Erlangian Approximations for the Transient Analysis of a Fluid Queue Model for Forest Fire Perimeter

This paper presents how the Erlangization method can be employed to estimate probabilities for the time‐dependent behaviour of the level in a Markov modulated fluid flow. Formulas are given for estimating the probability of transitions to any fluid level, starting from an initial level in either an increasing or a decreasing stage in the phase process, prior to a finite time‐point of interest. This methodology is applied to a model developed to study the evolution of uncontrolled fire perimeter for forest fires in Ontario, Canada. The model estimates the relative effectiveness of fire suppression under various fire‐weather and fuel type scenarios, focusing on containment and escape probabilities. Numerical results are provided for illustrative purposes.