  Nowadays, the Hierarchical Storage System (HSS) is considered as an ideal
model to meet the cost-performance demand. The data migration between storing
tiers of HSS is the way to achieve the cost-performance goal. The bandwidth
control is to limit the maximum amount of data migration. Most of previous
research about HSS focus on studying the data migration policy instead of
bandwidth control. However, the recent research about cache and networking
optimization suggest that the bandwidth control has significant impact on the
system performance. Few previous work achieves a satisfactory bandwidth control
in HSS since it is hard to control bandwidth for so many data migration tasks
simultaneously. In this paper, we first give a stochastic programming model to
formalize the bandwidth control problem in HSS. Then we propose a
learning-aided bandwidth control policy for HSS, named \Pascal{}, which learns
to control the bandwidth of different data migration task in an cooperative
way. We implement \Pascal{} on a commercial HSS and compare it with three
strong baselines over a group of workloads. Our evaluation on the physical
system shows that \Pascal{} can effectively decrease 1.95X the tail latency and
greatly improve throughput stability (2X $\downarrow$ throughput jitter), and
meanwhile keep the throughput at a relatively high level.
