Security decisions for complex systems such as airports and harbors aim to screen thoroughly without causing too much delay. The difficulty is that random arrival times, combined with uncertainty in when and where items needing additional screening appear, leads to congestion. This creates the need to incorporate stochasticity (randomness over time and space) in mathematical models of systems that are used to inform security decisions. We combine theoretic probabilistic and statistical analysis with applied numerical and simulation methodologies to develop and analyze such models.
Our basic research investigates performance analysis and control questions for abstract stochastic networks (that is, networks having flows random in time and space). Such networks can represent passenger flow in airports, goods flow from outside to inside the U.S. (and vice-versa), etc.
We use data to calibrate the input to our models, which could be probability distributions or could be raw between-node flow information. That allows us to simulate potential control policies for the network and analyze their performance.