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

Abstract 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 timepoint 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.

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