  The mobile edge computing (MEC) has been introduced for providing computing
capabilities at the edge of networks to improve the latency performance of
wireless networks. In this paper, we provide the novel framework for
MEC-enabled heterogeneous networks (HetNets), composed of the multi-tier
networks with access points (APs) (i.e., MEC servers), which have different
transmission power and different computing capabilities. In this framework, we
also consider multiple-type mobile users with different sizes of computation
tasks, and they offload the tasks to a MEC server, and receive the computation
resulting data from the server. We derive the successful edge computing
probability (SECP), defined as the probability that a user offloads and
finishes its computation task at the MEC server within the target latency. We
provide a closed-form expression of the approximated SECP for general case, and
closed-form expressions of the exact SECP for special cases. This paper then
provides the design insights for the optimal configuration of MEC-enabled
HetNets by analyzing the effects of network parameters and bias factors, used
in MEC server association, on the SECP. Specifically, it shows how the optimal
bias factors in terms of SECP can be changed according to the numbers of user
types and tiers of MEC servers, and how they are different to the conventional
ones that did not consider the computing capabilities and task sizes.
