Modeling and analysis of uncertain time-critical tasking problems

This paper describes modeling and operational analysis of a generic asymmetric service-system situation in which (a) Red agents, potentially threatening, but in another but important interpretation, are isolated friendlies, such as downed pilots, that require assistance and ‘arrive’ according to some partially known and potentially changing pattern in time and space; and (b) Reds 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 others. We discuss various service options by Blue service agents and devise several approximations allowing one to compute efficiently those proportions of tasks of different classes that are successfully served or, more generally, if different rewards are associated with different classes of tasks, the percentage of the possible reward gained. We suggest heuristic policies 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 for a number of specific examples.