Modeling and analysis of uncertain time-critical tasking problems (UTCTP)

Abstract

We consider modeling and operational analysis of a generic asymmetric service-system situation in which (a) Red agents, potentially threatening, but possibly requiring assistance, arrive according to some partially known and possibly changing pattern in time and space; and (b) Reds are impatient: have effectively limited unknown deadlines or times of availability for Blue service, i.e., detection, classification, and attack in a military setting, or emergency assistance in other settings, such as medical care. We discuss various service options by Blue service agents and devise several approximations allowing one to compute efficiently proportions of tasks of different types that are successfully served or, more generally, if different rewards are associated with different types of tasks, the percentage of the possible reward gained. We suggest a heuristic policy for a Blue server to select the next task to perform and to decide how much time to allocate to that service. We discuss this and related policies for a number of specific examples.