Express Points is a system for variable resolution analysis that greatly improves runtimes without compromising accuracy.

By default, analyses are performed based on a regular grid of "bins". Small bins are needed for high accuracy in critical areas such as population centers, but the smaller the bin size, the more bins are needed to analyze the whole network, which increases the runtime significantly. Traditionally cell planners have addressed this by analyzing the network in two or more phases: high resolution for downtown, low resolution eveywhere else. This makes the process more complicated and leads to poor accuracy in the borders between "high" and "low" resolution areas.

Using Express Points the whole network can be analyzed regardless of size whilst still maintaining high resolution in critical areas. Overture analyzes the density of subscribers in the network area and modifies the resolution accordingly.

Express Point Example

Consider the demo data, which contains population data for the Ann Arbor region.

Map of residential population in Ann Arbor

Here is the population density map for that area:

Map of residential population in Ann Arbor

Note that there is no signifcant population where there is water or in the fields of the surround rural area; clearly there is no point analyzing these areas in great detail.

The following Express Point map has been automatically generated by Overture; each distinct color is an analysis bin. More bins have been used in the high population areas and less in the low population areas.

Express points for Ann Arbor

The distribution pattern can also be seen in the analysis maps, such as this Serving Site map:

Service site map with variable resolution

Note the coarse resolution used in the rural cell edges, where accurate analysis is not required.

Controlling Express Point Distribution

Express Point properties can be modified by going to Analysis > Settings > Express > Properties.

  • Use Express Points. This should be True to enable express points.
  • Demand. A subscriber density map to use for the express point distribtution.
  • Maximum Area. The maximum area to allow for any one express point. This stops the analysis getting too "blocky" in areas like water where there are no subscribers at all.
  • Maximum Demand. The maximum number of demand units (typically subscribers) to allow for any one express point.
  • Maximum Service. The maximum bitrate from the aggregated services to allow for any one express points.

Express point generation works by dividing the whole network area into bins until each bin is below the Maximum property thresholds or the minimum bin size (as specified in the Analysis Region) has been reached.

Accuracy vs. Efficiency

Variable resolution analysis improves the intrinsic trade-off between calculation accuracy and efficiency. The user is encouraged to experiment to find the optimal settings, but the defaults have been found to offer a good balance in general.

Consider the example data again, the following table shows how the Maximum Demand property affects the number of express points used:

Maximum Demand # Points % Points (of total possible)
(Express Points off) 0 296905 100.00
0.1 244750 82.43
1 109316 36.82
10 34183 11.51
100 4632 1.56

This table tells us that if we focus the analysis on individual subscribers (Maximum Demand = 1), we only need ⅓ of the points, which means our analysis will be 3 times faster. Similarly, if we focus on blocks of 10 subscribers, the analysis will be 10 times faster.

Clearly there are performance benefits, but what is the effect on accuracy? If we run signal cover statistics for area and subscribers for different % of express points, we see the following pattern:

Graph of Statistic Accuracy vs. Express Point %

The accuracy of the statistics is maintained until the number of express points falls below 10%. Even when the number of express points is 1.56%, the area calculation is within 0.52% of the true answer and the subscriber calculation is within 0.27%. Given that this allows the statistic to run 64 times faster, it is clearly an attractive trade-off.

 
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