  We present a dynamic resource allocation strategy for energy-efficient and
Electromagnetic Field (EMF) exposure aware computation offloading at the
wireless network edge. The goal is to maximize the overall system sum-rate of
offloaded data, under stability (i.e. finite end-to-end delay), EMF exposure
and system power constraints. The latter comprises end devices for uplink
transmission and a Mobile Edge Host (MEH) for computation. Our proposed method,
based on Lyapunov stochastic optimization, is able to achieve this goal with
theoretical guarantees on asymptotic optimality, without any prior knowledge of
wireless channel statistics. Although a complex long-term optimization problem
is formulated, a per-slot optimization based on instantaneous realizations is
derived. Moreover, the solution of the instantaneous problem is provided with
closed form expressions and fast iterative procedures. Besides the theoretical
analysis, numerical results assess the performance of the proposed strategy in
striking the best trade-off between offloading sum-rate, power consumption, EMF
exposure, and E2E delay. To the best of our knowledge, this is the first work
addressing the problem of energy and exposure aware computation offloading.
