VCI, a Regional Volume/Capacity Index Model of Urban Congestion

This paper proposes a simple model of regional average congestion delay as a closed-form differentiable function of published regional transportation system volume and capacity. Three initially undefined parameters are calibrated by regression to best match the regional congestion delay estimates of Texas Transportation Institute’s (TTI) “mobility” analysis of 85 U.S. urban regions. The model fits the TTI delay data quite well with goodness of fit parameter $R_a^2=86\%$ and standard error of congestion delay estimate 0.046 min/mi. The model is analytic, that is, differentiable as opposed to discrete data tables. Use of the model is illustrated by closed-form estimates applicable to any urban area with numeric examples of several region descriptive statistics of interest including (1) regional total and average congestion delay for a region not in the TTI ensemble; (2) marginal congestion benefit of freeway lane-mile capacity addition and benefit/cost; (3) capacity addition necessary to improve the region to match congestion delay of the median congested U.S. city (Memphis); (4) “marginal external cost” (delay) of congestion imposed on all other vehicles, per vehicle-mile of added volume; (5) the volume-to-capacity index “point of diminishing return” beyond which further capacity addition would cost more to build than it would return in congestion delay savings and the potential long-term savings of building to that “least total cost” point; and (6) the economic implications of a hypothetical national “build-our-way-out” program which would eliminate all “excess” urban congestion that is costing us more than would the additional capacity to eliminate it.