Dynamic multi-agent team forming: Asymptotic results on throughput versus delay

In this paper we focus on problems in which tasks (demands for service) arrive in an environment sequentially over time. A task is completed when a robot (or team of robots) provides the required service, and the goal is to minimize the expected delay between a task´s arrival, and its completion. We develop a general framework in which these problems can be described, and propose a set of scaling laws for studying the relationship between the number of robots, the expected task delay, and the task arrival rate. We describe two existing problems in our framework, namely the dynamic traveling repairperson problem, and the dynamic pickup delivery problem, and present their asymptotic performance. We then introduce the dynamic team forming problem, in which tasks require services that can be provided only through complex teams of heterogeneous robots. We determine a lower bound on the problem´s achievable performance, and propose three policies for solving the problem. We show that for each policy, there is a broad class of tasks for which the policy´s performance is within a constant factor the optimal.