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I have a couple of doubts about if these scenarios are suitable to be modeled as a Poisson process. I will like to have your views and arguments why.

  1. Packets are lost due to packet overflow in the switch.

  2. Trucks pass by on a highway

  3. Goals are scored in a soccer game

  4. Buses arriving a bus stop.

My view : Thinking of one of the Poisson properties which is independence, I believe the first scenario of packets cannot be modeled as a Poisson process because, the next packet is dependent of the last packet(the packet that caused the overflow).

The second will be a Poisson process since the arrivals of trucks on a highway are independent of each other. Also the third can be modeled as a Poisson process because goals scored are independent to others (but it can be debatable since team motivation because of past goals can be a contributing factor to another goal)

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All these depend a lot on various circumstances that may or may not be the case in a particular application. For example, in (2) the Poisson model may be good if traffic is light and flowing freely, but not if it's a two-lane highway with few passing opportunities where traffic tends to bunch up behind the slower vehicles. Poisson would not be a good model for (4) if it's a well-run transit system where buses stick closely to a regular schedule.

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