Technology Category
Planning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsReasoning under Uncertainty: Decision/Utility TheoryApplication Domains: Transportation
How bad is time variability for users in mobility services?
🤖 AI Summary
This study addresses the absence of a theoretical upper bound on welfare losses caused by temporal variability in transportation services, which hinders early-stage economic decision-making. The authors develop an expected utility framework and derive, for the first time, a theoretical upper bound on the ratio of the cost of temporal variability to the cost of time (COTV/COT). Under a Poisson arrival assumption, they prove this ratio does not exceed 1/2, implying that the total cost under stochastic service is at most 1.5 times that under deterministic service. This bound is jointly determined by the coefficient of variation, relative risk aversion, and relative prudence. The result’s robustness is further confirmed in non-expected utility settings using quadratic utility, duality theory, and rank-dependent utility models, offering a data-light theoretical benchmark for transportation service design and reliability-based pricing.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
time variability
cost of time variability
welfare loss
transport appraisal
reliability
Innovation
Methods, ideas, or system contributions that make the work stand out.
cost of time variability
expected utility
theoretical upper bound
risk preferences
transport reliability
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