Dynamic travel time models for pricing and route guidance : a fluid dynamics approach

This thesis investigates dynamic phenomena that arise in a variety of systems that share similar characteristics. A common characteristic of particular interest in this work is travel time. We wish to address questions of the type: How long does it take a driver to traverse a route in a transportation network? How long does a unit of product remain in inventory before being sold? As a result, our goal is not only to develop models for travel times as they arise in a variety of dynamically evolving environments, but also to investigate the application of these models in the contexts of dynamic pricing, inventory management, traffic control and route guidance. To address these issues, we develop general models for travel times. To make these models more accessible, we describe them as they apply to transportation systems. We propose first-order and second-order fluid models. We enhance these models to account for spillback and bottleneck phenomena. Based on piecewise linear and piecewise quadratic approximations of the departure or exit flows, we propose several classes of travel time functions. In the area of supply chain, we propose and study a fluid model of pricing and inventory management for make-to-stock manufacturing systems. This model is based on how price and level of inventory affect the time a unit of product remains in inventory. The model applies to non-perishable products. Our motivation is based on the observation that in inventory systems, a unit of product incurs a delay before being sold. This delay depends on the level of inventory of this product, its unit price, and prices of competitors.