Emergency modeling in transportation via queuing and game theory

In modern transportation network, emergencies on roadway and man-made emergencies in the infrastructure can incur enormous costs to society directly and indirectly. The direct costs include transportation cost due to incident delay and traffic congestion, and various risks brought upon the infrastructure by man-made emergencies. The indirect cost can include economic and psychological impacts on society.;Emergencies on roadways include accidents, disabled vehicles, adverse weather conditions, spilled loads, hazardous materials, etc. Under these cases, non-recurrent congestion will slow down the traffic flow on certain road link. In previous research, deterministic queuing models are often used for traffic flow modeling. However, due to the random environment of traffic flow, it is necessary to introduce stochastic elements into current traffic flow modeling. In our research, we use stochastic queuing models, such as Markov-modulated queuing systems, for traffic flow modeling under incidents. And non-recurrent and recurrent congestion models will be combined together to improve travel time estimation.;Man-made emergencies in the infrastructure are terrorist attacks, suicide bombings, etc. Human casualties are the major goal of intelligent adversaries. We use game theory in order to allocate first responders' resources inside the transit infrastructure to minimize human casualty. In the static zero-sum game model, we show that both the adversary and the first responder choose the same group of locations to attack and defend. In the dynamic case when the first responder is mobile while the adversary is hidden in a cell, the equilibrium solution for the first responder becomes the best patrol policy within the infrastructure. This model utilizes partially observable Markov decision process (POMDP) in which the payoff functions depend on an exogenous people flow, thus, are time varying. People flow are modeled as an open queuing network in the infrastructure. And illustration example is shown to provide insight into the competitive nature of this game between first responder and adversary.