User-Optimal and System-Optimal Route Choices for a Large Road Network

Abstract

Solutions to the route choice problem for assumptions of user-optimality and system-optimality are presented for the road network of the Chicago region. Regionwide results show a 5% decrease in total travel time would be achieved during the morning peak period, if a system-optimal solution based on travel times were implemented. Among the costs of this solution is a 1.5% increase in vehicle-miles travelled. Findings for differences in link flows and individual origin-destination pairs complete the paper. IntroductionRoad pricing theory and analysis suggest that savings in travel time and related resources could be achieved if drivers were directed to travel along minimum marginal time routes. Equivalently, tolls based on the difference between marginal and average travel times might be used to induce drivers to shift to routes corresponding closer to a societal optimal. This theory has been well known since Beckmann et al. (1956); see Small (1992) and McDonald et al. (1999) for recent findings and syntheses of the road pricing literature. The objective of this paper is to seek answers to questions related to the magnitude and distribution of these travel time savings in a large, congested urban road network. Obtaining such answers depends upon a capability to determine the route choices under two alternative criteria suggested by Wardrop (1952) and Beckmann et al. (1956):• Drivers individually choose to follow their shortest time routes from their origins to destinations, leading to the situation that all used routes have equal travel time and no unused route has a lower travel time. Such a route pattern is called useroptimal or user-equilibrium, since it corresponds to a Nash equilibrium.

The potential of social routing advice

“…Note that the total vehicle kilometres travelled increases at higher network efficiency. These findings are in line with findings by Boyce and Xiong (2004), who compared SO-routes with UE-routes for several OD-pairs. The observed trend is present for all equilibria although it appears to be stronger at higher social trip shares, as expected.…”

“…In real-world networks, however, savings up to only 10% of total travel time would typically be attained (see e.g. Boyce & Xiong, 2004;Jahn et al, 2005). Note that potential travel time savings highly depend on the prevailing congestion level (e.g.…”

Towards improving resilience of cities: an optimisation approach to minimising vulnerability to disruption due to natural disasters under budgetary constraints

“…Thus far the literature reviewed attempted to minimise total travel time in a bid to assess a degraded network within the normative system optimal state. Whilst the system optimal objective of minimising total travel time is known to be a good benchmark to compare network states, the literature recognises that minimising total travel time makes some drivers travel longer to achieve efficiency (Boyce & Xiong 2004, Jahn et al 2005. In this research our aim is to minimise the vulnerability to disruption to keep up the connectivity levels which is completely different to the objective of improving efficiency.…”

Dynamic traffic diversion model based on dynamic traffic demand estimation and prediction

“…Traffic assignment has been developed from a single time value to more factors, such as the number of route choices set [5], customers’ pickup demands [6], whether information is provided or not [7, 8], driver characteristics [2], and the location of variable message signs [9, 10]. In most of the literature on this topic, the control objective for the routing control is to reach either system‐optimum or user‐equilibrium [11–16]. For the system‐optimal case, a set of control formulations usually aims at minimising a specific network performance index under the constraints of splitting rates at diversion points over a preset time horizon [17–21].…”