Innovative Sampling Plans for Estimating Transit Passenger-Kilometers

Abstract

Estimating passenger-kilometers or passenger-miles to meet National Transit Database requirements usually involves costly sampling. Three innovative sampling plans are described that have been developed to reduce sampling requirements. The first method, which proved to be very effective when total boardings is known, uses a small number of ride checks (ons and offs by stop) on each route. Average trip length is estimated as a combined ratio estimator from a stratified sample. The second method was applied where the boardings total is not known. It uses both a sample of ride checks and another sample (needed for another purpose) that measures only boardings. A “mixed estimator” is derived that optimally combines two separate estimators: a simple mean from the ride check sample and an average trip length from the ride check sample multiplied by average boardings from the other sample. This second method proved effective for a single light-rail line but only marginally effective for a large bus system with widely varying route lengths. The third method exploits the pattern of symmetry in boarding and alighting patterns in opposite directions to estimate average trip length by route using boardings data only. Average trip length is the algebraic difference between the boardings centroids in the two directions. For the two routes analyzed, this method turned out to be ineffective in comparison with other methods because of high between-trip variability in the boardings centroids.

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