Dynamically Computing Fastest Paths for Intelligent Transportation Systems - ADITI BHAUMICK ab3585

OBJECTIVE: To gather real time data about traffic flow in order to compute the fastest paths between two locations. Data is gathered over a continuous traffic flow and not at discrete locations.

RESULTS: Table 1: Algorithmic running time comparisons for fastest path algorithms.

RESULTS: Table 2:Actual running time comparison for fastest path algorithms.

OUTLINE: ASSUMPTIONS PROBLEMS ADDRESSED ALGORITHMS

ASSUMPTIONS: The traffic flow is analysed assuming a complete simulation of continuous traffic flow of a freeway system can be obtained at any given point in time. A free flowing transportation system is characterized as a directed graph G=(V,E) where a vertex V is defined as a location and an edge E is defined as a section connecting two vertices.

PROBLEMS ADDRESSED: From this representation of traffic flow, there are two separate problems that need to be addressed: To gather the speed and location of all the vehicles in the entire transportation system. To use this data optimally in order to determine the fastest path.

ALGORITHMS: Pre-computated class of algorithms: Takes advantage of the fact that the graph is static. The worst case time to pre-compute. Three kinds

CONSTANT UPDATE ALGORITHM: Updates the speed in constant time. The algorithm computes the fastest path when requested by a vehicle. Worst case running time is O (Vm).

CONSTANT QUERY ALGORITHM: Sacrifices the speed of updating an edge for the time to retrieve fastest path. This algorithm always maintains the fastest path between all pairs of vertices by recalculating the fastest paths for all pairs of vertices that have a path containing the updated edge, whenever an edge update occurs. Worst case running time is O ( V^2 mlogm)

HYBRID ALGORITHM: Attempts a compromise by maintaining the amount of time it takes to traverse each path whenever an edge update occurs. To retrieve the fastest path the application will only have to compare the times to traverse all m paths from the source to the destination and can be achieved in O (V^2m).

CONCLUSION: With respect to Table 1, the constant update algorithm will work best in a live setting. With respect to Table 2, the constant query algorithm is the fastest but not the most cost effective. In a real-time situation, the number of edge updates will greatly exceed the number of fastest path queries, hence the Constant Update Algorithm executes the fastest.