This letter analyses the effective capacity of communications system using unified models. In order to obtain a simple closed-form mathematically tractable expression, two different unified approximate models have been used. The mixture gamma (MG) distribution which is highly accurate approximation approach has been firstly employed to represent the signal-to-noise-ratio (SNR) of fading channel. In the second approach, the mixture of Gaussian (MoG) distribution which is another unified representation approach has been utilised. A comparison between the simulated and numerical results using both distributions over composite $α-η-μ$/gamma fading channels has been provided.