Can a stack of raspberry pi zero Ws effectively run Hadoop? Would it be better to have a
Pi Model 3 B as the router node and use pi zeros for the slave nodes?
Are IoT and data processing not suggested applications for the Pi Zero W?
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You may be confused about what the Pi is and isn't. While the Pi3 has a 4 core chip, it is an ARM chip designed for cellphones. It also only has 1GB of Memory, and 100Mbps Ethernet. While there are many things that the Pi does well memory intensive and number crunching workloads are not one of them.
Could a Pi run Hadoop probably, but the performance is likely to be unacceptable. In fact, if you can run it satisfactorily on a PI, I would argue that you don't really need Hadoop for your workload (i.e. you don't really have big data). You would be far better off, even if only as a learning exercise, running Hadoop in the cloud (e.g. AWS or Hadoop as a service).
IoT applications are a common use of the Raspberry Pi, However, you will need to better define that term. All IoT workloads are not created equal. A dryer that tweets when it is finished requires far less in terms of spec than a project designed to automate an entire house (security, HVAC, lights etc.).