For several years, mobile edge computing (MEC) has been highlighted as a promising technique to support emerging computation-intensive applications in cellular networks, e.g., 5G and 6G. Most previous studies have mainly focused on jointly optimizing communication (i.e., radio) and computation resources to improve offloading performance without considering specific communication protocols required for operating the MEC systems in practice. In this article, we newly design a contention-based access reservation protocol (ARP) for efficiently supporting simultaneous task offloading requests from a number of edge devices (EDs), and further define necessary signalings required to determine an optimal offloading factor. Thereafter, we formulate an optimization problem to find the optimal offloading factor that minimizes the task-completion latency. Through simulations, we mainly evaluate the task-completion latency performance of the MEC system incorporated with our proposed access reservation protocol under a multiple-input multiple-output (MIMO) environment. Particularly, we thoroughly investigate several practical aspects such as the effect of the number of edge devices attempting to join the task offloading, the number of antennas equipped at the edge device, and the amount of reserved radio resources required for configuring access reservation protocol on the optimal offloading decision. From the results, we verify the validity of our approach, and provide meaningful insights regarding how the network should be configured to fruitfully exploit the offloading with the MEC systems. INDEX TERMSMobile edge computing, Computation offloading, Offloading decision, Access reservation protocol, Multiple-input multiple-output VOLUME 4, 2021