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Here, 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 …