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When it comes to packet switching, it does not create a permanent physical path like Circuit switching. It uses packets and they use different paths to reach the destination. Also packet switching maintains a VC (virtual circuit). Has two parts, PVC and SVC. PVC provides a permanent path to forward the data and eliminates the need of call setup.

Now my question is, if packet switching has no permanent paths like circuit switching, then what happens in PVC ? What kind of Permanent Virtual Circuit is that? If packet switching uses many paths to send data, why it uses a Permanent Virtual Circuit ?

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Also packet switching maintains a VC (virtual circuit). Has two parts, PVC and SVC. PVC provides a permanent path to forward the data and eliminates the need of call setup.

To be clear: packet switching does not maintain a virtual circuit. There are certain packet switching technologies, or technologies designed for packet switching that do (ie Frame Relay, MPLS, TCP), but as a whole, this isn't how packet switching works. Circuits were required in circuit-switched networks. Since circuits (used in this context) are not relevant anymore, but the technology used that relied on them (the phone system) is, we now have the need to emulate them in packet switched networks, hence "virtual circuits."

In relation to Frame Relay (actually not just Frame Relay - this is relevant in ATM and X.25), SVC and PVC are two different types of virtual circuits. Virtual circuits are paths that are determined through a Frame Relay or ATM/X.25 network (although not many of these exist anymore, aside from some DSL ISPs). PVC is predetermined and configured explicitly (hence "permanent") and SVC is set up "on the fly" in a more dynamic fashion (as-needed basis). IIRC there wasn't much support for SVC's in Frame Relay and from an operational perspective PVC's were more desirable because there were less moving parts (things to troubleshoot/go wrong).

This Wikipedia snippet on virtual circuits in the context of Frame Relay and ATM goes into detail on what "virtual circuit" actually means.

If packet switching uses many paths to send data, why it uses a Permanent Virtual Circuit?

Packet switching can use many paths to send data, but some network layer protocols that run on top of the packet switched network (ie MPLS, ATM, Frame Relay, etc) have a requirement that data is always sent over the same path - the path is the virtual circuit. In MPLS it's called an LSP. In Frame Relay (and ATM) it's called a PVC.

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