Matthew A. Rigdon

Formulating and Solving Service Network Pricing and Resource Allocation Games as Differential Variational Inequalities

In this chapter we show how certain noncooperative Cournot-Nash dynamic games arising in service pricing and resource allocation may be articulated as differential variational inequalities. We show how such problems may be solved using a fixed point algorithm having continuous time optimal control subproblems.

Computing Dual Time Scale Dynamic User Equilibria

This chapter presents a dual time-scale model of dynamic network traffic flows that integrates a day-to-day demand growth model with a differential variational inequality formulation of within-day Dynamic User Equilibrium (DUE); this model is compatible with a variety of network loading models. The differential variational inequality formulation are given for within-day DUE advantages: (1) the differential variational inequality may be very easily analyzed using the minimum principle from optimal control theory; (2) the fixed point algorithm is able to consider non-differential and non-analytic path delay operators; and (3) the rapidly growing literature on different variational inequalities will likely yield additional computational tools in the years ahead that may be exploited to find DUE flows.