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.
Here is the population density map for that area:
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.
The distribution pattern can also be seen in the analysis maps, such as this Serving
Site map:
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 .
- 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:
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.