Flattening the curve: Insights from queueing theory.

The worldwide outbreak of the coronavirus was first identified in 2019 in Wuhan, China. Since then, the disease has spread worldwide. As it is currently spreading in the United States, policy makers, public health officials and citizens are racing to understand the impact of this virus on the United States healthcare system. They fear a rapid influx of patients overwhelming the healthcare system and leading to unnecessary fatalities. Most countries and states in America have introduced mitigation strategies, such as using social distancing to decrease the rate of newly infected people. This is what is usually meant by flattening the curve. In this paper, we use queueing theoretic methods to analyze the time evolution of the number of people hospitalized due to the coronavirus. Given that the rate of new infections varies over time as the pandemic evolves, we model the number of coronavirus patients as a dynamical system based on the theory of infinite server queues with time inhomogeneous Poisson arrival rates. With this model we are able to quantify how flattening the curve affects the peak demand for hospital resources. This allows us to characterize how aggressive societal policy needs to be to avoid overwhelming the capacity of healthcare system. We also demonstrate how curve flattening impacts the elapsed lag between the times of the peak rate of hospitalizations and the peak demand for the hospital resources. Finally, we present empirical evidence from Italy and the United States that supports the insights from our model analysis.

Beyond safety drivers: Applying air traffic control principles to support the deployment of driverless vehicles.

By adopting and extending lessons from the air traffic control system, we argue that a nationwide remote monitoring system for driverless vehicles could increase safety dramatically, speed these vehicles' deployment, and provide employment. It is becoming clear that fully driverless vehicles will not be able to handle "edge" cases in the near future, suggesting that new methods are needed to monitor remotely driverless vehicles' safe deployment. While the remote operations concept is not new, a super-human driver is needed to handle sudden, critical events. We envision that the remote operators do not directly drive the vehicles, but provide input on high level tasks such as path-planning, object detection and classification. This can be achieved via input from multiple individuals, coordinated around a task at a moment's notice. Assuming a 10% penetration rate of driverless vehicles, we show that one remote driver can replace 14,840 human drivers. A comprehensive nationwide interoperability standard and procedure should be established for the remote monitoring and operation of driverless vehicles. The resulting system has potential to be an order of magnitude safer than today's ground transportation system. We articulate a research and policy roadmap to launch this nationwide system. Additionally, this hybrid human-AI system introduces a new job category, likely a source of employment nationwide.