Indexing moving objects (MO) is a hot topic in the field of moving objects databases since many years. An impressive number of access methods have been proposed to optimize the processing of MO-related queries. Several methods have focused on spatio-temporal range queries, which represent the foundation of MO trajectory queries. Surprisingly, only a few of them consider that the objects movements are constrained. This is an important aspect for several reasons ranging from better capturing the relationship between the trajectory and the network space to more accurate trajectory representation with lower storage requirements. In this paper, we propose T-PARINET, an access method to efficiently retrieve the trajectories of objects moving in networks. T-PARINET is designed for continuous indexing of trajectory data flows. The cornerstone of T-PARINET is PARINET, an efficient index for historical trajectory data. The structure of PARINET is based on a combination of graph partitioning and a set of composite B+-tree local indexes. Because the network can be modeled using graphs, the partitioning of the trajectory data makes use of graph partitioning theory and can be tuned for a given query load and a given data distribution in the network space. The tuning process is built on a good quality cost model that is supplied with PARINET. The advantage of having a cost model is twofold; it allows a better integration of the index into the query optimizer of any DBMS, and it permits tuning the index structure for better performance. The tuning process can be performed before the index creation in the case of historical data or online in the case of indexing data flows. In fact, massive online updates can degrade the index quality, which can be measured by the cost model. We propose a specific maintenance process that results into T-PARINET. We study different types of queries and provide an optimized configuration for several scenarios. T-PARINET can easily be integrated into any RDBMS, which is an essential asset particularly for industrial or commercial applications. The experimental evaluation under an off-the-shelf DBMS shows that our method is robust. It also significantly outperforms the reference R-tree-based access methods for in-network trajectory databases.