We consider a generic deterministic time-invariant fluid model of a single server switched network, which consists of finitely many infinite size buffers (queues) and receives constant rate inflows of jobs from the outside. Any flow undergoes a multi-phase service, entering a specific buffer after every phase, and ultimately leaves the network; the route of the flow over the buffers is pre-specified, and flows may merge inside the network. They share a common source of service, which can serve at most one buffer at a time and has to switch among buffers from time to time; any switch consumes a nonzero switchover period. With respect to the long-run maximal scaled wip (work in progress) performance metric, near-optimality of periodic scheduling and service protocols is established: the deepest optimum (that is over all feasible processes in the network, irrespective of the initial state) is furnished by such a protocol up to as small error as desired. Moreover, this can be achieved with a special periodic protocol introduced in the paper. It is also shown that the exhaustive policy is optimal for any buffer whose service at the maximal rate does not cause growth of the scaled wip.