Chaos in a simple deterministic queueing system

The authors present a simple discrete-time deterministic queueing model, with one server and two queueing lines. The input rates of both queues are constant and their sum equals the server-capacity. In each time period the server has to decide how much time to spend on each of the two queues. The servers decision rule is a nonlinear, but increasing function of the difference between the two queue-lengths. The authors investigate how the dynamical behaviour of the queue-lengths and the service process depend on the ‘steepness’ of the decision function and the ratio of the input rates of the two queues. They show that if the decision function is steep, then for many input-ratios chaotic dynamics occurs.