A provider edge router (PE router) is a router between one network service provider's area and areas administered by other network providers.
[1] A network provider is usually an Internet service provider as well (or only that).
The term PE router covers equipment capable of a broad range of routing protocols, notably: PE routers do not need to be aware of what kind of traffic is coming from the provider's network, as opposed to a P router that functions as a transit within the service provider's network.
However, some PE routers also do labelling.
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