rdf Stream Processing (rsp) is a rapidly evolving area of research that focuses on extensions of the Semantic Web in order to model and process Web data streams. While state-of-the-art approaches concentrate on server-side processing of rdf streams, we investigate the Triple Pattern Fragments Query Streamer (tpf-qs) method for server-side publishing of rdf streams, which moves the workload of continuous querying to clients. We formalize tpf-qs in terms of the rsp-ql reference model in order to formally compare it with existing rsp query languages. We experimentally validate that, compared to the state of the art, the server load of tpf-qs scales better with increasing numbers of concurrent clients in case of simple queries, at the cost of increased bandwidth consumption. This shows that tpf-qs is an important first step towards a viable solution for Web-scale publication and continuous processing of rdf streams.