Three-Dimensional Models
The feature of the cusp catastrophe surface that makes it of interest in the traffic flow context is that while two of the variables (the control variables) exhibit smooth continuous change, the third one (the state variable) can undergo a sudden "catastrophic" jump in its value. Navin suggested that speed was the variable that underwent this catastrophic change, while flow and occupancy were the control variables. While Navin's presentation was primarily an intuitive one, without recourse to data, Gilchrist and Hall verified it by using data from the QEW Freeway in Mississauga, Ontario. A visualization of this model along with probable field observations is shown in Figure 10 (below).
Figure 10: Catastrophe theory surface (Hall 1989)
