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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
https://mapproxy.org/ is also worth a look. It caches the request to a mapping service, that way you could also reduce the expensive request to the map box api, if mapbox uses a standardized wms or tiling service map proxy should work.
NOTE:
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