How bad is time variability for users in mobility services?

TL;DR

This paper develops a theoretical framework to quantify the worst-case impact of time variability on users in mobility services, providing upper bounds on costs and guiding service design and pricing decisions.

Contribution

It introduces an expected utility framework to establish upper bounds on the cost ratio of variability to total cost, applicable across different utility and risk preference models.

Findings

For quadratic utility, the cost ratio is at most 1/2 CV^2.

Under Poisson assumptions, the ratio is at most 1/2.

The ratio depends on risk preferences, including RRA and RP.

Abstract

Time variability is a pervasive feature of mobility services and a major source of welfare loss. Although literature has quantified the cost of time variability (COTV), it remains theoretically unclear how bad time variability can be in the worst case. Without such a benchmark, quantified variability costs lack a principled reference for assessing whether they are economically meaningful. Meanwhile, this benchmark is critical for strategic prioritization in transport appraisal, service design, and pricing -- particularly in early-stage decision making where detailed valuation is often infeasible. To fill this gap, this paper develops an expected utility (EU) framework to quantify the cost of time (COT) and COTV, establishing theoretical upper bounds on the ratio $COTV/COT$. For users with quadratic utility, we show $COTV/COT \le 1/2 CV^2$, where $CV$ is the coefficient of variation of service time. For Poisson processes, a common assumption, this bound simplifies to $COTV/COT \le 1/2$, implying the total cost of a stochastic service is at most 1.5 times that of an otherwise identical deterministic service. In more general settings, the ratio depends on three interpretable factors: $CV$ and users' second- and third-order risk preferences, captured by relative risk aversion (RRA) and relative prudence (RP). We identify benchmark values of RRA and RP that characterize preferences over mean-, variance-, and skewness-related reductions. Our analysis extends to non-EU frameworks, including dual theory and rank dependent utility, showing that key structural insights remain robust. By quantifying the cost induced by time variability and the $COTV/COT$ ratio, this study provides a data-light benchmark for early-stage decision making and a principled upper bound on users' willingness to pay for reliability improvements, informing the pricing and design of reliability-oriented services.