This is how I visualize how SONET carry ATM, and how ATM carry IP:
Is my visualization correct?
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The only thing that i would advise changing is that SONET devices are not 'switches' They do not decapsulate or encapsulate at layer-2. They put received frames into containers and transmit them within the configured time slot along a pre-determined path, that does not change. Normally they would be referred to as 'SONET ring' or layer-1 path.