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Re:AWS Lambda Makes Serverless Applications a Reality by stephenitis on Tuesday November 24, 2015 @07:00PM (#10624490)
I used to work at Iron.io they have a product called IronWorker which gave 10GB temp disk. They allowed you to use your own docker containers also. they have a priority queueing system however and come at a premium over lamdba pricing due due to being more feature rich.

custom docker image use came with the overhead of burning in your instances though which I don't think is publicly available yet on the service.

Re:AWS Lambda Makes Serverless Applications a Reality by eistrati on Tuesday November 24, 2015 @07:20PM (#10624566)
We have used a combination of AWS Lambda + Amazon ECS, which is kind of similar what you're describing. We are working now to extend the abstracted library that empowers developers to choose programmatically what service to use: https://www.npmjs.com/package/deep-resource ;)