The dynamic team forming problem: Throughput and delay for unbiased policies

The dynamic team forming problem (DTFP) for a heterogeneous group of robots is described as follows. Each robot is capable of providing a specific service. Tasks arrive sequentially over time, assume random locations in the environment, and require several different services. A task is completed when a team of robots travels to the task location and provides the required services. The goal is to minimize the expected delay between a task’s arrival and its completion. We restrict our attention to unbiased policies for the DTFP, i.e., policies for which the expected delay is the same for all tasks. We introduce three intuitive policies, and in certain asymptotic regimes we analyze their delay as a function of the arrival rate of tasks (or throughput). For each policy we show that there is a broad class of system parameters for which the policy’s performance is within a constant factor of the optimal.