  The Age-of-Information is an important metric for investigating the
timeliness performance in information-update systems. In this paper, we study
the AoI minimization problem under a new Pull model with replication schemes,
where a user proactively sends a replicated request to multiple servers to
"pull" the information of interest. Interestingly, we find that under this new
Pull model, replication schemes capture a novel tradeoff between different
values of the AoI across the servers (due to the random updating processes) and
different response times across the servers, which can be exploited to minimize
the expected AoI at the user's side. Specifically, assuming Poisson updating
process for the servers and exponentially distributed response time, we derive
a closed-form formula for computing the expected AoI and obtain the optimal
number of responses to wait for to minimize the expected AoI. Then, we extend
our analysis to the setting where the user aims to maximize the AoI-based
utility, which represents the user's satisfaction level with respect to the
freshness of the received information. Furthermore, we consider a more
realistic scenario where the user has no prior knowledge of the system. In this
case, we reformulate the utility maximization problem as a stochastic
Multi-Armed Bandit problem with side observations and leverage a special linear
structure of side observations to design learning algorithms with improved
performance guarantees. Finally, we conduct extensive simulations to elucidate
our theoretical results and compare the performance of different algorithms.
Our findings reveal that under the Pull model, waiting does not necessarily
lead to aging; waiting for more than one response can often significantly
reduce the AoI and improve the AoI-based utility in most scenarios.
