Highlights • A unified model of time duration perception is proposed that subsumes, within one expression, systematic bias and random variability in perception. • A new functional form is proposed to represent bias in perception as an alternate to the more popularly used Stevens’ power law. • This study provides a psychology theoretical grounding for use of multiplicative error terms to represent random variability in perceived quantities. • Proposed perception model is embedded into an order response framework that allows extraction of how quantities are perceived from categorical responses. • The ideas are illustrated through an application on the determination of level of service at toll plazas.

Abstract This work attempts to bring to the fore the importance of explicitly modelling how time (or other physical quantities like distance) is perceived in the analyses of phenomena or behaviors where time (or other physical quantities) plays an important role. To do so the application area of level of service at toll plazas is chosen. Principles arising out of past work on the psychophysics of time perception are seamlessly incorporated into a novel unified model that accounts for both bias and random errors in perception. Multiplicative error terms arise naturally in this model. Results indicate that it is important to include both bias and random errors while modelling perception as ignoring the bias leads to high variance in the error term. Interestingly the pattern of bias in perception of time seems to remain steady across various waiting line situations from disparate contexts. Finally, the proposed model creates a framework that can be used to determine how time durations are perceived by humans when responses about perceptions are provided through categories like very small, small, etc. whose definitions are also concurrently identified. Such a framework can be used to study a wide range of situations both in transportation (such as route choice, mode choice, gap acceptance, and overtaking) and elsewhere. From a narrower perspective, this methodology can be used, as has been done here, to (i) determine level of service category definitions in terms of observable and “engineerable” variables (actual or measured delay faced by vehicles) even though it is the perceived value (a latent variable) that determines travelers’ responses on the quality of service, and (ii) identify parameters that define the systematic bias and randomness in perceptions.