I am reading Network Layer in 'Computer Networking: A top-down approach'. It says,
Data plane operates at the nanosecond time scale and is implemented in hardware.
Whereas router's control functions operate at the millisecond or second timescale. These control plane functions are implemented in software and execute on the routing processor (typically a traditional CPU).
Now my question is about routing processor. Is routing processor (or traditional CPU) a hardware or software?
Routers are computers at all, so yes, their processor is an hardware
This is the point of moving from traditional legacy systems (hardware) on new enviroment implementing network functions virtually on software. You can start reading article like this. The main concept is that telecommunication operator want not only to improve Quality of user Experince (QoE) but also operational costs. Buying a network device for specific network function costs much more than moving this network function to dummy device. The function is implmented now on software.
Regarding routing process we realize that it is refered on SDN and not on NFV. The same logic is expanded on the other layers. SDN relies on l2 and l3 while NFV on the other layers.
So, despite the fact that implementig a router in specific hardware the is faster than implementig it in software, telecommunication operator has fewer costs (read about CAPEX). Another benefit moving to SDN and NFV enviroment that overcomes the above delay is that the "dummy" hardware will be moved on data centers in order to avoid networking delays. So, all the network functions such as DNS, routing, firewall etc will be transferd on data centers to reduce time and costs. So, user will have better QoE and telecommunication operator much better Return of Investment (RoI) - CAPEX.