Dual-channel service system with reactive capacity allocation: stability and chaos

We study the dynamics and performance of a dual-channel service system in which a manager allocates capacity through a reactive capacity allocation (RCA) policy. Modeling the system as two deterministic queues with forward-looking consumers, we show that feedback between managerial decisions and consumer behavior can generate rich dynamic patterns, including stable equilibria, periodic cycles, and chaotic fluctuations. These dynamics are shaped by managerial reactiveness, the anchor queue length used in RCA decisions, and behavioral factors such as social interaction intensity and purchase persistence. We further compare shared and dedicated capacity structures and identify a nuanced operational trade-off. When capacity is optimally chosen, shared capacity dominates by leveraging resource pooling and demand amplification from social interactions. However, when total capacity is fixed, dedicated capacity may outperform shared capacity, particularly under highly reactive policies or strong social interaction effects. Our results provide new insights into the management of dual-channel service systems.