The standard of IEEE 1588-2008 introduced P2P (peer to peer) mechanism to measure communication delay,what is the advance compared to request response mechanism in IEEE 1588-2002.
This answers your question precisely. In short, the original mechanization, which uses four separate timestamps, does not require that each switch in the path be IEEE 1588 compliant. This same algorithm is used in NTP.
The peer to peer option's advantage is that it reduces the number of timestamps needed, but each switch has to be an IEEE 1588 switch. In this case, the switch already knows the delay introduced by the network.
Both options assume the delay in both directions is the same. In the peer to peer method, where there's only a single link involved, that assumption is fairly accurate!
http://blog.meinbergglobal.com/2013/09/19/end-end-versus-peer-peer/
One last comment I might have is that in order to achieve the nanosecond accuracies often touted for IEEE 1588, you cannot have many non-IEEE 1588 switches in the path. Even with the end to end scheme.
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