Analyzing and Managing Service Networks with Self-routing Users

Motivated by networks with self-routing users who choose service facilities, we develop a network congestion model to analyze and improve decentralized system performance in cases where control by a centralized planner is not possible. We assume that individuals choose a facility for service based on a utility function that depends on travel time and the utility of service provided at a facility, where the latter is a function of the number of people (congestion) and a facility-specific scalar called a “congestion weight.” We develop models that capture individual behavior in this context and present an algorithm for finding a stable decentralized solution. Our approach demonstrates that the bounds on worst- and best-case decentralized system performance (prices of anarchy and stability, respectively) depend on the congestion weights. A major finding is that changing congestion weights makes it possible to achieve a stable decentralized solution that is also centrally optimal. We describe ways that congestion weights can be changed in practice and present efficiently-solvable optimization models capable of finding appropriate weights. Computational results for a problem motivated by the 2009 – 2010 H1N1 pandemic influenza vaccination campaign illustrate the usefulness of our models and algorithms for supporting policy and planning decisions.