A Time-Dependent Spatial Queueing Model for the Daily Deployment of Airtankers for Forest Fire Control

Abstract

Each day forest fire managers must decide how many airtankers to acquire for the day and where to deploy them to minimize their initial attack response time. We developed an initial attack airtanker system (IAAS) model and a heuristic procedure that fire managers can use to help resolve their daily airtanker deployment decisions. The IAAS model is a spatial time-dependant multi-server queueing system with fires as customers and airtankers as mobile servers. The differential-difference equations that describe the system are solved numerically and the results are used to predict the time-dependent performance of the airtanker system in terms of expected virtual response time (the elapsed time from the time a fire is reported until the time an airtanker arrives at the fire to begin initial attack action) over time given a specified deployment of airtankers to airports. We evaluate the IAAS model by comparing its results with those produced by a more realistic simulation model. The spatial deployment heuristic uses the IAAS model to identify improved daily airtanker deployment strategies. We also suggest a myopic replanning heuristic to provide pragmatic solutions to the daily airtanker deployment problem.

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