Abstract For the ultra‐dense distributed network (UDN), the intensive deployment leads to the collision problem of the unlicensed spectrum access due to the random contention access mechanism of the unlicensed spectrum, which is difficult to improve the user quality of service (QoS). Here, the wireless access process of the licensed assisted access (LAA) network is modelled as a four‐state semi‐Markov model. Then, the effective capacity (EC) of the UDN based on the random access is derived, and the network capacity limit under the QoS requirements in the unlicensed spectrum is given. Based on the obtained EC, two power control algorithms are proposed to maximize the EC and effective energy efficiency (EEE) respectively under the user QoS requirements. Finally, numerical results verify the accuracy of the proposed theory, and the capacity‐delay domain of the UDN is given. The simulation results show that the proposed algorithms improve the EC and the EEE compared with existing classical schemes.