Mode Locking and Chaos in a Deterministic Queueing Model with Feedback
研究一个简单的确定性排队系统，通过两种反馈机制（服务率随队长增加、到达率依赖等待时间感知）展现持续振荡、模式锁定、准周期和混沌行为，说明确定性系统也能产生看似不可预测的动态，对理解需求波动下的服务系统管理有启示。
We consider a simple, deterministic queueing system with feedback, which exhibits the phenomena of sustained oscillation, mode locking, quasi-periodic behaviour, and chaos. This implies that a fully deterministic queueing system can exhibit seemingly unpredictable behaviour. We ignore variability, and focus on two forms of feedback: (i) the service rate increases as queue length increases, and (ii) the arrival rate depends on customers' perception of past waiting times. We model a customer's decision to seek service as a two stage process: (i) deciding whether or not to use a facility, and (ii) deciding the frequency of visit (daily, weekly, monthly, etc.). This frequency is initially constant, and later on replaced by a deterministic, time-dependent pattern. Although highly stylised, this model captures the essential features of many real-life systems whose average arrival rate varies over time. Reducing the amplitude of cycles in demand makes the system more predictable and thus easier to manage. Although we represent this model as a queue of customers waiting for service, the model can be interpreted more generally as any situation where an increase in demand lowers the quality of service.