  We consider the problem of jointly optimizing users' offloading decisions,
communication and computing resource allocation in a sliced multi-cell mobile
edge computing (MEC) network. We minimize the weighted sum of the gap between
the observed delay at each slice and its corresponding delay requirement, where
weights set the priority of each slice. Fractional form of the objective
function, discrete subchannel allocation, considered partial offloading, and
the interference incorporated in the rate function, make the considered problem
a complex mixed integer non-linear programming problem. Thus, we decompose the
original problem into two sub-problems: (i) offloading decision-making and (ii)
joint computation resource, subchannel, and power allocation. We solve the
first sub-problem optimally and for the second sub-problem, leveraging on novel
tools from fractional programming and Augmented Lagrangian method, we propose
an efficient algorithm whose computational complexity is proved to be
polynomial. Using alternating optimization, we solve these two sub-problems
iteratively until convergence is obtained. Simulation results demonstrate the
convergence of our proposed algorithm and its effectiveness compared to
existing schemes.
