Traditionally, station location models have relied on the concept of “coverage” to determine the best locations. The main drawback to these models is the binary nature of “coverage”, where demand locations are either “covered” or “uncovered”.

What does this mean?

If a demand point can be reached within a target response time, the demand point is considered covered. For example, these models say that if a call is 7:59 minutes away, it is covered, but if it is 8:01 minutes away, it is uncovered. This can often bias station spacing, encouraging sub-optimal placement that hinders your service to the community. As well, this measurement provides no accurate way to project the impact of new resources on your performance targets and standards.

Binary coverage has three primary drawbacks:

  • Biased station locations
  • Underestimation of necessary stations
  • Poor performance prediction

Binary vs. probabilistic coverage models

Consider, for example, figures 1 and 2. In both figures, the centre of the circle is the location of the emergency services stations.

Figure 1: Binary Coverage

Figure 1 is a representation of a Binary Coverage Model. The dark circle represents the area around the station that is “covered” by that station. The light grey circle is the area around the station that is “uncovered”. As you can see, with the Binary Coverage Model, all demand from node B would be considered “covered,” whereas all demand from node A would be considered “uncovered”.

Figure 2: Probabilistic Coverage

Figure 2 is a representation of a Probabilistic Coverage Model. In this figure, we represent coverage as a gradient, where demand nodes closer to the station have improved coverage compared to those that are farther away. Instead of evaluating only the travel time to assess coverage, we model the probability that a unit can arrive at a location within a certain time target. As you can see, with the Probabilistic Coverage Model, all demand from both nodes A and B would receive coverage; however, node B would receive better service.

Use expected performance when possible

Whenever possible, you should use expected performance when re-configuring stations. This approach has been shown to be very accurate in terms of predicting coverage changes as it accommodates the realistic variability that occurs. You will not only place stations where they are needed the most, but you will be able to more accurately predict the impact of adding or moving stations.

Daniel Haight

Daniel Haight

Daniel Haight is the President and co-founder of Darkhorse Analytics and Darkhorse Emergency Services. He is a Certified Analytics Professional and an award-winning lecturer at the University of Alberta School of Business. His current work focuses on predictive analytics and data visualization. His goal is to help managers make better decisions by combining their experience with the power of analytics. His even bigger goal is to design a company where Monday mornings are more exciting than Friday afternoons.

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