Collision Calculator?

Hello,

I am thinking about packet collision. Everything I found so far about this is highly academical (I have no objection to this). Still, some numbers would be pretty interesting. I am totally aware that a perfect calculation is highliy complex (in reality, the 8 channels available are not used evenly, is it a full duplex gateway or not? If no, how many downlinks per uplink will the gateway send?), but having some rough numbers would be nice to get a feeling. Maybe someone even coded a calculator?

What I am looking for is something like:
Assumption1: Indoor Monitoring of a big building using 500 sensors. 50% send on SF7, 25% on SF8 and 25% on SF9. Each sensor sends each 10 minutes. The payload length is 15 Bytes. Question: How many packets (0.01%, 0.1%, 1%, 10%) will get lost due to collision?

Calculating the airtime for an uplink is easy, but calculating the probability that 2 packets will be sent simultaneously seems the complex part - but is it really that complex or a rather simple formula?

What are your experiences regading this very theoretical topic?

Thanks & best regards
Philipp

One of the big questions is how random things really are. If you have ten minute intervals, how do you get them well distributed, instead of pathologically clustered? Is your randomization of uplink frequencies actually fair?

Academics may be tempted to assume a nice distribution. Firmware developers may worry less about theoretical capacity than trying to make the best of whatever the situation actually is.

In a real setup you’ll run into things you didn’t think about, such as nodes nearer the gateway (eg, your SF7 ones) swamping out the ability to hear really far nodes even on different frequencies.

Did you read the white paper from Olivier Seller on how to predict the network capacity ? https://lora-developers.semtech.com/uploads/documents/files/Predicting_LoRaWAN_Capacity_FINAL.pdf
There are some details on the collision probability.
He did a presentation of this paper a during last TTN conference: around 10min he discusses collision rate: https://youtu.be/VmYuItA6q4I?t=606

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