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