  In this paper, we consider stochastic clearing systems with multiple drifted
Brownian motion inputs. First, we propose an instantaneous rate policy, which
is shown to be the optimal one among a large class of renewal type clearing
policies in terms of average cost. Second, we propose a service measure about
average weighted delay rate, and provide a unified method to calculate the
service measure under different clearing policies. Moreover, we prove that
under a fixed clearing frequency, the instantaneous rate policy outperforms a
large class of clearing policies, and the instantaneous rate hybrid policy
performs better than time-based policy, in terms of average weighted delay
rate.
