The multiple access technique allows users to share the allotted spectrum in the most effective manner. It can be classified in the orthogonal multiple access (OMA) techniques which is based on the time/frequency/code domain (TDMA, OFDMA, ...) or in the non-orthogonal multiple access (NOMA) techniques. Nowadays, with The exponential growth of mobile data traffic in 5G and IoT wireless networks which imposes requirements in terms of quality of service, low latency etc., the OMA technique may not meet this stringent emerging requirements. So, NOMA principle emerges as a solution to improve the spectral efficiency under delay quality of service constraints. Unlike previous work, in this paper, we study the performance of NOMA in the uplink transmission, in particular the performance in terms of the effective capacity of the channel (EC). We derive the closed-form expression of EC per user and prove the accuracy using Monte Carlo method.