Hi,
As per the request you mentioned above:
PUT /d431-bibliotheque/v1/livre/2753800189 HTTP/1.1
When you create a virtual service using RR pairs, select transport protocol and while configuring provide target host and select Gateway. In this case whatever you will provide in the request will appear in "base path" of step "virtual https listener".
For Ex. - If you provide PUT /d431-bibliotheque/v1/livre/2753800189 HTTP/1.1 in request
The Basepath will be looks like - /d431-bibliotheque/v1/livre/2753800189
--
Kailash