  We consider computation offloading for edge computing in a wireless network
equipped with intelligent reflecting surfaces (IRSs). IRS is an emerging
technology and has recently received great attention since they can improve the
wireless propagation environment in a configurable manner and enhance the
connections between mobile devices (MDs) and access points (APs). At this point
not many papers consider edge computing in the novel context of wireless
communications aided by IRS. In our studied setting, each MD offloads
computation tasks to the edge server located at the AP to reduce the associated
comprehensive cost, which is a weighted sum of time and energy. The edge server
adjusts the IRS to maximize its earning while maintaining MDs' incentives for
offloading and guaranteeing each MD a customized information rate. This problem
can be formulated into a difficult optimization problem, which has a
sum-of-ratio objective function as well as a bunch of nonconvex constraints. To
solve this problem, we first develop an iterative evaluation procedure to
identify the feasibility of the problem when confronting an arbitrary set of
information rate requirement. This method serves as a sufficient condition for
the problem being feasible and provides a feasible solution. Based on that we
develop an algorithm to optimize the objective function. Our numerical results
show that the presence of IRS enables the AP to guarantee higher information
rate to all MDs and at the same time improve the earning of the edge server.
