Braess’ paradox deals with networks where when users selfishly choose the best route, under certain circumstances, adding additional capacity increases travel time. We also applied the concept of Nash equilibrium to analyze Braess’ paradox. A Stanford professor Sunil Kumar explores the question of how to increase capacity and throughput without risking increasing delays in his research paper Customer Choice and Routing in Queuing Networks. In a summary of his work, an article describes a scenario where additional choice can be added to queuing networks in order to make them more efficient.

The paper involves analyzing a simple two-station service system and what rules are necessary to maximize efficiency. An example of such a station is a Starbucks that has a payment and a coffee counter, and people choose which to go to first. In this situation, if the coffee counter became overwhelmed, the coffee server would give priority to those who have already paid (in order to encourage people to use the cashier first). If the cashier became overwhelmed, those who have picked up their coffee would receive priority. The dynamic change in rules would increase efficiency even after customers have made their decisions.

The cause of the suboptimal queues is that customers’ selfish decisions result in a Nash equilibrium that is not Pareto optimal or a social welfare maximizer. Simply stated, the “user-determined equilbria” deviates from the “system-optimal equilibria.”(1) Kumar’s research deals with creating theoretical rules that would balance the load. His theories have applications in many situations where queues are used such as communication networks, manufacturing, and even the DMV.