Well, i'm studying to a test, based on the following layers: link, internet, transport and application (Architecture TCP-IP) i would like to know which layer or layers "routers" work and why it can't work in another layers.
Generally speaking, routers utilize the IP protocol (i.e. IP addresses) to make decisions while directing traffic and do not care about the transport protocol. The IP protocol would map to the internet layer.
The TCP or UDP protocols would operate at the transport layer. Typically a device that would direct traffic based on transport layer protocols (or application layer) would include proxies, load balancers, or shaping devices depending on its exact function.
Devices that operate at the link layer (most often Ethernet today) would include switches or bridges.