Spatial-temporal environments contain large number of continuously moving objects on which variety of queries are executed, preferably within a real time. In such a dynamic system, processing location-based queries is a challenging problem. In this paper, the dynamic system has objects moving over a road of network. This paper proposes a new uncertainty model for this type of dynamic system. We applied this model on the indexing scheme that has recently been proposed, namely MON-tree. With our uncertainty model, we also explored a probabilistic query execution algorithm. For the purpose of an experimental evaluation, we set up a simulation environment that visualizes the movements and also provides a query processing capability. To achieve a better index storage utilization and query execution performance, we decreased the location update frequency of the dataset.