  We consider a mobile cloud computing system with multiple users, a remote
cloud server, and a computing access point (CAP). The CAP serves both as the
network access gateway and a computation service provider to the mobile users.
It can either process the received tasks from mobile users or offload them to
the cloud. We jointly optimize the offloading decisions of all users, together
with the allocation of computation and communication resources, to minimize the
overall cost of energy consumption, computation, and maximum delay among users.
The joint optimization problem is formulated as a mixed-integer program. We
show that the problem can be reformulated and transformed into a non-convex
quadratically constrained quadratic program, which is NP-hard in general. We
then propose an efficient solution to this problem by semidefinite relaxation
and a novel randomization mapping method. Furthermore, when there is a strict
delay constraint for processing each user's task, we further propose a
three-step algorithm to guarantee the feasibility and local optimality of the
obtained solution. Our simulation results show that the proposed solutions give
nearly optimal performance under a wide range of parameter settings, and the
addition of a CAP can significantly reduce the cost of multi-user task
offloading compared with conventional mobile cloud computing where only the
remote cloud server is available.
