Fire Engine Travel Times: Analysis of Travel Times and Optimal Dispatching Decisions

This master’s thesis looks into the problems concerning travel times of fire engines. First, we start with the problem of finding a distribution of the travel times of fi re engines, conditioned on the distance. Here, we fully describe and clarify a previously proposed model, and apply it to GPS-data of the fi re department in the area of Amsterdam, the Netherlands. Second, we look at decision processes. We start with considering nonconcurrent incidents, where we look at the minimum of different travel time distributions, to decide which two out of three re engines we should send to an incident. We find that it is optimal to send fi re engines with independent travel times. We then use this information when we consider concurrent incidents. In this case we use a discounted rewards in nite horizon Markov Decision Process to model how many re engines should be sent to an incident when sending more re engines is better for the current incident, since it reduces the expected travel time, but re engines take time to return, so at the next incident, there will be less re engines available. We prove that it is optimal to send more re engines, when there is more than one re engine available.

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