Control of multiclass queueing systems with abandonments and adversarial customers

摘要

This thesis considers the defensive surveillance of multiple public areas which are the open, exposed targets of adversarial attacks. We address the operational problem of identifying a real time decision-making rule for a security team in order to minimise the damage an adversary can inflict within the public areas. We model the surveillance scenario as a multiclass queueing system with customer abandonments, wherein the operational problem translates into developing service policies for a server in order to minimise the expected damage an adversarial customer can inflict on the system. We consider three different surveillance scenarios which may occur in realworld security operations. In each scenario it is only possible to calculate optimal policies in small systems or in special cases, hence we focus on developing heuristic policies which can be computed and demonstrate their effectiveness in numerical experiments. In the random adversary scenario, the adversary attacks the system according to a probability distribution known to the server. This problem is a special case of a more general stochastic scheduling problem. We develop new results which complement the existing literature based on priority policies and an effective approximate policy improvement algorithm. We also consider the scenario of a strategic adversary who chooses where to attack. We model the interaction of the server and adversary as a two-person zero-sum game. We develop an effective heuristic based on an iterative algorithm which populates a small set of service policies to be randomised over. Finally, we consider the scenario of a strategic adversary who chooses both where and when to attack and formulate it as a robust optimisation problem. In this case, we demonstrate the optimality of the last-come first-served policy in single queue systems. In systems with multiple queues, we develop effective heuristic policies based on the last-come first-served policy which incorporates randomisation both within service policies and across service policies.