Running computationally demanding real‐time applications at the mobile user equipment (UE) is complicated because of limited battery life time of the UEs. One solution is to offload demanding computing tasks to a centralized cloud. Nevertheless, this option introduces significant delay consisting in delivery of the offloaded tasks to the cloud and back. Such delay is inconvenient for real‐time applications. To cope with high delay, a concept of mobile edge computing has been introduced. The feasible way enabling mobile edge computing is to enhance the small cell base stations (SCeNBs) with computing capabilities. However, a high density of the SCeNBs together with even low mobility of users can result in often outage situation or handover when delay sensitive data cannot be delivered from the computing SCeNBs in time and become irrelevant. In this paper, we propose distributed cloud‐aware power control algorithm, which targets to increase the ratio of delivery of computation results to the UE within required delay. Then, we enhance cloud‐aware power control by adaptive algorithm. This algorithm exploits iterative process to find appropriate time when the power control is triggered in order to further improve the performance of the cloud‐aware power control. The simulations demonstrate notable increase in the ratio of delivered offloaded tasks from the computing SCeNBs comparing with competitive schemes. At the same time, the amount of served data to the users exploiting common, non‐cloud, services is increased. As the proposed solution is distributed, related signaling overhead is negligible. Copyright © 2015 John Wiley & Sons, Ltd.