Background (non-math): I'm planning to use Open Street Maps data to find the fastest route by car between points. Data is a directed graph where vertices represent locations, and edges are routes. Routes have weights that refer to: length and travel speed. There are numerous route finding algorithms, and I don't want to bother anyone with such obvious questions. The actual problem refers to the fact that I want to use traffic historical data. Traffic data is represented by an additional edge weights, that are used to modify travel speed per edge. Unfortunately the traffic data is available only for a subset of roads (edges). I need to find a "tool" to extrapolate the traffic data to edges that lack it. Without applying extrapolated traffic data the algorithms would automatically choose roads where the traffic data is missing.
Question: I don't have traffic data for all graph edges representing roads (only for a subset), and the missing data has to be extrapolated. What mathematical tools can I use to extrapolate/ fill/ guess the missing traffic data given following assumptions:
Assumptions:
- Ideal arbitrage is performed by drivers. Taking a route without (or partially without) traffic data shouldn't give an advantage.
- The solution can be either: geo-agnostic (refer only on nodes and edge weights) or take into account spatial data ie. physical proximity (or direction!) of graph edges. Any heuristic can take advantage of the fact that the routing happens for morning or evening rush hours. The traffic significantly differs depending on the direction. Thank you for your help!