  With the widespread use of Internet of Things (IoT) devices and the arrival
of the 5G era, edge computing has become an attractive paradigm to serve
end-users and provide better QoS. Many efforts have been done to provision some
merging public network services at the edge. We reveal that it is very common
that specific users call for private and isolated edge services to preserve
data privacy and enable other security intentions. However, it still remains
open to fulfill such kind of mixed requests in edge computing. In this paper,
we propose the framework of hybrid edge computing to offer both public and
private edge services systematically. To fully exploit the benefits of this
novel framework, we define the problem of optimal request scheduling over a
given placement solution of hybrid edge servers, so as to minimize the response
delay. This problem is further modeled as a mixed integer non-linear problem
(MINLP), which is typically NP-hard. Accordingly, we propose the
partition-based optimization method, which can efficiently solve this NP-hard
problem via the problem decomposition and the branch and bound strategies. We
finally conduct extensive evaluations with a real-world dataset to measure the
performance of our methods. The results indicate that the proposed method
achieves elegant performance with low computation complexity.
