Incorporating Human Interaction into Stair Egress with an Application to Minimum Stair Width

Recently, this journal published an article (Peacock et al. in Fire Technol 53:845–871, 2017) describing a study done by the National Institute of Standards and Technology’s Engineering Laboratory. That article provides a description of data collected during fire drill evacuations of 11 office buildings and 3 residential buildings throughout the United States. A total of 32 stairs were observed. These data were analyzed with two goals in mind: to present the self-exciting Hawkes point process as a means to capture occupant interactions in stair exit processes, and to use this point process representation to derive a minimum stair width determination that compensates for human interaction. By way of accomplishing these goals, it is shown by modeling occupant exit times as a point process more information than flow rate is extracted. This additional information resides in the process’s intensity function, i.e., the instantaneous exit rate of occupants through a stair exit, which has units of persons per unit time. For example, it is shown that the following behavior is captured by a Hawkes intensity. When a slow moving occupant on a stair is met, occupants behind either decrease their speed and follow that occupant or move to pass the occupant. Our results indicate that a larger minimum stair width would help accommodate movement in stairs caused by these types of interactions. By modeling the exit process as a Hawkes point process and using hydraulic model equations, we derived a point estimate 1.308 m for minimum stair width and a 95% confidence interval [1.193 m, 1.334 m] bounding minimum stair width, whereas the normative minimum stair width value set by the U.S. building code is 1.12 m.