  This paper proposes a generalised framework for density estimation in large
networks with measurable spatiotemporal variance in edge weights. We solve the
stochastic shortest path problem for a large network by estimating the density
of the edge weights in the network and analytically finding the distribution of
a path. In this study, we employ Gaussian Processes to model the edge weights.
This approach not only reduces the analytical complexity associated with
computing the stochastic shortest path but also yields satisfactory
performance. We also provide an online version of the model that yields a 30
times speedup in the algorithm's runtime while retaining equivalent
performance. As an application of the model, we design a real-time trip
planning system to find the stochastic shortest path between locations in the
public transit network of Delhi. Our observations show that different paths
have different likelihoods of being the shortest path at any given time in a
public transit network. We demonstrate that choosing the stochastic shortest
path over a deterministic shortest path leads to savings in travel time of up
to 40\%. Thus, our model takes a significant step towards creating a reliable
trip planner and increase the confidence of the general public in developing
countries to take up public transit as a primary mode of transportation.
