Dynamics of switched arrival systems with thresholds

Examines a controlled single server fluid model where upper and lower limits are placed on the buffers. The authors study the case of a three buffer system in detail and describe the variety of possible closed loop behaviour between chaotic and periodic. The method of analysis is significantly different from the analysis in Chase, Serrano, and Ramadge (1993) for switched arrival systems with no thresholds. In particular, the authors take a topological rather then statistical approach to chaos in this paper. Also, they employ symbolic dynamics as an aid in the study of such systems end relate switched arrival systems with no upper limits to a particular subshift of finite type