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Edge computing takes localised processing a bit further than Fog Computing, because it allows for actions to be taken on-site, in the processing point. This poses an advantage over Fog Computing as there are less points of failure. Each item in the chain is more independent and capable of determining what information should be stored locally and what needs to be sent to the cloud for further use. This is achieved by giving intelligence to the edge through programmable automation controllers (PAC). The sensors connect to the PAC’s which allows the edge to handle processing, communication and more. [1].
A cleaning system in a Fog computing scenario, for example: the vacuum cleaner roams over the floor and encounters dirt, sends that information to the closer fog node, where this information is analysed and processed and a command is issued to the vacuum cleaner to execute.
 

Fig.1. Fog Computing Scenario

 
In an Edge computing scenario the vacuum cleaner is smart enough to know what to do, and only needs to send the information that found dirt and what was the decision made.
 

Fig.2. Edge Computing Scenario

Of course this is a fairly harmless situation, but in a situation where an important system on an airplane fails, we will want a quick response to solve this failure from the device and not wait for the solution that the nearest fog node can give us.
There are not many IoT devices that support this real-time processing, but the evolution of processing power (as can be seen in the Eyeriss Project [2] from MIT and the Curie Module [3] from Intel) associated to the machine learning growth, will offer a higher level of performance and complex computations on-site, that previously would be only available within the cloud [4].
References

  1. How does fog computing differ from edge computing?, http://readwrite.com/2016/08/05/fog-computing-different-edge-computing-pl1/
  2. Eyeriss: An Energy-Efficient Reconfigurable Accelerator for Deep Convolutional Neural Networks, http://www.mit.edu/~sze/eyeriss.html
  3. Intel Curie Model, http://www.intel.com/content/www/us/en/wearables/wearable-soc.html
  4. Ready for the disruption from edge computing?, https://www.ibm.com/blogs/internet-of-things/edge-computing/