my company develops a web application that makes heavy use of web APIs (google adwords, recurly billing, facebook etc.)
can you recommend a product / service that could help us monitor the usage of the api calls for the purpose of limiting usage to predefined quotas, track billing, etc.?
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Facebook already has that built in, check out your Facebook app's Insights information. See https://developers.facebook.com/docs/insights/.
For any production level app where overages in API consumption could cause application failure (e.g. heavy use of your app by one or more users could spoil the experience for other users), my baseline recommendation would be to keep track of the call volumes to stay within your allotted quota. That being said, it's not easy.
Runscope is a suite of tools built for API usage monitoring, API testing and debugging. The feature you're looking for is called Runscope Metrics. You have visual graphs that show usage (resolution by hour or day), and the ability to drill down to the endpoint path and method level. Additionally, Metrics also reports performance/latency.