I have a dataset of some measurements along a bus route (image below). The purpose of my study is to be able to detect the values at any location along the route using Kriging interpolation. I have very weak background in geostatistics, I attended a few online tutorials on using geostat in R and how to calculate and plot the variogram of spatial data. My concern is can I calculate the variogram of data that is spatially distributed linearly along routes instead of covering a wide plane?

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You would calculate it exactly as you would any variogram: by estimating the values of (Z(i) - Z(j))^2/2 as a function of the distance between data locations i and j. You have many choices of distance, but the natural ones would be either distance along the routes or travel time along the routes.

If the routes are one-way, additional techniques borrowed from time series analysis could be helpful: these exploit the direction of time (or, analogously, of distance along the route). Such directionality is not available in higher dimensions. That, and the fact that most time series are sampled at regular intervals while most spatial datasets have supports at irregularly spaced locations, are the basic reasons why the techniques of kriging and of time series analysis seem to differ.

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