In order to deal with the unstable transmission caused by the wireless communication, random delay jitters and external interference, this paper investigates the robust stability analysis of a kind of joint scheduling algorithms with the existence of unstable transmission. Firstly, we define the queue length of base station as system state and the unstable transmission is modelled by the random disturbance with unknown distribution function. Then, we use a Markov random walk model with a elastic barrier to describe the change of system state. Within this framework, by analyzing the expected stopping time of the system state with the joint scheduling algorithm, we obtain the state transition probability matrix of the proposed Markov model. Meanwhile, we deduce the sufficient condition that the Markov model can be positive recurrent, i.e., the queue length maintains robust stable in presence of unstable transmission. Finally, a numerical example is given to illustrate the effectiveness of the developed theoretical results.