An asymptotic approximation of the traveling salesman problem with uniform non-overlapping time windows

We develop a continuous asymptotic approximation of the traveling salesman problem with time windows in the Euclidean plane, constructing upon the well-known Beardwood-Halton-Hemmersley theorem. The time windows are taken to be a partition of a given time horizon. Computational experiments on random TSP with time windows instances show that the proposed asymptotic approximations of tour lengths and arrival times are close to the actual optimal values.