrarily large efficiency losses by overexploring servers that are likely congested. In the single-server case, we prove that the lower bound on PoA decreases as buffer size grows, while in the multi-server case the upper bound decreases as the number of servers increases. We further show that existing informational, non-monetary mechanisms for exploration-exploitation with exogenous information fail in our setting, as customers' choices directly reshape the queue states and still lead to infinite PoA. To address this challenge, we design a dynamic side-payment mechanism that periodically charges some customers and rewards others, discouraging excessive exploration while maintaining ex-post budget balance. The mechanism coordinates congestion management and information acquisition across heterogeneous servers, and guarantees PoA below 2. Beyond worst-case analysis, experiments using real datasets demonstrate that the proposed mechanism also achieves strong average-case performance.

Submission history

From: Hongbo Li [view email]
[v1] Tue, 16 Jun 2026 18:35:53 UTC (1,296 KB)