Read your writes, also known as read my writes, requires that if a process performs a write w, then that same process performs a subsequent read r, then r must observe w’s effects.
Note that read your writes does not apply to operations performed by different processes. There is no guarantee, for instance, that if process 1 writes a value successfully, that process 2 will subsequently observe that write.
Read your writes is sticky available: if a network partition occurs, every node can make progress, so long as clients never change which server they talk to.
Viotti and Vukolić define read your writes straightforwardly: for any write, and any read, if the write falls before the read in a given session (process), then the write must be visible to the read. In other terms, the session order (restricted to just writes -> reads), is a subset of the visibility order.