Of forests and fire

David Martell applies math to a tricky problem.

What do forest fires and bank machine customers have in common? Seemingly nothing, until you talk with David Martell, a professor in U of T’s Faculty of Forestry and a leader in research into how to manage forest fires and the resources used to fight them.

Over the past 30 years, Martell and his graduate students have developed important new insights into the perplexing problem of how to deal with fires that can grow to more than 50,000 hectares (about 125,000 acres).

As expert as he is, Martell’s roots are not in forests, but industrial engineering. A native of Kirkland Lake in northeastern Ontario, he has childhood memories of “seeing forests that had been burned, but I never thought that forestry could be a career.”

But a couple of things happened during his undergraduate years at U of T that spawned what would become his life’s work. “I studied operations research and learned how to develop mathematical models that can be used to model human-managed systems, such as bank machines.” A key component of that was queueing theory – the science of dealing with congestion when designing facilities that serve customers.

He took a summer job working with the then Ontario Department of Lands and Forests, helping build a simulation model of the use of airtankers in fighting forest fires.

The knowledge of queueing theory was (and still is) essential to the job. And 30 years later, Martell is still working on similar problems. Much of his research is used regularly by forest fire managers today.

“Bank machines are a perfect example of queueing systems,” he says. “When the bank decides how much to invest in the machines to serve customers it has to balance the cost of the machines with the risk of annoying customers with long lineups.”

The same theory can be applied to deploying resources to forest fires.

The fire becomes the “customer.” The “servers” are the resources used to control the fire – airtankers, helicopters and fire fighters. The longer fires “wait,” the more “annoyed” (and damaging) they become. “Airtankers cost roughly $30 million each. They are an expensive but crucial part of the operation. So the government has to figure out how it can balance airtanker costs with response time. I develop queueing models that can be used to help determine an optimal number of airtankers.”

While he has had success in designing effective service models using queueing theory, it remains a tricky problem because fires are unpredictable. “The number of customers that use bank machines is relatively stable. With forest fires, every day is different. So we have to develop models that are flexible enough to deal with variation in the number of fires, the weather and the location.”

Martell notes that the forest fire research community has built a productive relationship with fire management agencies and huge progress has been made. “This is a very complex, computationally intractable problem we can never really solve. The challenge is to keep getting better, which we are. We just keep banging away to improve our models.”