  With the emergence of millimeter-Wave (mmWave) communication technology, the
capacity of mobile backhaul networks can be significantly increased. On the
other hand, Mobile Edge Computing (MEC) provides an appropriate infrastructure
to offload latency-sensitive tasks. However, the amount of resources in MEC
servers is typically limited. Therefore, it is important to intelligently
manage the MEC task offloading by optimizing the backhaul bandwidth and edge
server resource allocation in order to decrease the overall latency of the
offloaded tasks. This paper investigates the task allocation problem in MEC
environment, where the mmWave technology is used in the backhaul network. We
formulate a Mixed Integer NonLinear Programming (MINLP) problem with the goal
to minimize the total task serving time. Its objective is to determine an
optimized network topology, identify which server is used to process a given
offloaded task, find the path of each user task, and determine the allocated
bandwidth to each task on mmWave backhaul links. Because the problem is
difficult to solve, we develop a two-step approach. First, a Mixed Integer
Linear Program (MILP) determining the network topology and the routing paths is
optimally solved. Then, the fractions of bandwidth allocated to each user task
are optimized by solving a quasi-convex problem. Numerical results illustrate
the obtained topology and routing paths for selected scenarios and show that
optimizing the bandwidth allocation significantly improves the total serving
time, particularly for bandwidth-intensive tasks.
