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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 …