Modeling Spatio-Temporal Networks

Growing importance of application domains such as location-based services and evacuation planning highlights the need for efficient modeling of spatio-temporal networks (e.g. road networks) that takes into account changes to the network over time. The model should provide the necessary framework for developing efficient algorithms that implement frequent operations posed on such networks. A frequent query that is posed on such networks is to find the shortest route from one place to another or a search for the nearest neighbor. The shortest route would depend on the time dependent properties of the network such as congestion on certain road segments, which would increase the travel time on that segment. The result of nearest neighbor search could also be time sensitive if it is based on a road network. Modeling such a network poses many challenges. Not only should the model be able to accomodate changes and compute the results consistent with the existing conditions, it should do so accurately and simply. In addition, the need to answer frequent queries quickly means fast algorithms are required for computing the query results. The model should thus provide sufficient support for the design of correct and efficient algorithms for the frequent computations. Often dynamic networks have been modeled as time expanded networks, where the entire network is replicated for every time instant. The changes in the network, especially the travel time variations, can be very frequent and for modeling such frequent changes, the time expanded networks would require a large number of copies of the original network, thus leading to network sizes that are too memory expensive. For example, traffic sensors on highway networks send measurement data every 30 seconds. A one-year dataset may need over one million copies of the road network, which itself may have a million nodes and edges for each time instant. Such large sized networks would also result in computationally expensive algorithms. The proposed model, a time-aggregated graph, models the changes in a spatio-temporal network by collecting the node/edge attributes into a set of time series. The model can also account for the changes in the topology of the network. The edges and nodes can disappear from the network during certain instants of time and new nodes and edges can be added. The time-aggregated graph keeps track of these changes through a time series attached to each node and edge that indicates their presence at various instants of time. Our analysis shows that this model is less memory expensive and leads to algorithms that are computationally more efficient than those for the time expanded networks.